Curves of genus 2 over \$\F_3\$, given by \$v^2=f(u), \deg f=5\$ We first state the polynomial \$f\$ and then the characteristic polynomial of the Frobenius. In the second part we provide the group order of the divisor class group over extension fields. For each characteristic polynomial we state the degree of extension, then the group order and then the factorization of the group order. u^5 + u^4 + u T^4 - T^3 + 2*T^2 - 3*T + 9 u^5 + 2*u^4 + u T^4 + T^3 + 2*T^2 + 3*T + 9 u^5 + u^4 + u^3 + u T^4 + 2*T^3 + 2*T^2 + 6*T + 9 u^5 + 2*u^4 + u^3 + u T^4 - 2*T^3 + 2*T^2 - 6*T + 9 u^5 + 2*u^4 + u^2 + u T^4 - 2*T^2 + 9 u^5 + u^4 + 2*u T^4 + 2*T^3 + 4*T^2 + 6*T + 9 u^5 + 2*u^4 + 2*u T^4 - 2*T^3 + 4*T^2 - 6*T + 9 u^5 + u^3 + 2*u T^4 + 4*T^2 + 9 u^5 + u^4 + 2*u^3 + 2*u T^4 - T^3 - 2*T^2 - 3*T + 9 u^5 + 2*u^4 + 2*u^3 + 2*u T^4 + T^3 - 2*T^2 + 3*T + 9 u^5 + 2*u^4 + 1 T^4 + T^3 + 3*T^2 + 3*T + 9 u^5 + u^4 + 2*u^3 + 1 T^4 - T^3 + 3*T^2 - 3*T + 9 u^5 + u^4 + u^2 + 1 T^4 + T^3 + T^2 + 3*T + 9 u^5 + 2*u^4 + 2*u^3 + u^2 + 1 T^4 + 3*T^3 + 5*T^2 + 9*T + 9 u^5 + 2*u^4 + 2*u^3 + 2*u^2 + 1 T^4 - T^3 + T^2 - 3*T + 9 u^5 + 2*u^4 + u + 1 T^4 + T^3 + 5*T^2 + 3*T + 9 u^5 + u^4 + u^3 + u + 1 T^4 - T^3 - T^2 - 3*T + 9 u^5 + 2*u^4 + u^3 + u^2 + u + 1 T^4 + 3*T^3 + 7*T^2 + 9*T + 9 u^5 + 2*u^2 + u + 1 T^4 + T^3 - T^2 + 3*T + 9 u^5 + 2*u^4 + 2*u^2 + 2*u + 1 T^4 - T^3 + 5*T^2 - 3*T + 9 u^5 + 2*u^4 + 2*u^3 + u^2 + 2 T^4 - 3*T^3 + 5*T^2 - 9*T + 9 u^5 + 2*u^4 + u^3 + u^2 + u + 2 T^4 - 3*T^3 + 7*T^2 - 9*T + 9 -------------------------------------------------------------------------- Group orders: T^4 - T^3 - 2*T^2 - 3*T + 9 53 375710212613604480101718874966207256412828653922604 = [ <2, 2>, <3843733, 1>, <169648140269685313, 1>, <76550097839185078424917350485641, 1> ] 59 199667811101600108430746003374936210680031938344416211956 = [ <2, 2>, <3843733, 1>, <169648140269685313, 1>, <76550097839185078424917350485641, 1> ] 61 16173092699229956532006233747504511853403535324747603318004 = [ <2, 2>, <367, 1>, <1831, 1>, <6016981496104017150886947673619972057601500990639413, 1> ] 67 8595044557171428376028507845827519946822116034824788698763973676 = [ <2, 2>, <65514218114933361283, 1>, <32798394014612636072729557397950708994712793, 1> ] 71 56392087339601734626028498123790157309529339799380620894028417866436 = [ <2, 2>, <6625579, 1>, <3951254445829, 1>, <538516909452594067941259250603464808121692252599, 1> ] 73 4567759074507740386242650642892853122904149222267102782337117836013604 = [ <2, 2>, <1753, 1>, <11957839, 1>, <54476422549807602727143554953754691323312596085286267394303, 1> ] 79 2427494450315468068729500553086112352996313013124698468295253275052656785756 = [ <2, 2>, <2704856056699, 1>, <56109453039949, 1>, <6966329746533613, 1>, <574002829441692060892395671588653, 1> ] 83 15926791088519786002693157420958368189781454991666181609506418411545793587271316 = [ <2, 2>, <499, 1>, <35328121, 1>, <750183135154661627701240369, 1>, <301078615834797342797222034710618637237679, 1> ] 89 8464149782874043593246456776934936064363296412802258876739425444983156884432022709404 = [ <2, 2>, <2671, 1>, <8011, 1>, <277163399857, 1>, <4426198087243, 1>, <80611314451041893961818056872683804005369110294345121, 1> ] ---------------------------------------------------------------------------- T^4 - 2*T^3 + 2*T^2 - 6*T + 9 53 375710212613565582954258723906742347671299930224884 = [ <2, 2>, <3753936698749, 1>, <45349374073261, 1>, <551740376362695319644389, 1> ]59 199667811101604967778690445389889887784425007041531467156 = [ <2, 2>, <49916952775401241944672611347472471946106251760382866789, 1> ] 61 16173092699229944614352376379779099336973126813590905333204 = [ <2, 2>, <4043273174807486153588094094944774834243281703397726333301, 1> ] 67 8595044557171426883661551257387992338308447455624049410354582196 = [ <2, 2>, <2148761139292856720915387814346998084577111863906012352588645549, 1> ] 71 56392087339601731572860352262474541975429589645258408201156371141636 = [ <2, 2>, <569, 1>, <8521, 1>, <58608296707318971817802863901, 1>, <49613086643015350669569328241141, 1> ] 73 4567759074507740439131412473975310642699804917804248232541644405818084 = [ <2, 2>, <944329, 1>, <13865609190161, 1>, <87212937702404033680812066758842774840297487802209, 1> ] 79 2427494450315468070310133107586512421693815588360826534230645903915449528356 = [ <2, 2>, <32344891949, 1>, <57086467074771078626622881, 1>, <328669484133615519879342691892040753581, 1> ] 83 15926791088519786003306539591610834374552644854413054153191192273343581294254836 = [ <2, 2>, <22711928736461, 1>, <175313062062309879696511832316917703054035425998412801946215553969, 1> ] 89 8464149782874043593258178983741633634730578646859877871891466573694458510604894116004 = [ <2, 2>, <131009, 1>, <389814661, 1>, <41434685628621784375978769013508086052022759147379630169032207781670549, 1> ] ------------------------------------------------------------------------------ T^4 - T^3 + 3*T^2 - 3*T + 9 53 375710212613679756199641542603088203684598244562679 = [ <3, 2>, <372986441, 1>, <111922511358255381430471517567127923107591, 1> ] 59 199667811101602812542919642204691397776132342716009408201 = [ <3, 2>, <37171, 1>, <13390523, 1>, <44572168407420139554987671812676572324616833, 1> ] 61 16173092699229757072401283104584509216314215157222676123809 = [ <3, 2>, <367, 1>, <112363, 1>, <507457903, 1>, <5920206161, 1>, <14505220166592197933802817270907, 1> ] 67 8595044557171424197375399519037096642421651470841808995875118351 = [ <3, 2>, <2011, 1>, <31525913, 1>, <53804351, 1>, <279968056480286576071425825595212909618176323, 1> ] 71 56392087339601733667759367730477917203519151292936465032197301430141 [ <3, 2>, <569, 2>, <2772409, 1>, <6980617279333679269568188386932952718018794586227781901, 1> ] 73 4567759074507740399787585930629245903670615556145699398007178361477519 = [ <3, 2>, <26981429600714164046539, 1>, <18810300031062177668658535222255989635013896869, 1> ] 79 2427494450315468070464880319738645977076082962187662284574577503059258541281 = [ <3, 2>, <577333, 1>, <6165243812525477, 1>, <75777294950035498002134864628363904410184381966273649, 1> ] 83 15926791088519786002474550770574572850604618223275172156963315667701517211356931 = [ <3, 2>, <2663803, 1>, <1584876941033, 1>, <419168003025629582510368429448272488677040799226744077428841, 1> ] 89 8464149782874043593247361974716714513599972160870002150417786942335335069098996768229 = [ <3, 2>, <179, 2>, <1069, 1>, <357479537, 1>, <332777100660087923564759240428483, 1>, <230808842545682500495221124604053459, 1> ] ----------------------------------------------------------------------------------- T^4 + 3*T^3 + 5*T^2 + 9*T + 9 53 375710212613659259993210448047991285034098091682313 = [ <3, 3>, <54104521, 1>, <678767528819, 1>, <378908738728299765716797013281, 1> ] 59 199667811101602849882278481625295599266188615174357805899 = [ <3, 3>, <926537, 1>, <7981445009615568104964586836283350410710492110601, 1> ] 61 16173092699230043941851222387440929696976914015782751674483 = [ <3, 3>, <4637, 1>, <620609609, 1>, <208148708321034513134552595267775235730801013, 1> ] 67 8595044557171426212810528825601244495682166917042872946732564849 = [ <3, 3>, <269, 1>, <4451784406225321362464437043, 1>, <265826310987458526190974641847061, 1> ] 71 56392087339601732057876368775805259124232594276867423155049150209727 = [ <3, 3>, <2088595827392656742884309954659454041638244232476571227964783341101, 1> ] 73 4567759074507740370083179722321890459636290873941290711677050952179633 = [ <3, 3>, <36689426387, 1>, <676203723197237, 1>, <6819004001768496640427096408421337252436941, 1> ] 79 2427494450315468070181321146663054055007837868778839668631596085606549919203 = [ <3, 3>, <2213, 1>, <6163, 1>, <57249778303, 1>, <244362663393728440925010793, 1>, <471207550279204223594502663089, 1> ] 83 15926791088519786003965158000438898752163728768669321452885256536852191134595773 = [ <3, 3>, <12419472353690413974615540091, 1>, <47496474457820028707056089442733313285295972860389, 1> ] 89 8464149782874043593239196656387074115100129776713140024633386608425862177640074681527 = [ <3, 3>, <64793, 1>, <4838285447430045651501674938814877758914360191351912171944378198391265504584157, 1> ] ----------------------------------------------------------------------------------- T^4 + T^3 + 5*T^2 + 3*T + 9 53 375710212613750065911595823481614395819784966143289 = [ <19, 1>, <19774221716513161363768201235874441885251840323331, 1> ] 59 199667811101601696241214225258124517082745549427224124579 = [ <19, 1>, <9219678779, 1>, <1139826279759176253944332241424340940055637379, 1> ] 61 16173092699229882562486817678274704604693996874416224059211 = [ <19, 1>, <851215405222625398025621983067089716036526151285064424169, 1> ] 67 8595044557171424574843409594607501615286575629343437104194103841 = [ <19, 1>, <269, 1>, <37451996609, 1>, <44902164448385238905064314392222162476416455443559, 1> ] 71 56392087339601733564494052917617861904281640159931972622598137325351 = [ <19, 1>, <2968004596821143871815476469348308521277981061049051190663059859229, 1> ] 73 4567759074507740360825344126684870261124276873531041556323268747177569 = [ <19, 1>, <11492283421, 1>, <1296316374094229, 1>, <16137351299624342641188048661561299582192539, 1> ] 79 2427494450315468069607689639082020098191729139391341624948531575227590259099 = [ <19, 1>, <2371, 1>, <309335597830099, 1>, <174198010236483842701826447324432729323922925278803356449, 1> ] 83 15926791088519786003189650913360722462504540261780302058575832853461215478400749 = [ <19, 1>, <164406401, 1>, <60444564911, 1>, <84352644857533763026240829404592747899431307271607803411761, 1> ] 89 8464149782874043593250317273850800241682205314731201435682797055986180034234685245791 = [ <19, 1>, <179, 2>, <1069, 1>, <23437261, 1>, <142409715164351, 1>, <5597514343054499, 1>, <696152332628644679028269581944793801369, 1> ] ----------------------------------------------------------------------------------- T^4 + 2*T^3 + 4*T^2 + 6*T + 9 53 375710212613653098128100347109971496173966083269166 = [ <2, 1>, <11, 1>, <456013, 1>, <995349736975667, 1>, <37625076338028832371353606243, 1> ] 59 199667811101604134510460440407555858260122784894915441502 = [ <2, 1>, <11, 1>, <9075809595527460659566383654888902648187399313405247341, 1> ] 61 16173092699229762031888414432680154327251725242181101149022 = [ <2, 1>, <11, 1>, <22016356244822899859, 1>, <33390655976989072647363277904640215039, 1> ] 67 8595044557171430559500656692774207598636490304470466494795162542 = [ <2, 1>, <11, 1>, <1609, 1>, <1786489, 1>, <3926340033887, 1>, <34616340399717451847508961424154436796603, 1> ] 71 56392087339601732843913283072891727545923573474516383266262760073078 = [ <2, 1>, <11, 1>, <1847, 1>, <13633, 1>, <491747, 1>, <7428731, 1>, <101553289, 1>, <274401710460556855353638031676619622863, 1> ] 73 4567759074507740388422578346489478474448880071898806054898345545569286 = [ <2, 1>, <11, 1>, <207625412477624563110117197567703567020403639631763911586288433889513, 1> ] 79 2427494450315468068423137578949333464564899808963436693539763458097285935878 = [ <2, 1>, <11, 1>, <18108697, 1>, <80262863821327692629490710821, 1>, <75916068903574622261786606359685519677, 1> ] 83 15926791088519786002588650533986387910869757294276722851794174340573940201559758 = [ <2, 1>, <11, 1>, <167, 2>, <997, 1>, <57341905391, 1>, <454051779610021306358299688959000182744354027862175959912463, 1> ] 89 8464149782874043593246212844643437910755708743128983587878928867795683970877976309606 = [ <2, 1>, <11, 1>, <1069, 1>, <8213858575257914328919663263011968213, 1>, <43816303192916717772986484498690149980614409, 1> ] ----------------------------------------------------------------------------------- T^4 - 3*T^3 + 5*T^2 - 9*T + 9 53 375710212613613260657949823305429347340274921251297 = [ <3, 1>, <107, 4>, <955425074400944254369398594943412406176699, 1> ] 59 199667811101604085765094813804953953467375372172706898067 = [ <3, 1>, <66555937033868028588364937934984651155791790724235632689, 1> ] 61 16173092699229717845586014545054575786450286938345175203771 = [ <3, 1>, <18911, 1>, <20839919, 1>, <121682557, 1>, <112417253977045653204147296337010836589, 1> ] 67 8595044557171428051266903806338611024306731255314010061601772233 = [ <3, 1>, <269, 1>, <2011, 2>, <10453, 1>, <39475463, 1>, <6382374350974605035874345075344192238356701, 1> ] 71 56392087339601734768735666722349520953127106526395480310541931268119 = [ <3, 1>, <8383946819, 1>, <384925957908294131046693121, 1>, <5824668340062719463569149807327, 1> ] 73 4567759074507740442872395153028644288009516099105593159158776705968297 = [ <3, 1>, <95923, 1>, <3813890015691201013, 1>, <4161894017014317555147732074014252967809113901, 1> ] 79 2427494450315468068536602520668109310343425973463460271448370606695765584907 = [ <3, 1>, <2687, 1>, <301140609144705131936062835959323819667960051291832312547868826038427687, 1> ] 83 15926791088519786002163139180920864085740354347132499355285272834486746225406277 = [ <3, 1>, <1158847, 1>, <4581217678295692759603047736506160602087061348372563233192208242182889897, 1> ] 89 8464149782874043593269631725971939607216516829645897431325083990196546899830083074511 = [ <3, 1>, <2679536727589108392266642142791, 1>, <1052936961792097328610496025759206360201053058467468307, 1> ] ----------------------------------------------------------------------------------- T^4 - T^3 - T^2 - 3*T + 9 53 375710212613579242706913201566755303428019365576115 = [ <5, 1>, <107, 4>, <20353, 1>, <15099280877, 1>, <556879266941, 1>, <3349670894096063, 1> ] 59 199667811101602300665601842092887906981699247789343524885 = [ <5, 1>, <39933562220320460133120368418577581396339849557868704977, 1> ] 61 16173092699229744438977198627122433471465729694828399430765 = [ <5, 1>, <8419, 1>, <506911, 1>, <12324690687553, 1>, <379878472640243, 1>, <161886313965020751823, 1> ] 67 8595044557171425465032197376141720451686322904210771586566857035 = [ <5, 1>, <3865002379829, 1>, <87446442367965122983, 1>, <5086115483690678735332737044501, 1> ] 71 56392087339601736015146745803337939517163884933928663698934973964705 = [ <5, 1>, <539009537447, 1>, <2092433748267272003440385008491800937369022247327\ 3609803, 1> ] 73 4567759074507740422249458604350208500561060923804389916751334717409915 = [ <5, 1>, <439, 2>, <1753, 1>, <52307499571, 1>, <51696157996959402298260133029404728246775606823421, 1> ] 79 2427494450315468069133137361297250463315454292880613142627821128337127309885 = [ <5, 1>, <3042449, 1>, <29261759, 1>, <276031828621, 1>, <19756287738516131249824601838597604853664028223507, 1> ] 83 15926791088519786002945574597602393946916151180759484156313383699527740254296295 = [ <5, 1>, <9381227453942869699, 1>, <32834698954751997290557, 1>, <10341072298880046789779035628035731613, 1> ] 89 8464149782874043593250890055219250160053345501603092526343685117828723191022406742185 = [ <5, 1>, <179, 4>, <1069, 1>, <1170892836277, 1>, <11724505298098294284061296847, 1>, <112360025862338592567349109354107, 1> ] ---------------------------------------------------------------------------------- T^4 - T^3 + 2*T^2 - 3*T + 9 53 375710212613556366354645587655743296006314970051096 = [ <2, 3>, <311747, 1>, <150647084259654610290814982844960535308405121, 1> ] 59 199667811101598263682666433758179156722123758358920371048 = [ <2, 3>, <44877289, 1>, <602682523, 1>, <1095123083683, 1>, <1536078156293, 1>, <548563126692017, 1> ] 61 16173092699229814611650515554993891359353940628360099011176 = [ <2, 3>, <2021636587403726826456314444374236419919242578545012376397, 1> ] 67 8595044557171426017332889491714216167600068987728219135045013272 = [ <2, 3>, <85627, 1>, <1154947, 1>, <126034907, 1>, <9890594807, 1>, <8715094614115898509786304688566239, 1> ] 71 56392087339601732876436073901242435960075681546062381988934404228744 = [ <2, 3>, <7669, 1>, <10344995894964992043229019, 1>, <88850345875907828136705516309447947863, 1> ] 73 4567759074507740451538017903823901358992186180555376515595217591879496 = [ <2, 3>, <1616606024555769308429400607, 1>, <353190496410753890960516951961540300467191, 1> ] 79 2427494450315468069987310955893104113316273630325700780506834061983936821752 = [ <2, 3>, <184703, 1>, <1642836371306548939369765891656540576842467116347393369\ 698132990519873, 1> ] 83 15926791088519786002592619414450412811788753529824122652377041617826326943370152 = [ <2, 3>, <19908488860649732503240774268063016014735941912280153315471302022282\ 90867921269, 1> ] 89 8464149782874043593257070038446434390898504462291081641237918059961106351146529194872 = [ <2, 3>, <179, 4>, <307823903773, 1>, <254600779983419, 1>, <7267338560574919, 1>, <33033411854630279, 1>, <54776002261557697, 1> ] ------------------------------------------------------------------ T^4 + T^3 + T^2 + 3*T + 9 53 375710212613625276010609398267464327362127079796245 = [ <3, 1>, <5, 1>, <3923, 1>, <66976226261053, 1>, <95328499970780405307751262345357, 1> ] 59 199667811101608701237096352785702769573952363321771313135 = [ <3, 1>, <5, 1>, <1889, 1>, <51449, 1>, <29181637, 1>, <174559077838697, 1>, <26887833629625063191096621, 1> ] 61 16173092699229843174414448989427144692790288546652311029015 = [ <3, 1>, <5, 1>, <258366233, 1>, <4173169873745290127087272788578669693468363968097, 1> ] 67 8595044557171425514248362599391636036682889886267634688461086205 = [ <3, 1>, <5, 1>, <3217, 1>, <1063693, 1>, <1534888529, 1>, <24353772911177, 1>, <4479674088474415114057559296039, 1> ] 71 56392087339601735104734749753758967451261938078148108904200542298315 = [ <3, 1>, <5, 1>, <533366627, 1>, <7048570906006052644001759006912765022730720155356115410423, 1> ] 73 4567759074507740351102649526885680006414902131989194993056387458345645 = [ <3, 1>, <5, 1>, <39102625785006671, 1>, <7787642530916991342832218649084871595332228836769933, 1> ] 79 2427494450315468069437998130088699716604819734220391074088235153764413132535 = [ <3, 1>, <5, 1>, <3778571, 1>, <42829144497844433242761141360736633268764298006140259092449414584939, 1> ] 83 15926791088519786003167989759825521604032137979183038025317978406550767881904145 = [ <3, 1>, <5, 1>, <1061786072567985733544532650655034773602142531945535868354531893770051192126943, 1> ] 89 8464149782874043593273642206399491564848889133710519580141285708890631774134077462435 = [ <3, 1>, <5, 1>, <5519, 1>, <122242391, 1>, <157090848585930059190941, 1>, <5324256446112010029331075316963600664916877472761, 1> ] ------------------------------------------------------------------------------ T^4 - T^3 + T^2 - 3*T + 9 53 375710212613647244640550961929452372484266676258237 = [ <7, 1>, <14676443, 1>, <3657077366514169725112266760018587731609537, 1> ] 59 199667811101598234410276942782514200237872291457468788103 = [ <7, 1>, <2042581, 1>, <7943171, 1>, <1505234325648017, 1>, <1167972731551986030013535887, 1> ] 61 16173092699229918613022787941681658675134836250758461303727 = [ <7, 1>, <38431, 1>, <317634199, 1>, <14942301239, 1>, <324427251331, 1>, <39043728131753901969341, 1> ] 67 8595044557171428749829070032548148616832883422493848112201916453 = [ <7, 1>, <2407724344174991633818526435057, 1>, <509968473400170409169173628637347, 1> ] 71 56392087339601731721877285744395832992905762332548973698729288316883 = [ <7, 1>, <2273, 1>, <3711313, 1>, <9549774388459835212947199763005502065407671\ 07865819870181, 1> ] 73 4567759074507740461852925348464855014503367450834510433021321236641077 = [ <7, 1>, <98798117469559, 1>, <8585893391965211518030501, 1>, <769256169265075251021996691729, 1> ] 79 2427494450315468069279925537242463648271885098122724763892992727321114120623 = [ <7, 1>, <4583, 1>, <62165417, 1>, <3383065330937, 1>, <979519573577214835141, 1>, <367314433204714373686425224147, 1> ] 83 15926791088519786002960307421534241233826529010071964106436831019109099647276553 = [ <7, 1>, <167, 2>, <14606952605737, 1>, <130744049433998287604610037501, 1>, <42718475848133713573757557306003, 1> ] 89 8464149782874043593235186175959522157467766866715128032096284437879109452489329898987 = [ <7, 1>, <343446017, 1>, <1780350134011, 1>, <1977522321488595009233056851308825357583828182082659641047274343, 1> ] --------------------------------------------------------------------------------- T^4 - 2*T^2 + 9 53 375710212613636260325580192419709633646108358784968 = [ <2, 3>, <12081457, 1>, <6092082881, 1>, <638084062940084306204024120722313, 1> ]59 199667811101603467823686647749637999237913561925275922312 = [ <2, 3>, <287921, 1>, <1495242606904993, 1>, <57973973029763689380913665154263713, 1> ] 61 16173092699229880893718618465344198892897253094021301070408 = [ <2, 3>, <4625745859774213680305977, 1>, <437040133351038181544790542919313, 1> ] 67 8595044557171427132038716315969595979849827712329873914040790792 = [ <2, 3>, <1609, 1>, <28409, 1>, <194569, 1>, <435769, 1>, <1075457737, 1>, <257764335348243033655460296732708697, 1> ] 71 56392087339601733413306017749077360316920838632731058313683914023752 = [ <2, 3>, <21017, 1>, <4968985337743959664053869609, 1>, <67497819567402281896339403158010473, 1> ] 73 4567759074507740406477787437675267255294535021673851211707098344446088 = [ <2, 3>, <1753, 1>, <147371233, 1>, <22101338127047114998112634533814940687370\ 53137435891243289, 1> ] 79 2427494450315468069358961833665581682604975295403561248432815573078291735752 = [ <2, 3>, <30343680628943350866987022920819771032562191192544515605410194663478\ 6466969, 1> ] 83 15926791088519786003064148590679881418931920830259091274640791919283499240067592 = [ <2, 3>, <19908488860649732503830185738349851773664901037823864093300989899104\ 37405008449, 1> ] 89 8464149782874043593254414191179506861158316625453212545093990879921227185346774476168 = [ <2, 3>, <128873, 1>, <152251976753, 1>, <53922308240372246240357439794906402039947700768376414375044617790809, 1> ] ---------------------------------------------------------------------------------- T^4 + T^3 + 2*T^2 + 3*T + 9 53 375710212613716154296514823802530761776154191596848 = [ <2, 4>, <23481888288357259643532176487658172611009636974803, 1> ] 59 199667811101608671964706861810429208732065076287873972944 = [ <2, 4>, <58057, 1>, <3617705271116029, 1>, <59415574531167713582211532819022953, 1> ] 61 16173092699229947175786721376809757734208787689442045282512 = [ <2, 4>, <13421, 1>, <1150949, 1>, <5192311339, 1>, <68285928976553, 1>, <184561108221233598856399, 1> ] 67 8595044557171428246744543140225562807292022231855922415690858288 = [ <2, 4>, <7871429, 1>, <682455860077267120648022038011265394702475737875543501\ 67, 1> ] 71 56392087339601733950175961596912306942070720505126591581185253149968 = [ <2, 4>, <7809859, 1>, <3212697188063585861, 1>, <140470523591202522866812283657933438455327, 1> ] 73 4567759074507740361417556971526633528455548648012482810562340606406288 = [ <2, 4>, <293, 1>, <974351338418886595865519831810288721940176759388328244573878115701, 1> ] 79 2427494450315468068730612711438059251955917091706297864168937401114035134704 = [ <2, 4>, <151718403144716754295663294464878703247244818231643616510558587569627195919, 1> ] 83 15926791088519786003535677766909350026091035782750358875342409514326110619929424 = [ <2, 4>, <22079, 1>, <24071, 1>, <1872987023336317699263167914158793093640941531373782978448295967232221, 1> ] 89 8464149782874043593251758343912579331418113836122966923818208733159185437042770217968 = [ <2, 4>, <8011, 1>, <10859, 1>, <13981719705655522553, 1>, <434936846283155375562771856951000706432942226923241953359, 1> ] ----------------------------------------------------------------------------------- T^4 + 3*T^3 + 7*T^2 + 9*T + 9 53 375710212613734493685616079390556779692127987329139 = [ <29, 1>, <12955524572887396333986761358295061368694068528591, 1> ] 59 199667811101601733624862430006500833703139717799685407181 = [ <29, 1>, <1233101, 1>, <5583562850519130885994276722599220868227666721589, 1> ] 61 16173092699230003352908360435039702213128856102219094229029 = [ <29, 1>, <17947538578306702493269, 1>, <31073500651040417136236195678349829, 1> ] 67 8595044557171424174754446347333147808099750617302869812406321291 = [ <29, 1>, <6542930759742856489, 1>, <45297873030015479000337297219944374079987\ 311, 1> ] 71 56392087339601733296435462608251500093625738451321954968969298433801 = [ <29, 1>, <8521, 1>, <79391792461, 1>, <47940309504221, 1>, <2180907959869591, 1>, <27492600960571721756459, 1> ] 73 4567759074507740430977677746010296225066631445719249966486254164489339 = [ <29, 1>, <439, 1>, <549691, 1>, <3280621, 1>, <13219571, 1>, <44137991, 1>, <1139601770338799, 1>, <299214713256269922160061, 1> ] 79 2427494450315468069599896744274652950653534249503939887769164396652440232981 = [ <29, 1>, <39659, 1>, <2023981, 1>, <1055880427318431346988441, 1>, <987636922971878198890170671279196749551, 1> ] 83 15926791088519786002478995570338656668125366997086458778730047989874875385454151 = [ <29, 1>, <5403301, 1>, <5018343179, 1>, <154049234677024553551, 1>, <131477434749582148863750677023272505015211, 1> ] 89 8464149782874043593257980704081917814563510727312153913261499602069580160624876382289 = [ <29, 1>, <179, 2>, <9109179922355993875581803813951647958126399179620242935787551942682898915747901, 1> ] ----------------------------------------------------------------------------------- T^4 + T^3 - T^2 + 3*T + 9 53 375710212613693277944247104753360843648123509157723 = [ <13, 1>, <153781115017, 1>, <3100939139239, 1>, <3906841870787, 1>, <15512706163891, 1> ] 59 199667811101604634981771453408134976490150860144601442109 = [ <13, 1>, <730051803067, 1>, <3674356095501941, 1>, <5725715745900916114917794519, 1> ] 61 16173092699230017348460038305129779479240452455564381525781 = [ <13, 1>, <9151, 1>, <135950612368803891533166096224286370377684258597752087, 1> ] 67 8595044557171428799045235255798102416014540248637308943096550387 = [ <13, 1>, <98657582957390758039, 1>, <6701535288109772410313881812249300479130841, 1> ] 71 56392087339601730811465289694816896522806260673473286266353861747897 = [ <13, 1>, <4337852872277056216266560745755145886369712359497945097411835519069, 1> ] 73 4567759074507740390706116271000326108352639518844044103023727961311043 = [ <13, 1>, <439, 2>, <17624683, 1>, <134589402413, 1>, <8726888589804661, 1>, <88072269029762923621130747789, 1> ] 79 2427494450315468069584786306033912901632699322263855088770244661850475432069 = [ <13, 1>, <283588343817217, 1>, <77929266800732351484721, 1>, <8449401099899601650443621152499037609, 1> ] 83 15926791088519786003182722583757368890961583781102384605489286189946062994917439 = [ <13, 1>, <167, 2>, <71713, 1>, <612567706683169430860934222525173740624040582733981759265765186354379, 1> ] 89 8464149782874043593257938327139763562263274966645694349368172800649462042499863093121 = [ <13, 1>, <1069, 1>, <11393, 1>, <1271927599973, 1>, <29493384237924797, 1>, <1425073240260306967319666741696024199843593772521, 1> ] ---------------------------------------------------------------------- T^4 - 2*T^3 + 4*T^2 - 6*T + 9 53 375710212613619422523059929872106647862256961305022 = [ <2, 1>, <3, 1>, <5538857963, 1>, <11305285166587069317218739503542271037599, 1> ] 59 199667811101602801136912855095464994156093181437345700718 = [ <2, 1>, <3, 1>, <6491, 1>, <23320221132937, 1>, <219842944962386277899052489621152500559, 1> ] 61 16173092699229999755548822499376994061927400748882824825198 = [ <2, 1>, <3, 1>, <8053, 1>, <24767, 1>, <161773, 1>, <83541964363445567406230522291091378010941971, 1> ] 67 8595044557171423704576775939166298092902944115295004705576163134 = [ <2, 1>, <3, 1>, <3217, 1>, <4691, 1>, <177416084044464583285729, 1>, <535041413790927052790889297349703, 1> ] 71 56392087339601733982698752425263015259862447019133466441665862196582 = [ <2, 1>, <3, 1>, <2557, 1>, <12781, 1>, <287588394916442033116139727359479129529855445946564160073241, 1> ] 73 4567759074507740424532996528861056251198299276694264704089559924788342 = [ <2, 1>, <3, 1>, <20879, 1>, <15678259075606862759118131, 1>, <2325650277416417812910214288605925836893, 1> ] 79 2427494450315468070294786088381829900808253663391068661134466175669364637814 = [ <2, 1>, <3, 1>, <32355196571963, 1>, <12504402731291000235379091726168914028315319210383700204661163, 1> ] 83 15926791088519786003539646647373374927009549176358695560612110572624718247371614 = [ <2, 1>, <3, 1>, <997, 1>, <2662452539037075560605089710359975748413498692136191166936160242832617560577, 1> ] 89 8464149782874043593262615537715575811560927134049487527810550529712667191202644965078 = [ <2, 1>, <3, 1>, <28837, 1>, <592919, 1>, <93158859458355316679, 1>, <1759341340235725158039661, 1>, <503399029914753401751358891609, 1> ] -------------------------------------------------------------------------------- T^4 - T^3 + 5*T^2 - 3*T + 9 53 375710212613522454739564588670922208809045305831041 = [ <11, 1>, <20286538939369441, 1>, <1683652099356985178203311250210691, 1> ] 59 199667811101605239406159070204724201287758855695989202491 = [ <11, 1>, <46021, 1>, <1313957849, 1>, <96920848751, 1>, <3097138866378364840535450176939, 1> ] 61 16173092699229879224950419252411138197264795147377189237219 = [ <11, 1>, <14685832338351929, 1>, <100115616234826306730690212588997043714001, 1> ] 67 8595044557171429689234023037332673708459725964755962036875588329 = [ <11, 1>, <82009, 1>, <2512501, 1>, <410211074434092005646419, 1>, <9244433590766166793286364509, 1> ] 71 56392087339601733262117982580536913587606760754132632798693884264239 = [ <11, 1>, <286789390847699, 1>, <33691402119736789, 1>, <483145604550899581, 1>, <1098159152378815039, 1> ] 73 4567759074507740452130230748665664650186727891973044246510884989137801 = [ <11, 1>, <1874299284284638224821, 1>, <221549903175541927413278825115334865638120314671, 1> ] 79 2427494450315468069110234028249143266768188745963834670233811586843924845651 = [ <11, 1>, <645082228711517368111, 1>, <34575383562087591054858599, 1>, <9894263591636886474046259569, 1> ] 83 15926791088519786002938646267999040375362921319208481718412098336507665567191941 = [ <11, 1>, <34031, 1>, <5031705569343571, 1>, <16257033150059158778734793509, 1>, <520120984084357398234371348159, 1> ] 89 8464149782874043593258511108508213480634424929524920856606245656539913880912434450599 = [ <11, 1>, <64081, 1>, <132611, 1>, <42862579, 1>, <1968064342917347999990700889831, 1>, <1073406530123153449170594386505380651, 1> ] ----------------------------------------------------------------------------------- T^4 + 4*T^2 + 9 53 375710212613636260325580195717831752961570886475774 = [ <2, 1>, <7, 1>, <715289, 1>, <36308287, 1>, <1033326717529883237145320575583612687, 1> ] 59 199667811101603467823686647745916200713953746107386754446 = [ <2, 1>, <7, 1>, <1063, 1>, <22607204017801854127, 1>, <593471548162441806087754116060889, 1> ] 61 16173092699229880893718618465715265321084811990533778731614 = [ <2, 1>, <7, 1>, <367, 2>, <75128089, 1>, <2314110859805808464129, 1>, <49334009051918837301089, 1> ] 67 8595044557171427132038716315969907937439201751577967234435007406 = [ <2, 1>, <7, 1>, <238502447, 1>, <35472913277182936908180767, 1>, <72565534815257262687699928321, 1> ] 71 56392087339601733413306017749077357975854197499650917973582397062206 = [ <2, 1>, <7, 1>, <24882195404543, 1>, <34062201815837143321, 1>, <4752572168143443113710209975544943, 1> ] 73 4567759074507740406477787437675267230633286405977043337392414391889774 = [ <2, 1>, <7, 1>, <86287, 1>, <1737073966087, 1>, <45052780533703, 1>, <173346777392183, 1>, <278723829413023151949161, 1> ] 79 2427494450315468069358961833665581682419639311452138584502190669280324068446 = [ <2, 1>, <7, 1>, <1423, 1>, <5689, 1>, <10903, 1>, <3017801, 1>, <35949583, 1>, <18107517302601208561412188953851179027774056762863, 1> ] 83 15926791088519786003064148590679881418937516720065157808954562636426019373538286 = [ <2, 1>, <7, 1>, <167, 2>, <17929, 1>, <26561, 1>, <22248607663, 1>, <3850028804818373268481658040817124198890968788748427703, 1> ] 89 8464149782874043593254414191179506861158316248298936834592422184002558387900949849134 = [ <2, 1>, <7, 1>, <11927, 1>, <38449, 1>, <437881, 1>, <75989558178144331823, 1>, <39621326882470415199144637878786261233782975228369, 1> ] -------------------------------------------------------------------------------- T^4 + T^3 + 3*T^2 + 3*T + 9 53 375710212613592764451518746608153591828133271772287 = [ <17, 1>, <1874500901399319348997, 1>, <11790125427775411753362578563, 1> ] 59 199667811101604123104453653229960263622081755357258876913 = [ <17, 1>, <204023, 1>, <263849, 1>, <8656735121111171, 1>, <25204055345477166117077046917, 1> ] 61 16173092699230004715035953827469132069093589760042514956617 = [ <17, 1>, <367, 1>, <21194573, 1>, <54807769, 1>, <5460649276138323331, 1>, <408664592200833545849, 1> ] 67 8595044557171430066702033112903203966498392521963765496067556503 = [ <17, 1>, <269, 1>, <4423, 1>, <425987, 1>, <275314840309552031, 1>, <3623297748084612199640753050717481, 1> ] 71 56392087339601733158852667767676812783455446929961895731855600705173 = [ <17, 1>, <28873997, 1>, <338521079251096942185197033051, 1>, <339372482265606870320241289627, 1> ] 73 4567759074507740413167988944721288768984646298633124283969214059679287 = [ <17, 1>, <3943, 1>, <3027652166477, 1>, <65366993065988065781237, 1>, <344320597719625743449555058673, 1> ] 79 2427494450315468068253043347592517388387688065986593644631374688157723644713 = [ <17, 1>, <41081, 1>, <3475908356540189708786290710594016395711325066527955022\ 332314334747169, 1> ] 83 15926791088519786003653746410785189987284984864960520251293073086633335503997883 = [ <17, 1>, <9368700640305756472737497888697170580755873449976776618407690050960\ 78559058699, 1> ] 89 8464149782874043593261466407642299208716656694243182037430622582812749482917607313597 = [ <17, 1>, <517981, 1>, <18252833, 1>, <112093858005913183, 1>, <469795109838288846774284110845122131114246832725551599, 1> ] ------------------------------------------------------------------------------------ T^4 + 2*T^3 + 2*T^2 + 6*T + 9 53 375710212613706937696901616587128448324983418165380 = [ <2, 2>, <5, 1>, <52072289, 1>, <779945839721, 1>, <462542762545334383541219220101, 1> ] 59 199667811101601967868682850067957050590833828779576982180 = [ <2, 2>, <5, 1>, <709, 1>, <1181, 1>, <1889, 1>, <81421, 1>, <68390689506542065021, 1>, <1133487033179226626029, 1> ] 61 16173092699229817173084860551644845350492966238875710232420 = [ <2, 2>, <5, 1>, <464089, 1>, <2049803741, 1>, <850059888967754021864615718064299256394929, 1> ] 67 8595044557171427380415881374551467053783405635644711842603783620 = [ <2, 2>, <5, 1>, <269, 2>, <1609, 2>, <2190901, 1>, <2887679812163891369, 1>, <362601585103574971653913289, 1> ] 71 56392087339601735253751683235680264070169075359522921533488197592980 = [ <2, 2>, <5, 1>, <133481, 1>, <2610529, 1>, <1817047621, 1>, <4453217339726778108140810582157674179440104581, 1> ] 73 4567759074507740373824162401375224015089137816411657976245889223809780 = [ <2, 2>, <5, 1>, <5144910988213023701, 1>, <44391040826288961033265197375269005197234639011189, 1> ] 79 2427494450315468068407790559744650943693784274581913919325449903871494444980 = [ <2, 2>, <5, 1>, <10429, 1>, <12641, 1>, <920670337799694455993784135374739528849559905898027510900723757341, 1> ] 83 15926791088519786002821757589748928463313803164958964073068014074807780102575620 = [ <2, 2>, <5, 1>, <368189, 1>, <2021633843740122016397849, 1>, <1069855143599640829524009601663907301812205168121, 1> ] 89 8464149782874043593250649398617380087586045561558204453207619466811347279466565360820 = [ <2, 2>, <5, 1>, <7121, 1>, <208261, 1>, <13399432277819326152797055834155724949, 1>, <21296979418499240389722808454244871889, 1> ] ----------------------------------------------------------------------------------- T^4 - 3*T^3 + 7*T^2 - 9*T + 9 53 375710212613538026965544261727078973260808819671995 = [ <5, 1>, <1061, 1>, <528335272651, 1>, <106608394573263281, 1>, <1257380158148018089, 1> ] 59 199667811101605202022510865504062124518974873141533625045 = [ <5, 1>, <118938455154123696811, 1>, <335749797393736453249163678726109619, 1> ] 61 16173092699229758434528876497049731585786415657993916082605 = [ <5, 1>, <75641, 1>, <6797441671, 1>, <629100919775704688943119102919058443672\ 6311, 1> ] 67 8595044557171430089322986284607180187052654784302763769790924755 = [ <5, 1>, <6299, 1>, <1104561339112999776011, 1>, <247068103386298088732017590353858368159, 1> ] 71 56392087339601733530176572889903221247786092059623253986784234546945 = [ <5, 1>, <478399, 1>, <2357533662888163793409960007855502258482400341958208691\ 3553011, 1> ] 73 4567759074507740381977897129340238321368426730717381696407753637754595 = [ <5, 1>, <439, 1>, <69685801, 1>, <15298445021, 1>, <4479093439125341, 1>, <13516473050453831, 1>, <32242118718031031, 1> ] 79 2427494450315468069118026923056510414308302981765503734247711451422331197245 = [ <5, 1>, <3319, 1>, <146278665279630495276771733838897885767297558407080670939\ 904275469860271, 1> ] 83 15926791088519786003649301611021106169760653868101226604180595523451070405950655 = [ <5, 1>, <32371, 1>, <98401600744615773399952436508115944331411781335771070428\ 350038759698930561, 1> ] 89 8464149782874043593250847678277095907753116443378525590593135995379825662483883338505 = [ <5, 1>, <179, 2>, <4451, 1>, <84479869, 1>, <2285640752022701, 1>, <61473575957201396447179284243812627734692873930258919, 1> ] ---------------------------------------------------------------------------------- T^4 + T^3 - 2*T^2 + 3*T + 9 53 375710212613668040549441418841968893601187783141572 = [ <2, 2>, <3, 1>, <31309184384472336712453451570164074466765648595131, 1> ] 59 199667811101606827216627292156424882245154681512761048668 = [ <2, 2>, <3, 1>, <5410920607335183819944959, 1>, <3075074551253071151683426036771, 1> ] 61 16173092699229805255431003184121521896837346688119802398812 = [ <2, 2>, <3, 1>, <367, 1>, <5866542625243, 1>, <625984435418638628483822171241544142514121, 1> ] 67 8595044557171425888048924786112106942487919830959679110102800068 = [ <2, 2>, <3, 1>, <716253713097618824004077065509342245207326652579973259175233\ 339, 1> ] 71 56392087339601732200583537374364625810909733511056381652966295425868 = [ <2, 2>, <3, 1>, <901934907193, 1>, <205542446238825348691, 1>, <25348963593318370686943964095484803, 1> ] 73 4567759074507740426712924232457681345565807893042742929510006525048172 = [ <2, 2>, <3, 1>, <41642193204109, 1>, <37650858980289825994343863, 1>, <242780308774299713301205616443, 1> ] 79 2427494450315468069988423114245051012246492618247365848140245277448630387668 = [ <2, 2>, <3, 1>, <17539, 1>, <113551905881329, 1>, <101572874627500061165618458162642154425246266333191867869, 1> ] 83 15926791088519786003435139760401394648090605771632029536813020956548272978212668 = [ <2, 2>, <3, 1>, <499, 1>, <1943197, 1>, <1400749858178493057722918552716477, 1>, <977167633068752586841324841433642319, 1> ] 89 8464149782874043593262371605424077657953335264453317906957546255917457290803488904852 = [ <2, 2>, <3, 1>, <548953, 1>, <12848929056576858725097855380187492763426218128\ 65175146590805019725042837729807, 1> ]