source 1986 Chudnovsky--Chudnovsky "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", page 414, formula (4.2ii)
compute S = 4 X1 Y1^2
compute M = 3 X1^2+a Z1^4
compute T = M^2-2 S
compute X3 = T
compute Y3 = M(S-T)-8 Y1^4
compute Z3 = 2 Y1 Z1