name Hessian curves parameter d coordinate x coordinate y satisfying x^3+y^3+1=3 d x y addition x = (y1^2 x2-y2^2 x1)/(x2 y2-x1 y1) addition y = (x1^2 y2-x2^2 y1)/(x2 y2-x1 y1) doubling x = y1(1-x1^3)/(x1^3-y1^3) doubling y = x1(y1^3-1)/(x1^3-y1^3) negation x = y1 negation y = x1 toweierstrass u = x^2+x y+y^2+d(x+y) toweierstrass v = (x^2+x y+y^2+d(x+y)+d^2)y a0 = 1 a1 = d a2 = 0 a3 = 1 a4 = d a6 = d^3+1 fromweierstrass x = (1+v+u d)/(u+d^2) fromweierstrass y = v/(u+d^2)