name Jacobi quartics parameter a coordinate x coordinate y satisfying y^2 = x^4 + 2 a x^2 + 1 addition x = (x1 y2+y1 x2)/(1-(x1 x2)^2) addition y = ((1+(x1 x2)^2) (y1 y2+2 a x1 x2)+2 x1 x2 (x1^2+x2^2))/(1-(x1 x2)^2)^2 doubling x = (x1 y1+y1 x1)/(1-(x1 x1)^2) doubling y = ((1+(x1 x1)^2) (y1 y1+2 a x1 x1)+2 x1 x1 (x1^2+x1^2))/(1-(x1 x1)^2)^2 negation x = -x1 negation y = y1 neutral x = 0 neutral y = 1 toweierstrass u = a + (y+1)/x^2 toweierstrass v = (a + (y+1)/x^2)/x a0 = 2 a1 = 0 a2 = -2 a a3 = 0 a4 = a^2-1 a6 = 0 fromweierstrass x = u/v fromweierstrass y = (u-a)(u/v)^2-1