Function: ellztopoint
Section: elliptic_curves
C-Name: pointell
Prototype: GGp
Help: ellztopoint(E,z): coordinates of point P on the curve E corresponding
 to the complex number z.
Doc:
 $E$ being an \var{ell} as output by
 \kbd{ellinit}, computes the coordinates $[x,y]$ on the curve $E$
 corresponding to the complex number $z$. Hence this is the inverse function
 of \kbd{ellpointtoz}. In other words, if the curve is put in Weierstrass
 form $y^2 = 4x^3 - g_2x - g_3$, $[x,y]$ represents the Weierstrass
 $\wp$-function\sidx{Weierstrass $\wp$-function} and its derivative. More
 precisely, we have
 $$x = \wp(z) - b_2/12,\quad y = \wp'(z) - (a_1 x + a_3)/2.$$
 If $z$ is in the lattice defining $E$ over $\C$, the result is the point at
 infinity $[0]$.