Function: elltaniyama
Section: elliptic_curves
C-Name: elltaniyama
Prototype: GDP
Help: elltaniyama(E, {d = seriesprecision}): modular parametrization of elliptic curve E (minimal
 model).
Doc:
 computes the modular parametrization of the
 elliptic curve $E$, where $E$ is a \var{smallell} as output by \kbd{ellinit},
 in the form of a two-component vector $[u,v]$ of power series, given to $d$
 significant terms (\tet{seriesprecision} by default). This vector is
 characterized by the
 following two properties. First the point $(x,y)=(u,v)$ satisfies the
 equation of the elliptic curve. Second, the differential $du/(2v+a_1u+a_3)$
 is equal to $f(z)dz$, a differential form on $H/\Gamma_0(N)$ where $N$ is the
 conductor of the curve. The variable used in the power series for $u$ and $v$
 is $x$, which is implicitly understood to be equal to $\exp(2i\pi z)$. It is
 assumed that the curve is a \emph{strong} \idx{Weil curve}, and that the
 Manin constant is equal to 1. The equation of the curve $E$ must be minimal
 (use \kbd{ellminimalmodel} to get a minimal equation).
