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Source code changes of the file "src/functions/elliptic_curves/elltaniyama" between
pari-2.13.0.tar.gz and pari-2.13.1.tar.gz

About: PARI/GP is a computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other mathematical functions.

elltaniyama  (pari-2.13.0):elltaniyama  (pari-2.13.1)
skipping to change at line 22 skipping to change at line 22
properties. First the point $(u,v)$ satisfies the equation of the elliptic properties. First the point $(u,v)$ satisfies the equation of the elliptic
curve. Second, let $N$ be the conductor of $E$ and $\Phi: X_0(N)\to E$ curve. Second, let $N$ be the conductor of $E$ and $\Phi: X_0(N)\to E$
be a modular parametrization; the pullback by $\Phi$ of the be a modular parametrization; the pullback by $\Phi$ of the
N\'eron differential $du/(2v+a_1u+a_3)$ is equal to $2i\pi N\'eron differential $du/(2v+a_1u+a_3)$ is equal to $2i\pi
f(z)dz$, a holomorphic differential form. The variable used in the power f(z)dz$, a holomorphic differential form. The variable used in the power
series for $u$ and $v$ is $x$, which is implicitly understood to be equal to series for $u$ and $v$ is $x$, which is implicitly understood to be equal to
$\exp(2i\pi z)$. $\exp(2i\pi z)$.
The algorithm assumes that $E$ is a \emph{strong} \idx{Weil curve} The algorithm assumes that $E$ is a \emph{strong} \idx{Weil curve}
and that the Manin constant is equal to 1: in fact, $f(x) = \sum_{n > 0} and that the Manin constant is equal to 1: in fact, $f(x) = \sum_{n > 0}
\kbd{ellan}(E, n) x^n$. \kbd{ellak}(E, n) x^n$.
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