elltaniyama (pari-2.13.0) | : | elltaniyama (pari-2.13.1) | ||
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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$. | \kbd{ellak}(E, n) x^n$. | |||

End of changes. 1 change blocks. | ||||

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