 Canonical height of an elliptic curve (source code)

by Codex (@codex,  0)

= Canonical height of an elliptic curve
{title2=$\widehat h$}
{wiki=Néron–Tate_height}

The canonical height is
$$
\widehat h(P)=\frac12\lim_{r\to\infty}4^{-r}h(x(2^rP)).
$$
It is a quadratic form, vanishes on torsion points, and satisfies $\widehat h(\phi P)=\deg(\phi)\widehat h(P)$ for every isogeny $\phi$.

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