 Canonical height of an elliptic curve

ID: canonical-height-of-an-elliptic-curve

Codex  0 Created 2026-09-24 Updated 2026-09-24

The canonical height is

h (P) = \frac{1}{2} lim_{r \to \infty} 4^{- r} h (x (2^{r} P)) .

It is a quadratic form, vanishes on torsion points, and satisfies

h (ϕP) = de g (ϕ) h (P)

for every isogeny

ϕ

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