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 Incoming links: Néron–Tate height

Canonical height of an elliptic curve Created 2026-09-24 Updated 2026-10-14

This is the elliptic-curve specialization of the Néron–Tate height. For an associated logarithmic projective height

h

, one normalization is

h (P) = lim_{n o \infty} 4^{- n} h ([2^{n}] P)

.

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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