Bornes optimales pour la diff\'erence entre la hauteur de Weil et la hauteur de N\'eron-Tate sur les courbes elliptiques sur \Qbar

TL;DR

This paper presents an algorithm to compute the minimum and maximum difference between naive and canonical heights on elliptic curves over algebraic closures of rationals, aiding in understanding their height functions.

Contribution

The paper introduces a novel algorithm for explicitly calculating the extremal differences between naive and canonical heights on elliptic curves over rac{rac{Qbar}.

Findings

Algorithm computes infimum and supremum of height differences.

Provides explicit bounds for height discrepancies.

Enhances understanding of height functions on elliptic curves.

Abstract

We give an algorithm that, given an elliptic curve $E$ over $\Qbar$ in Weierstra{\ss} form, computes the infimum and supremum of the difference between the na\"{\i}ve and canonical height functions on $E(\Qbar)$. ----- Nous donnons un algorithme qui, \'etant donn\'ee une courbe elliptique $E$ sur $\Qbar$ sous la forme de Weierstra\ss, calcule l'infimum et le supremum de la diff\'erence entre la hauteur na\"{\i}ve et la hauteur canonique sur $E(\Qbar)$.