Archimedean local height differences on elliptic curves

TL;DR

This paper introduces an efficient method to compute upper bounds for local height differences at archimedean places on elliptic curves, aiding in the calculation of Mordell-Weil group generators.

Contribution

It presents a novel, elementary approach for bounding local height differences at archimedean places, improving upon previous algorithms.

Findings

Method is elementary and fast

Provides tighter bounds in some cases

Enhances computation of Mordell-Weil generators

Abstract

To compute generators for the Mordell-Weil group of an elliptic curve over a number field, one needs to bound the difference between the naive and the canonical height from above. We give an elementary and fast method to compute an upper bound for the local contribution to this difference at an archimedean place, which sometimes gives better results than previous algorithms.