La constante de Manin et le degr\'e modulaire d'une courbe elliptique

TL;DR

This paper revisits the calculation of the Manin constant and modular degree of elliptic curves over Q using modular symbols, with implementation in Pari/GP, providing a computational perspective on these invariants.

Contribution

It applies modular symbols to compute the Manin constant and modular degree, leveraging Pari/GP for implementation, without claiming methodological innovation.

Findings

Successful computation of Manin constants and modular degrees

Implementation of modular symbols in Pari/GP for elliptic curves

Provides computational tools for elliptic curve invariants

Abstract

We revisit the calculation of the strong Weil curve in an isogeny class of elliptic curves over Q, of the Manin constant and modular degree of an elliptic curve, using modular symbols as defined in [Pollack-Stevens], now implemented in Pari/GP. There is no innovation claim.