Numerical modular symbols for elliptic curves

TL;DR

This paper introduces a numerical method for computing modular symbols of elliptic curves, which is more efficient than existing methods especially for curves with large conductors.

Contribution

It proposes a novel numerical approximation approach that improves computational efficiency for modular symbols of elliptic curves.

Findings

Numerical method outperforms traditional algorithms for large conductors.

Implementation reduces computation time significantly.

Method is applicable to a wide range of elliptic curves.

Abstract

We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementation as the conductor of the curve increases.