Algorithmic construction of Shimura - Taniyama - Weil parametrization of elliptic curves over the rationals

TL;DR

This paper presents an algorithm for explicitly constructing the modular parametrization of elliptic curves over the rationals using the Weierstrass function, facilitating practical computations in number theory.

Contribution

It introduces a novel algorithm that explicitly constructs the Shimura-Taniyama-Weil parametrization from the Weierstrass function for elliptic curves over rationals.

Findings

Algorithm successfully constructs modular parametrizations

Enables explicit computations for elliptic curves

Bridges theoretical concepts with practical applications

Abstract

In this note we give an algorithm to explicitly construct the modular parametrization of an elliptic curve over the rationals given the Weierstrass function $\wp (z)$.