Covers of Elliptic Curves with Unique, Totally Ramified Branch Points

TL;DR

This paper introduces a new technique for computing totally ramified covers of elliptic curves with a single branch point, addressing a complex problem in algebraic geometry and number theory.

Contribution

It presents a novel method specifically for constructing totally ramified covers of elliptic curves with one branch point, advancing computational approaches in the field.

Findings

Developed a new computational technique for elliptic curve covers.

Successfully applied the method to specific cases of ramified covers.

Provides a framework for future research in algebraic curve coverings.

Abstract

A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing such covers in the case of totally ramified covers of elliptic curves branched at one point.