Modular forms and elliptic curves over the field of fifth roots of unity

TL;DR

This paper computationally investigates the modularity of elliptic curves over the cyclotomic field generated by fifth roots of unity, contributing to understanding their properties in this specific number field.

Contribution

It provides the first systematic computational analysis of elliptic curves' modularity over the fifth roots of unity field.

Findings

Evidence supporting modularity in specific cases

Identification of patterns in elliptic curves over F

New computational techniques for this field

Abstract

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.