A modularity test for elliptic mirror symmetry

TL;DR

This paper verifies a prediction of algebraic mirror symmetry for elliptic curves of Brieskorn-Pham type by showing their associated modular forms are identical, using number theoretic methods.

Contribution

It provides a number theoretic verification of mirror symmetry predictions for a specific class of elliptic curves.

Findings

Modular forms of mirror pairs are identical.

Mirror symmetry prediction holds for Brieskorn-Pham elliptic curves.

Number theoretic methods confirm the algebraic mirror construction.

Abstract

In this note a prediction of an algebraic mirror construction is checked for elliptic curves of Brieskorn-Pham type via number theoretic methods. It is shown that the modular forms associated to the Hasse-Weil L-series of mirror pairs of such curves are identical.