Modularity of abelian varieties over $\Q$ with bad reduction in one prime only

TL;DR

This paper proves that specific abelian varieties over the rational numbers, which only have bad reduction at a single prime, are modular, using Odlyzko's tables and class field theory techniques.

Contribution

It introduces a novel approach to establish modularity for abelian varieties with limited bad reduction, expanding understanding of their structure.

Findings

Certain abelian varieties over re modular.

Methodology combines Odlyzko's tables with class field theory.

Results contribute to the modularity conjecture for abelian varieties.

Abstract

We show that certain abelian varieties over $\Q$ with bad reduction at one prime only are modular by using methods based on the tables of Odlyzko and class field theory.