Torsion growth of rational elliptic curves in sextic number fields

TL;DR

This paper classifies the possible torsion subgroup structures of rational elliptic curves when extended to sextic (degree six) number fields, providing a comprehensive understanding of torsion growth in this context.

Contribution

It offers a complete classification of torsion structures of rational elliptic curves over sextic fields, advancing the understanding of torsion growth in elliptic curve theory.

Findings

Complete classification of torsion structures over sextic fields

Identification of possible torsion subgroup types

Extension of known results to degree six fields

Abstract

We classify the possible torsion structures of rational elliptic curves over sextic number fields.