Torsion groups of Mordell curves over cubic and sextic fields

TL;DR

This paper classifies all possible torsion groups of Mordell curves over cubic and sextic fields, providing explicit descriptions and comprehensive classifications for these algebraic structures.

Contribution

It offers the first complete classification of torsion groups of Mordell curves over cubic and sextic fields, including explicit descriptions and enumeration.

Findings

All torsion groups over cubic fields are classified.

All torsion groups over sextic fields are classified.

Explicit descriptions of these torsion groups are provided.

Abstract

In this paper, we classify torsion groups of rational Mordell curves explicitly over cubic fields as well as over sextic fields. Also, we classify torsion groups of Mordell curves over cubic fields and for Mordell curves over sextic fields, we produce all possible torsion groups.