TL;DR
This paper investigates how the torsion subgroup of rational elliptic curves can grow when extended to degree 6 fields, providing initial classifications of possible torsion groups and their frequency.
Contribution
It offers the first systematic study of torsion growth of rational elliptic curves over sextic fields, identifying which torsion groups can occur and their frequency.
Findings
Classified possible torsion groups over sextic fields.
Determined which torsion groups occur infinitely often.
Identified torsion groups that occur only finitely often.
Abstract
Given an elliptic curve with torsion subgroup we study what groups (up to isomorphism) can occur as the torsion subgroup of base-extended to , a degree 6 extension of . We also determine which groups can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields.
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