Torsion groups of elliptic curves that appear infinitely often over septic fields

TL;DR

This paper characterizes the torsion groups of elliptic curves that occur infinitely often over degree 7 number fields, expanding understanding of elliptic curve torsion structures in this context.

Contribution

It explicitly determines the set of torsion groups appearing infinitely often over septic fields, a new classification in elliptic curve torsion theory.

Findings

Identifies the set (7) of torsion groups occurring infinitely often.

Provides a classification of torsion groups over degree 7 number fields.

Advances understanding of elliptic curve torsion structures in septic fields.

Abstract

In this short note we determine the set $\Phi^\infty(7)$ of Abelian groups that appear as torsion groups of infinitely many elliptic curves (up to $\overline \mathbb Q$-isomorphism) over number fields of degree 7.