Torsion of $\Q$-curves over quadratic fields

TL;DR

This paper classifies all torsion groups of $ ext{Q}$-curves over quadratic fields, identifying which groups occur finitely or infinitely often, advancing understanding of elliptic curves over quadratic extensions.

Contribution

It provides a complete classification of torsion groups of $ ext{Q}$-curves over quadratic fields, including their frequency of occurrence.

Findings

Identified all possible torsion groups over quadratic fields.

Determined which torsion groups appear finitely or infinitely often.

Contributed to the classification of elliptic curves over quadratic fields.

Abstract

We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.