Torsion of rational elliptic curves over quadratic fields

TL;DR

This paper investigates how the torsion subgroup of a rational elliptic curve changes when extended from the rationals to quadratic fields, providing insights into the structure of elliptic curves over such fields.

Contribution

It analyzes the relationship between torsion subgroups over Q and quadratic fields, offering new classifications and understanding of torsion growth.

Findings

Characterization of torsion subgroup changes over quadratic fields

Identification of possible torsion subgroup structures

Extension of known classifications to quadratic fields

Abstract

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)_tors and the torsion subgroup E(K)_tors, where K is a quadratic number field.