Torsion of rational elliptic curves over quartic Galois number fields

Abstract

Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let $K$ be a number field of degree four that is Galois over $\mathbb{Q}$. The goal of this article is to classify the different isomorphism types of $E(K{)}_{\text{tors}}$.

To appear in the Journal of Number Theory