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 $E(K{)}_{\text{tors}}$.

arXiv commentTo appear in the Journal of Number Theory

References in corpus (3)

• On the arithmetic of certain modular curves
• Torsion of rational elliptic curves over quadratic fields
• A criterion to rule out torsion groups for elliptic curves over number fields

Cited by in corpus (9)

• Growth of torsion groups of elliptic curves upon base change
• Complete classification of the torsion structures of rational elliptic curves over quintic number fields
• Torsion subgroups of rational elliptic curves over the compositum of all cubic fields
• Galois representations attached to elliptic curves with complex multiplication
• On the torsion of rational elliptic curves over quartic fields
• Torsion of rational elliptic curves over the maximal abelian extension of Q
• An algorithm for determining torsion growth of elliptic curves
• Groups of generalized $G$-type and applications to torsion subgroups of rational elliptic curves over infinite extensions of $\mathbb{Q}$
• Torsion of elliptic curves with rational $j$-invariant defined over number fields of prime degree