Complete classification of the torsion structures of rational elliptic curves over quintic number fields

Abstract

We classify the possible torsion structures of rational elliptic curves over quintic number fields. In addition, let E be an elliptic curve defined over Q and let G = E(Q)_tors be the associated torsion subgroup. We study, for a given G, which possible groups G \subseteq H could appear such that H=E(K)_tors, for [K:Q]=5. In particular, we prove that at most there is a quintic number field K such that E(Q)_tors\neq E(K)_tors.

The file contains text colored in blue; this text can be clicked on and is a link to the Magma code used to obtain that particular result. To appear in Journal of Algebra

References in corpus (4)

• Growth of torsion groups of elliptic curves upon base change
• Torsion subgroups of elliptic curves over quintic and sextic number fields
• Torsion of rational elliptic curves over quadratic fields
• On the torsion of rational elliptic curves over quartic fields

Cited by in corpus (7)

• Growth of torsion groups of elliptic curves upon base change
• On the torsion of rational elliptic curves over quartic fields
• Computing isomorphisms and embeddings of finite fields
• 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
• Torsion groups of Mordell curves over number fields of higher degree