Complete classification of the torsion structures of rational elliptic curves over quintic number fields
Number Theory
2018-04-20 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1607.01920,
title = {Complete classification of the torsion structures of rational elliptic curves over quintic number fields},
author = {Enrique González-Jiménez},
journal= {arXiv preprint arXiv:1607.01920},
year = {2018}
}
Comments
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