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

JOURNAL OF ALGEBRA

卷:478

Article

Gonzalez-Jimenez, Enrique¹ 

[1] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain

关键词: Elliptic curves;    Torsion subgroup;    Rationals;    Quintic number fields;   

DOI  :  10.1016/j.jalgebra.2017.01.012

来源: Elsevier

【 摘 要 】

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 subset of H could appear such that H = E(K)(tors), for [K : Q] = 5. In particular, we prove that at most there is one quintic number field K such that the torsion grows in the extension K/Q, i.e., E(Q)(tors) subset of E (K)(tors). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free