Torsion of rational elliptic curves over quadratic fields II
Number Theory
2016-02-26 v2 Algebraic Geometry
Abstract
Let E be an elliptic curve defined over Q and let G=E(Q)_tors be the associated torsion group. In a previous paper, the authors studied, for a given G, which possible groups G\leq H could appear such that H=E(K)_tors, for [K:Q]=2. In the present paper, we go further in this study and compute, under this assumption and for every such G, all the possible situations where G\neq H. The result is optimal, as we also display examples for every situation we state as possible. As a consequence, the maximum number of quadratic number fields K such that E(Q)_tors\neq E(K)_tors is easily obtained.
Cite
@article{arxiv.1411.3468,
title = {Torsion of rational elliptic curves over quadratic fields II},
author = {Enrique Gonzalez-Jimenez and Jose M. Tornero},
journal= {arXiv preprint arXiv:1411.3468},
year = {2016}
}
Comments
To appear in Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'atica RACSAM