Article
Torsion of rational elliptic curves over quadratic fields II
Author/s | González Jiménez, Enrique
Tornero Sánchez, José María |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2016-03 |
Deposit Date | 2016-10-07 |
Published in |
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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 ... 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Junta de Andalucía |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2012-35849
FQM-218 P12-FQM-2696 |
Citation | González Jiménez, E. y Tornero Sánchez, J.M. (2016). Torsion of rational elliptic curves over quadratic fields II. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 110 (1), 121-143. |
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