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Torsion of rational elliptic curves over quadratic fields II

Opened Access Torsion of rational elliptic curves over quadratic fields II

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Autor: González Jiménez, Enrique
Tornero Sánchez, José María
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2016-03
Publicado en: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 110 (1), 121-143.
Tipo de documento: Artículo
Resumen: 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.
Cita: 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.
Tamaño: 275.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47168

DOI: 10.1007/s13398-015-0223-9

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