Abstract
Let \(E\) be an elliptic curve defined over \({\mathbb {Q}}\). We study the relationship between the torsion subgroup \(E({\mathbb {Q}})_{{{\mathrm{tors}}}}\) and the torsion subgroup \(E(K)_{{{\mathrm{tors}}}}\), where \(K\) is a quadratic number field.
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The authors would like to thank J. Silverman and N. Elkies for their suggestions and ideas.
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E. González-Jiménez was partially supported by the grant MTM2012-35849. J. M. Tornero was partially supported by the grants FQM-218 and P08-FQM-03894, FSE and FEDER (EU).
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González-Jiménez, E., Tornero, J.M. Torsion of rational elliptic curves over quadratic fields. RACSAM 108, 923–934 (2014). https://doi.org/10.1007/s13398-013-0152-4
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DOI: https://doi.org/10.1007/s13398-013-0152-4