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High rank elliptic curves with prescribed torsion group over quadratic fields

There are 26 possibilities for the torsion group of an elliptic curve defined over quadratic number fields. In this talk we will present examples of high rank elliptic curves in most of the cases and searching methods that we used. These results come from a joint work with A.Dujella, J.Aguirre and J.C.Peral.

elliptic curves; torsion group; rank; quadratic fields

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