The number of twists with large torsion of an elliptic curve

2013/12/31 by Najman, Filip
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1401.0205

Abstract

For an elliptic curve E/\Q, we determine the maximum number of twists E^d/\Q it can have such that E^d(\Q)_tors\supsetneq E(\Q)[2]. We use these results to determine the number of distinct quadratic fields K such that E(K)_tors\supsetneq E(\Q)_tors. The answer depends on E(\Q)_tors and we give the best possible bound for all the possible cases.

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