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arXiv · 1401.0205

The number of twists with large torsion of an elliptic curve

Filip Najman
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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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Filip Najman. 2013-12-31. The number of twists with large torsion of an elliptic curve. https://arxiv.org/abs/1401.0205

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