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arXiv:1404.7738 [math.NT]AbstractReferencesReviewsResources

Height of rational points on quadratic twists of a given elliptic curve

Pierre Le Boudec

Published 2014-04-30, updated 2014-05-27Version 2

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can only prove partial results in this direction.

Comments: The results are now stated using (the exponential of) the canonical height. Thanks to Joe Silverman for enlightening comments on the previous version
Categories: math.NT
Subjects: 11D45, 11G05, 14G05
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