Height of rational points on quadratic twists of a given elliptic curve
Number Theory
2017-05-17 v2
Abstract
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.
Cite
@article{arxiv.1404.7738,
title = {Height of rational points on quadratic twists of a given elliptic curve},
author = {Pierre Le Boudec},
journal= {arXiv preprint arXiv:1404.7738},
year = {2017}
}
Comments
The results are now stated using (the exponential of) the canonical height. Thanks to Joe Silverman for enlightening comments on the previous version