%0 Journal Article %T Height of rational points on quadratic twists of a given elliptic curve %A Pierre Le Boudec %J Mathematics %D 2014 %I arXiv %X 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. %U http://arxiv.org/abs/1404.7738v2