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

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.

The results are now stated using (the exponential of) the canonical height. Thanks to Joe Silverman for enlightening comments on the previous version

Cited by in corpus (2)

• Average rank in families of quadratic twists: a geometric point of view
• On the number of quadratic twists with a rational point of almost minimal height