Number Theory Seminar

Speaker: Pierre le Boudec (EPFL)

Title: Height of rational points on elliptic curves in families

Abstract: Given a family F of elliptic curves defined over Q, we are interested in the set H(Y) of curves E in F, of positive rank, and for which the minimum of the canonical heights of non-torsion rational points on E is bounded by some parameter Y. When one can show that this set is finite, it is natural to investigate statistical properties of arithmetic objects attached to elliptic curves in the set H(Y). We will describe some problems related to this, and will state some results in the case of families of quadratic twists of a fixed elliptic curve.