Number theory seminar – University of Copenhagen

Number theory seminar

In a recent collaboration with Pascal Autissier and Marc Hindry, we prove that up to isomorphisms, there are at most finitely many elliptic curves defined over a fixed number field, with Mordell-Weil rank and regulator bounded from above, when the rank at least 4. We will explain where the result comes from, and discuss links with the Birch and Swinnerton-Dyer conjecture and with asymptotics on the number of rational points of bounded height on elliptic curves.