Ranks of elliptic curves in families of quadratic twists

(Un exposé d'Alice Silverberg au séminaire de théorie des nombres de Chevaleret le 13 mars 2000)

Résumé :

We discuss ranks of quadratic twists of elliptic curves. In joint work with Karl Rubin we show that the unboundedness of the ranks of the quadratic twists of an elliptic curve over the field of rational numbers is equivalent to the divergence of certain infinite series.