An example of elliptic curve over $Q$ with rank $ \geqq 20$

Abstract

We construct an elliptic curve over Q with rank --> 20. Mestre [1] (resp. [2]) constructed elliptic curves over Q(T) with Q(T)-rank -> 11 (resp. with Q(T)-rank _> 12). In the families of elliptic curves over Q, which are obtained by specialization of above curves, Mestre