Elliptic surfaces over ℙ1 and large class groups of number fields

Abstract

Given a non-isotrivial elliptic curve over [Formula: see text] with large Mordell–Weil rank, we explain how one can build, for suitable small primes [Formula: see text], infinitely many fields of degree [Formula: see text] whose ideal class group has a large [Formula: see text]-torsion subgroup. As an example, we show the existence of infinitely many cubic fields whose ideal class group contains a subgroup isomorphic to [Formula: see text].