THE 2-CLASS GROUPS OF CUBIC FIELDS AND 2-DESCENTS ON ELLIPTIC CURVES

Abstract

We investigate the relationship between the 2-class groups of cubic fields and the Mordell-Weil groups of elliptic curves defined over Q. There is an exact sequence which connects those two groups together for a certain kind of cyclic cubic fields. Using the twists of elliptic curves, we give a more precise result for the simplest cubic fields.