engleski

Fields of definition of elliptic curves with prescribed torsion

We prove that all elliptic curves over quadratic fields with a subgroup isomorphic to C16, as well as all elliptic curves over cubic fields with a subgroup isomorphic to C2 × C14, are base changes of elliptic curves defined over Q. We obtain these results by studying geometric properties of modular curves and maps between modular curves, and then obtaining a modular description of these curves and maps.

elliptic curves ; torsion

nije evidentirano