Modularity of some elliptic curves over totally real fields

Abstract

We investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular $j$-invariants. By analyzing quadratic points on some modular curves, we show that all elliptic curves over certain real quadratic fields are modular.

Pleriminary version

Cited by in corpus (1)

• The modularity of elliptic curves over all but finitely many totally real fields of degree 5