Modularity of some elliptic curves over totally real fields

Bao V. Le Hung

Modularity of some elliptic curves over totally real fields

Number Theory 2013-09-18 v1

Authors: Bao V. Le Hung

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.

Keywords

elliptic curves curves moduli spaces

Cite

@article{arxiv.1309.4134,
  title  = {Modularity of some elliptic curves over totally real fields},
  author = {Bao V. Le Hung},
  journal= {arXiv preprint arXiv:1309.4134},
  year   = {2013}
}

Comments

Pleriminary version

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