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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2013
- arXiv:
- arXiv:1309.4134
- Bibcode:
- 2013arXiv1309.4134L
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- Pleriminary version