Modularity of some elliptic curves over totally real fields
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.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.1309.4134 |