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Questions about modular forms and related areas

3 votes
1 answer
303 views

Non-modular elliptic curves

Do we have any examples of non-modular elliptic curves over number fields $K \neq \mathbb{Q}$? In particular, I came across a paper by Freitas, Le Hung, and Siksek, "Elliptic curves over real quadrati …
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4 votes
1 answer
553 views

Are Frey elliptic curves semi-stable?

Are all Frey elliptic curves semi-stable? If so, where exactly is this needed in the modularity approach, now that we know modularity for all rational elliptic curves? Thank you!
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