Elliptic curves over totally real quartic fields not containing √5 are modular

Box, Josha

doi:10.1090/tran/8557

Elliptic curves over totally real quartic fields not containing $\sqrt {5}$ are modular
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by Josha Box PDF

Trans. Amer. Math. Soc. 375 (2022), 3129-3172

Abstract:

We prove that every elliptic curve defined over a totally real number field of degree 4 not containing $\sqrt {5}$ is modular. To this end, we study the quartic points on four modular curves.

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