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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Are there modular elliptic curves over a field extension of $\mathbb{Z}[i]$?

Let $E$ be an elliptic curve, $\mathbb{Q}$ the field of rational numbers, $\mathbb{Z}[i]$ the ring of Gaussian integers and let $K$ be a number field that is some field extension of $\mathbb{Q}$. Is …
Robert Betts's user avatar