Modularity of elliptic curves over imaginary quadratic fields

Proves the modularity conjecture for elliptic curves over imaginary quadratic fields: every elliptic curve over every imaginary quadratic field is modular, with matching local parameters at every place.

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Modularity of elliptic curves over imaginary quadratic fields

October 4, 2026 · source · cite as \cite{OAI:Modularity-of-elliptic-curves-over-imaginary-quadratic-fields-October-4-2026}

We prove the modularity conjecture for elliptic curves over imaginary quadratic fields: every such curve is modular, with matching local parameters at every place.

Result 030 · Number theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.