Imaginary-quadratic elliptic curve modularity adapter

Family 030: Modularity of elliptic curves over imaginary quadratic fields. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Arithmetic software teams could connect elliptic-curve data with matching automorphic local parameters across imaginary quadratic fields.

Applicability and commercial boundary

Modularity existence is not an efficient construction of forms, point counting or a new elliptic-curve security guarantee.

Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

Next verification action

Identify a finite local-parameter comparison workflow and effective algorithms.

Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Modularity of elliptic curves over imaginary quadratic fields.