A smooth projective curve of genus 1 with a rational base point; equivalently y² = x³ + ax + b with 4a³+27b² ≠ 0. The points form an abelian group (chord-tangent law).
Elliptic curve
Related concepts
- Galois theory
- Smooth manifold
- Modular form
- Galois representation
- Birch–Swinnerton-Dyer conjecture
- Mordell-Weil theorem
- Modularity theorem (Taniyama-Shimura-Weil)
- ℓ-adic Tate module
- Faltings' theorem (Mordell)
- Cyclotomic field ℚ(ζₙ)
- Roth's theorem
- Modular curves X_0(N)
- K3 elliptic genus and Mathieu-M₂₄ moonshine (string-theory)