elliptic curve

The non-singularity then requires that 4p3 + 27q2 ≠ 0. But the study of elliptic curves over the complex numbers (including points at infinity, so studying the curves within the complex projective plane (see projective space)) has a rich history. Such a curve is then topologically a torus and as a Riemann surface can be identified with ℂ/Λ, where Λ is some lattice aℤ+bℤ, where a/b is not real. Now ℂ/Λ is an abelian group, and this group structure on the curve manifests geometrically via a theorem due to Abel.

Elliptic curves over the rational numbers are of great interest in number theory; the Birch-Swinnerton-Dyer conjecture (see appendix 23) concerns them. And over Galois fields, elliptic curves have applications in cryptography. See also degree-genus formula.

• a
• a-
• A
• AAS
• abacus
• abc conjecture
• abelian group
• abelian group
• Abelianization
• Abel, Niels Henrik
• Abel Prize
• Abel's Limit Theorem
• Abel's partial summation formula
• Abel's test
• Abel summation
• above
• abscissa
• absolute error
• absolute frequency
• absolute geometry
• absolutely continuous
• absolutely convergent series
• absolutely summable
• absolute value
• absorbing set