Definition:Elliptic Curve

Definition

An elliptic curve is a plane curve $C$ embedded in the Cartesian plane such that:

$C$ can be defined by a polynomial equation such that:

the coefficients of $C$ are rational

the genus of $C$ is $1$

$C$ has at least $1$ rational lattice point.

Also see

• Results about elliptic curves can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): elliptical curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elliptical curve