Definition:Elliptic Curve

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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.

Standard Form

Definition:Elliptic Curve/Standard Form

Also see

  • Results about elliptic curves can be found here.