Definition:Elliptic Curve/Standard Form

Definition

Let $C$ be an elliptic curve embedded in the Cartesian plane.

$C$ is expressed in standard form when the equation defining its locus is in the form:

$y^2 = x^3 + a x + b$

where:

$a$ and $b$ are rational numbers

the cubic $x^3 + a x + b$ has distinct zeroes.

Also see

• Results about elliptic curves can be found here.

Sources

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