Definition:Elliptic Curve/Standard Form
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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