Discriminant: Difference between revisions
From Elliptic Curve Crypto
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:<math>\Delta = -64a^3-432b^2</math> | :<math>\Delta = -64a^3-432b^2</math> | ||
when the field characteristic is not 2 or 3 <ref>Wolfram MathWorld: Elliptic Discriminant. https://mathworld.wolfram.com/EllipticDiscriminant.html</ref>. | or | ||
:<math>\Delta = \frac{-432a^3}j</math> | |||
in terms of the [[j-invariant]] when the field characteristic is not 2 or 3 <ref>Wolfram MathWorld: Elliptic Discriminant. https://mathworld.wolfram.com/EllipticDiscriminant.html</ref>. | |||
Revision as of 16:47, 3 January 2025
The discriminant of an elliptic curve in Weierstraß normal form
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y^2 = x^3 + ax + b}
is defined to be
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta = -64a^3-432b^2}
or
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta = \frac{-432a^3}j}
in terms of the j-invariant when the field characteristic is not 2 or 3 [1].
- ↑ Wolfram MathWorld: Elliptic Discriminant. https://mathworld.wolfram.com/EllipticDiscriminant.html
