J-invariant: Difference between revisions
From Elliptic Curve Crypto
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in terms of the discriminant ''D'' of the cubic polynomial |
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:<math>j=\frac{-110592a^3}{\Delta}</math> | :<math>j=\frac{-110592a^3}{\Delta}</math> | ||
in terms of the elliptic [[discriminant]] Δ <ref>Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html</ref>. | in terms of the elliptic [[discriminant]] Δ <ref>Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html</ref>, or, | ||
:<math>j=\frac{64a^3}{D}</math> | |||
in terms of the discriminant ''D'' of the cubic polynomial <math>x^2+ax+b</math>. | |||
Revision as of 23:25, 25 February 2025
The j-invariant 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^2+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 j=\frac{6912a^3}{4a^3+27b^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 j=\frac{-110592a^3}{\Delta}}
in terms of the elliptic discriminant Δ [1], 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 j=\frac{64a^3}{D}}
in terms of the discriminant D of the cubic polynomial 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 x^2+ax+b} .
- ↑ Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html
