J-invariant: Difference between revisions

From Elliptic Curve Crypto
def
 
off by factor of 4
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is defined to be
is defined to be


:<math>j=\frac{1728a^3}{4a^3+27b^2}</math>
:<math>j=\frac{6912a^3}{4a^3+27b^2}</math>


or
or


:<math>j=\frac{-108a^3}{\Delta}</math>
:<math>j=\frac{-432a^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>.

Revision as of 16:45, 3 January 2025

The j-invariant of an elliptic curve in Weierstraß normal form

is defined to be

or

in terms of the elliptic discriminant Δ [1].

  1. Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html