View source for J-invariant

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

:<math>y^2=x^3+ax+b</math>

is defined to be

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

or

:<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>, or,

:<math>j=\frac{64a^3}{D}</math>

in terms of the discriminant ''D'' of the cubic polynomial <math>x^3+ax+b</math>.