J-invariant

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

$y^{2}=x^{3}+ax+b$

is defined to be

$j={\frac {6912a^{3}}{4a^{3}+27b^{2}}}$

or

$j={\frac {-110592a^{3}}{\Delta }}$

in terms of the elliptic discriminant Δ , or,

$j={\frac {64a^{3}}{D}}$

in terms of the discriminant D of the cubic polynomial $x^{3}+ax+b$.