J-invariant

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

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

is defined to be

$j={\frac {1728a^{3}}{4a^{3}+27b^{2}}}$

or

$j={\frac {-108a^{3}}{\Delta }}$

in terms of the elliptic discriminant Δ .