Discriminant

The discriminant of an elliptic curve in Weierstraß normal form

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

is defined to be

$\Delta =-64a^{3}-432b^{2}$

or

$\Delta ={\frac {-432a^{3}}{j}}$

in terms of the j-invariant when the field characteristic is not 2 or 3 .