Discriminant (Elliptic Curve)

An Elliptic Curve is of the form

$$y^2=x^3+a_2x^2+a_1x+a_0.$$

Let the Roots of $y^2$ be $r_1$, $r_2$, and $r_3$. The discriminant is then defined as

$$\Delta=k(r_1-r_2)^2(r_1-r_3)^2(r_2-r_3)^2.$$

See also Frey Curve, Minimal Discriminant