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Discriminant (Elliptic Curve)

An Elliptic Curve is of the form

\begin{displaymath}
y^2=x^3+a_2x^2+a_1x+a_0.
\end{displaymath}

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

\begin{displaymath}
\Delta=k(r_1-r_2)^2(r_1-r_3)^2(r_2-r_3)^2.
\end{displaymath}

See also Frey Curve, Minimal Discriminant




© 1996-9 Eric W. Weisstein
1999-05-24