Discriminant: Difference between revisions

Revision as of 16:47, 3 January 2025

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 ^[1].

@@ Line 7: / Line 7: @@
 :<math>\Delta = -64a^3-432b^2</math>
-when the field characteristic is not 2 or 3 <ref>Wolfram MathWorld: Elliptic Discriminant. https://mathworld.wolfram.com/EllipticDiscriminant.html</ref>.
+or
+:<math>\Delta = \frac{-432a^3}j</math>
+in terms of the [[j-invariant]] when the field characteristic is not 2 or 3 <ref>Wolfram MathWorld: Elliptic Discriminant. https://mathworld.wolfram.com/EllipticDiscriminant.html</ref>.