J-invariant: Difference between revisions

Revision as of 23:25, 25 February 2025

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

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

is defined to be

j={\frac {6912a^{3}}{4a^{3}+27b^{2}}}

or

j={\frac {-110592a^{3}}{\Delta }}

in terms of the elliptic discriminant Δ ^[1], or,

j={\frac {64a^{3}}{D}}

in terms of the discriminant D of the cubic polynomial $x^{2}+ax+b$ .

@@ Line 11: / Line 11: @@
 :<math>j=\frac{-110592a^3}{\Delta}</math>
-in terms of the elliptic [[discriminant]] Δ <ref>Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html</ref>.
+in terms of the elliptic [[discriminant]] Δ <ref>Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html</ref>, or,
+:<math>j=\frac{64a^3}{D}</math>
+in terms of the discriminant ''D'' of the cubic polynomial <math>x^2+ax+b</math>.