J-invariant: Difference between revisions

Revision as of 16:45, 3 January 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 {-432a^{3}}{\Delta }}

in terms of the elliptic discriminant Δ ^[1].

@@ Line 5: / Line 5: @@
 is defined to be
-:<math>j=\frac{1728a^3}{4a^3+27b^2}</math>
+:<math>j=\frac{6912a^3}{4a^3+27b^2}</math>
 or
-:<math>j=\frac{-108a^3}{\Delta}</math>
+:<math>j=\frac{-432a^3}{\Delta}</math>
 in terms of the elliptic [[discriminant]] Δ <ref>Wolfram MathWorld: j-Invariant. https://mathworld.wolfram.com/j-Invariant.html</ref>.