J-invariant

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

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

is defined to be

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j=\frac{6912a^3}{4a^3+27b^2}}

or

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j=\frac{-432a^3}{\Delta}}

in terms of the elliptic discriminant Δ .