Affine normal forms of a complex cubic polynomial
= Affine normal forms of a complex cubic polynomial
Up to invertible affine changes in source and target, every complex cubic polynomial is exactly one of
$$
z^3,
\qquad
z\left(\frac{z^2}{3}-1\right).
$$
The extension to the <Riemann sphere> has two finite units of ramification. A single finite critical point has ramification index three and gives the first form; two distinct simple critical points can be moved to $\pm1$, after which integration gives the second.