Fermat cubic curve
= Fermat cubic curve
{c}
{title2=$x^3+y^3+z^3=0$}
The Fermat cubic $x^3+y^3+z^3=0$ is a <smooth projective curve>: its three first partial derivatives vanish simultaneously only at the forbidden zero vector. The <genus of a smooth plane curve> formula gives genus one.
This is the degree-three case of a Fermat equation; in general $x^n+y^n+z^n=0$ defines a Fermat curve.