Klein quartic
= Klein quartic
{c}
{wiki}
The Klein quartic has the smooth projective plane model
$$
X^3Y+Y^3Z+Z^3X=0.
$$
Its affine chart $Z=1$ is $x^3y+y^3+x=0$. If $\zeta$ is a primitive seventh root of unity, the projective transformation
$$
[X:Y:Z]\longmapsto[\zeta^3X:\zeta Y:Z]
$$
is an automorphism of order seven.