Plane model y plus x cubed plus xy cubed equals zero of the Klein quartic
= Plane model y plus x cubed plus xy cubed equals zero of the Klein quartic
{title2=$y+x^3+xy^3=0$}
The <projective completion> of
$$
y+x^3+xy^3=0
$$
is the <smooth plane quartic>
$$
X^3Z+XY^3+YZ^3=0.
$$
The coordinate relabelling $[A:B:C]=[Y:X:Z]$ turns this equation into the standard <Klein quartic> equation $A^3B+B^3C+C^3A=0$.