 Plane model y plus x cubed plus xy cubed equals zero of the Klein quartic

ID: plane-model-y-plus-x-cubed-plus-xy-cubed-equals-zero-of-the-klein-quartic

y + x^{3} + x y^{3} = 0

X^{3} Z + X Y^{3} + Y Z^{3} = 0.

The coordinate relabelling

[A : B : C] = [Y : X : Z]

turns this equation into the standard Klein quartic equation

A^{3} B + B^{3} C + C^{3} A = 0

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