Hesse family

[gbanegas]

Hessian — x³ + y³ + 1 = 3dxy

Generalized Hessian — x³ + y³ + c = dxy

[SamFrengley]

It's probably $\epsilon$ better to call this a "Hesse family" rather than "Hessian" since that is something else (the locus of intersection with the hessian is the 3-torsion).