Bean curve

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The bean curve

The bean curve is a quartic plane curve with the equation:

$x^4+x^2y^2+y^4=x(x^2+y^2) \,$

It is not the same as another curve also called the bean curve, or crooked egg curve, but both curves belong to a family of similar bean-shaped curves. The bean curve is a plane algebraic curve of genus zero. It has one singularity at the origin, an ordinary triple point, meaning with multiplicity, delta invariant and branching number all equal to three.

For every plane algebraic curve, the singularities are classified by the corresponding link invariant, which is pictured below.