Trident curve

From Wikipedia, the free encyclopedia

In mathematics, Trident curve is the name for a family of curves that have the formula:

xy + ax³ + bx² + cx = d

Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x=0, y=∞, z=0; if we substitute x=x/z and y=1/z into the equation of the trident curve, we get

ax³ + bx²z + cxz² + xz = dz³,

which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus one.