A pivotal isotomic cubic is a self-isotomic cubic that possesses a pivot point, i.e., in which points lying on the conic and their isotomic conjugates are collinear with a fixed point known as the pivot of the cubic.

Let the trilinear coordinates of be , then has trilinear coordinates , or equivalently . If the trilinear coordinates of are , then collinearity requires

so the pivotal isotomic cubic with pivot point has a trilinear equation of the form

A pivotal isotomic cubic also passes through the triangle centroid of the reference triangle, the vertices of the anticomplementary triangle, the vertices of the reference triangle, and the vertices of the Cevian triangle of .

The following table summarizes some named pivotal isotomic cubics together with their pivot points and parameters .

triangle cubic | pivot point | Kimberling center | |

Lucas cubic | isogonal conjugate of the orthocenter |