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 |  |  |
