A self-isotomic cubic us a triangle cubic that is invariant under isotomic conjugation. The
term is commonly applied to mean a pivotal isotomic
cubic, in which points 
lying on the conic and their isotomic conjugates are collinear
with a fixed point 
known as the pivot point of the cubic.
Self-Isotomic Cubic
See also
Pivotal Isotomic Cubic, Self-Isogonal Cubic, Triangle CubicThis entry contributed by Floor van Lamoen
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References
Yff, P. "Two Families of Cubics Associated with a Triangle." In MAA Notes, No. 34. Washington, DC: Math. Assoc. Amer., 1994.Referenced on Wolfram|Alpha
Self-Isotomic CubicCite this as:
van Lamoen, Floor. "Self-Isotomic Cubic." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Self-IsotomicCubic.html