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X(1), X(2), X(87), X(192), X(366)

Given an isoconjugation with pole W = (p : q :r) swapping M and M*, the locus of M such that the trilinear polars of M and M* are parallel is the pivotal isocubic whose pivot is the pole W. It always contains the centroid G and the tangents at A, B, C are the medians. See Special Isocubics ยง1.4.2. The points at infinity of pK(W,W) are those of the isotomic pK with pivot W' isotomic conjugate of W. All these cubics form the CL007 class of cubics.

The simplest is K101 = pK(X1, X1).

Its isogonal transform is pK(X31, X6) and its isotomic transform is pK(X75, X2).

See also Table 37.