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X(6), X(69), X(206), X(219), X(478), X(577), X(1249), X(2165)

A', B', C' : midpoints of ABC

K260 is a member of the class CL033 (Deléham cubics).

The nodal tangents at X(6) are parallel to the asymptotes of the Jerabek hyperbola. The tangents at A, B, C concur at X(184).

For any point Q on the Euler line, the trilinear polar of Q meets the lines KA', KB', KC' at Qa, Qb, Qc. ABC and QaQbQc are perspective and the perspector is a point on K260. This gives a simple way to find a lot of reasonably simple points on the curve.

K260 is the isogonal transform of K555, the O-isoconjugate of K257 and the X(184)-isoconjugate of the Lemoine cubic K009.

Its anticomplement is K1315.

It is also psK(X184, X2, X6) in Pseudo-Pivotal Cubics and Poristic Triangles.

K260 meets the line at infinity at the same points as a family of pK(Ω, P) with Ω on K009 and P on K1315. P is the anticomplement of the X(184)-isoconjugate of Ω.

Examples of pairs {Ω, P} : {3,69}, {4,317}, {32,193}, {56,56927}, {1147,40697}, {14376,66}, {14379,253}, etc.

K260 is the locus of poles of all pKs having the same asymptotic directions as the Orthocubic K006. The locus of the pivots is K617 and the locus of the isopivots is K009.

See K429, a very similar cubic.