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 locus of poles of all pKs having the same asymptotic directions as the Orthocubic K006.
See K429, a very similar cubic.