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X(2), X(3), X(4), X(64), X(154), X(3424), X(5373) infinite points of the altitudes of ABC points of the Thomson cubic K002 on the circumcircle i.e. vertices of the Thomson triangle excenters of the Thomson triangle, the incenter being X(5373). Note that their reflections about O lie on the Stammler hyperbola 

K615 is the Thomson cubic's sister. See the related K376, K405 and K763 and other analogous cubics in Table 58. K615 is the isogonal transform of the Antreas cubic K047. It is the pivotal isogonal cubic with pivot H with respect to the Thomson triangle T. It is therefore invariant under isogonal conjugation with respect to T. Hence, it is a member of the Euler pencil of cubics in T also containing K078, the McCay cubic of T, and K764, the Darboux cubic of T. The tangents to K615 at the vertices of the Thomson triangle concur at X(154). K615 belongs to the pencils generated : 
