(see Special isocubics §6). The pK with pivot P is a pK60+ if and only if P lies on the Neuberg cubic. Its pole lies on the cubic Co.
When the pivot is X(1), the pole is X(2160) = [ a/(2SA + bc) : : ] and we find K097, a member of the class CL006 of cubics. See also Table 37.
The common point of the asymptotes is X = X(14844).