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X(30), X(98), X(468), X(523), X(868)

K217 is the nK0 with pole X(115), the center of the Kiepert hyperbola and root X(1640), intersection of the lines X(6)X(523), X(115)X(125).

K217 is a nodal cubic with node X(523) at infinity : it has two parallel asymptotes which are perpendicular to the Euler line and a third one which is parallel to the Euler line. Hence, K217 is in fact cK0(#X523, X1640), see Special Isocubics §8.