X(1), X(9), X(57), X(165), X(364), X(2124), X(2125), X(3062)
Foci of the Mandart ellipse (see Generalized Mandart Conics in the Downloads page and also K040)
K351 is the isogonal pK with pivot X(9), the Mittenpunkt (Lemoine point of the excentral triangle).
Its isotomic transform is pK(X76, X312).
See a generalization in CL060.