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∑ u x (y^2 - z^2) = 0

with u : v : w = X(298)

X(2), X(13), X(298), X(616)

3 (always real) mates of X(370) (blue points), see Table 10

K264a is the isotomic pK with pivot X(298), the isotomic conjugate of X(13). It belongs to the pencil of isotomic pKs generated by the Lucas cubic and the degenerated cubic which is the union of the medians of ABC. Hence, all these cubics have the same tangent, the same polar conic, the same osculating circle at G. The tangent at G is the line GK. The polar conic of G is the rectangular hyperbola homothetic of the Kiepert hyperbola under h(G,4), passing through G, X(8) and its extraversions.

K264a is the isogonal transform of pK(X32, X15).

One of the most interesting fact is that K264a contains the point X(13) and three mates of X(370), all related to equilateral triangles.

See table 10 : X(370) related curves.