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X(4), X(13), X(14), X(20), X(30), X(1294), X(3638), X(3639), X(6053)

CPCC or H-cevian (light blue) points, see Table 11

The Darboux cubic K004 and the Lucas cubic K007 generate a pencil of circum-cubics passing through H, X(20) and the four CPCC points.This pencil contains only one circular cubic which is K313. The singular focus is X(5972), the complement of X(125) = center of the Jerabek hyperbola.

K313 is the Orion cubic K(X30). See Table 11, Table 15.

K313 is also the orthopivotal cubic O(X20), see K001, property 3.

The isogonal transform of K313 is K523.