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X(3), X(4), X(64), X(182), X(1350)

infinite points of the altitudes

X6-OAP points, see Table 53

P, E see below

points of pK(X6, E) on the circumcircle

(Peter Moses, private message 2016-09-17)

K820 is an example of cubic passing through the X6-OAP points.

The intersection P = X(14927) of the lines X(4)X(182) and X(64)X(1350) lies on K820.

The abscissa in (X3, X20) of the third point E = X(14532) on the Euler line is sec2ω.

Let Q be the midpoint of X(20)E. K820 is spK(X20, Q) as in CL055 and also the column P = X20 in Table 54. These are the cubics of the pencil generated by the Darboux cubic K004 and the union of the line at infinity and the Jerabek hyperbola. This pencil also contains K376, K405, K615. See other analogous cubics in Table 58.