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X(2), X(3), X(4), X(13), X(14), X(542)

two imaginary points S1, S2 on the Kiepert hyperbola, the orthocentroidal circle, the line X(115)X(125)

other points below

See Table 59 for other similar cubics and a generalization.

K871 is a focal cubic with singular focus X(3) whose polar conic is the Lester circle. Its orthic line is the Fermat axis. See also K872.

It is the locus of contacts of the tangents drawn through X(3) to the circles passing through the Fermat points X(13), X(14).

The real asymptote is the homothetic of the Fermat axis under h(O,2), a line passing through X(542), X(1351).

The intersection with this asymptote is X = X(15356), on the lines X(2)X(2453), X(25)X(1989).

Y = X(15357) lies on the lines X(3)X(67), X(74)X(2794), X(110)X(620), X(115)X(125).