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X(15), X(16), X(511), X(842)

K641 is the locus of M such that the Euler line of the pedal triangle of M is parallel to the Fermat line X(13)X(14).

K641 is a circular cubic with focus X(23), the isogonal conjugate of G. The polar conic of X(23) is the degenerate circle which is the union of the line at infinity and another line passing through X(187) hence K641 is a K+.

The isogonal transform of K641 is the orthopivotal cubic O(X542). See Orthopivotal Cubics.

K641 belongs to the pencil of cubics generated by K148 and K292 that also contains K640.