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X(3), X(4), X(13), X(14), X(30), X(265), X(1511)*

For M on the Euler line of ABC, let (H) be the rectangular circum-hyperbola through M and (L) the line passing through X(265) and the reflection of O in M.

K638 is the locus of the intersections of (H) and (L) when M traverses (E).

If X(265) is replaced by X(399), we obtain the Neuberg cubic K001.

The isogonal transform of K638 is K639.