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X(2), X(6), X(31), X(32), X(39), X(75), X(76), X(83), X(2276)

P1 = X(14619) = X(31)X(39) /\ X(75)X(83)

P2 = X(14620) = X(31)X(32) /\ X(75)X(76)

P3 = X(14621) = X(2)X(31) /\ X(6)X(75)

P4 = X(14622) = X(31)X(83) /\ X(39)X(75)

P5 = X(14623) = X(31)X(76) /\ X(32)X(75)

K507 is a remarkable isogonal nK cubic that contains quite a few very common centers. It is a member of the class CL061.

Its root X(14613) lies on the lines X101-X668, X110-X670, etc.

Note that if K507 contains two non-isogonal conjugate points X, Y and if X*, Y* are their isogonal conjugates then the points XY /\ X*Y* and XY* /\ X*Y are two other points on the curve.