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X(6), X(69), X(193)

K707 is a central cubic with center K.

It is the locus of P such that spK(P, K) is a pivotal cubic. See CL055. Recall that spK(P, K) always contains the foci of the "ellipse K", the inconic with center K.

For example, spK(K, K) = K102 = pK(X6, X6), spK(X69, K) = K233 = pK(X25, X4), spK(X193, K) = K168 = pK(X3, X2).

K707 is anharmonically equivalent to the Orthocubic K006.

K707 is the image of the cubic K033 under the symbolic substitution SS{a -> SA}.

The symbolic substitution SS{a -> a^2} transforms K201 into K707.