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X(2), X(253), X(287), X(671), X(1503)

foci and infinite points of the Steiner circum-ellipse

K715 is the unique circum-cubic passing through the center, the foci and the infinite points of the Steiner circum-ellipse. See the similar cubic K353 related to the Steiner in-ellipse.

K715 is a member of a pencil of K0s generated by the Lucas cubic K007 and the Ehrmann strophoid K025, also containing K347, K348.

This pencil contains two pKs (namely K007 and K347), three nK0s (K348 and two of lesser interest with roots X6189, X6190), a central cubic with center G and two other cubics with concurring asymptotes.

See K002, property 23 for a generalization and also the analogous cubic K716.