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K631

∑ (b+c-a) x^2 (c^2 y - b^2 z) = 0

or

∑ a^2 [(c+a-b)y - (a+b-c)z] yz = 0

X(6), X(7), X(509), X(1486)

A'B'C' = cevian triangle of X(7)

K631 is the only Poncelet poristic cubic which is a pivotal cubic namely pK(X56, X7). See Pseudo-Pivotal Cubics and Poristic Triangles, §2.3.

See the related cubics K360, K577, K578.