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X(3), X(76), X(3224), X(39641), X(39642) Brocard points X(39641), X(39642) are the imaginary foci of the Brocard inellipse, on the Brocard axis and the Kiepert hyperbola vertices of the first Brocard triangle, midpoints of ABC infinite points of K410 points on the Steiner ellipse and K003 points on the circumcircle and K184 

See Tucker cubics. K512 is the isogonal transform of K444. K512 is also psK(X2, X2, X3) in PseudoPivotal Cubics and Poristic Triangles. K512 is a bicentric cubic : if M = u : v : w is a point lying on K512 then the points M1 = w : u : v and M2 = v : w : u also lie on K512. This is actually true for any psK(X2, X2, M) with M ≠ X2. 
