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∑ b^4 c^4 [3 a^4 + (b^2 - c^2)^2] x^2 ( y - z) = 0

X(2), X(3), X(6), X(182), X(3224), X(9306), X(11328), X(40799), X(40800), X(40801), X(40802), X(40803), X(40804), X(40805), X(40806), X(40807), X(40808), X(40809), X(40810), X(40811), X(40812), X(40813)

X(40800), X(40801), X(40802), X(40803), X(40804) are the isogonal conjugates of X(3168), X(6776), X(7735), X(9755), X(32545) respectively

points of pK(X2, P1) at infinity, where P1 = {X5,X264}/\{X76,X141} = isotomic conjugate of Ω, see below

points of pK(X2, P2) on the Steiner ellipse, where P2 = {X3,X3164}/\{X6,X194}, on K1179

Geometric properties :

See preamble just before X(40718) in ETC where K1179 is the (X(3),X(6))-CCC cubic. K1179 is the isogonal transform of K790 = pK(X7735, X6).

K1179 is pK(Ω, Ω) where Ω is the barycentric quotient X(32) ÷ X(7735), a point on the lines {X3, X232}, {X32, X1092} and obviously on K1179.

It follows that the tangents at A, B, C are the medians and the polar conic of X(2) is the circum-conic passing through Ω and X(i) for i in {2, 184, 232, 237, 647, etc}. This is the isogonal transform of the line passing through X(6) and X(264).

The points P1, P2, Ω are now X(40822), X(40807), X(40799) in ETC.