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X(2), X(13), X(14), X(51), X(476), X(618), X(619) T = X(3258) = complement of X(476) (2SA + bc + ca + ab)/(2SA+ bc) : : feet U, V, W of the trilinear polar of X(1989) 

Q004 is the locus of the common points of the asymptotes of all pK60+. See Special Isocubics §6.7 and CL006. It is a bicircular quartic with singular focus G, which is at the same time a flex on the curve. The tangent at G is the line GX(51). The tangents at X(13), X(14), X(476) pass through G, these four points lying on the circle (C') which also contains the Parry point X(111). This circle is tangent at G to the Euler line. (C) is the circle centered at G passing through X(51). (C) is tangent at X(51) to the trilinear polar of X(1989). The inversive image of Q004 in (C) is the circular cubic Q005 (denoted by (k) in Special Isocubics §6.7) 
