X(6), X(523), X(1989), X(9178), X(14559), X(14560)
points described below.
K396 = nK(X11060, X1989, X6).
This cubic is tangent at A, B, C to the circumcircle. One of its asymptotes is the line X(2)X(523) and the two other are parallel to those of the circumconic with perspector X(32). These latter are not always real.
K396 meets its real asymptote at X = a^2(b^2-c^2) / (b^2+c^2-2a^2) : : = X(9178)
The isoconjugate of X is X* = (b^2+c^2-2a^2) / [(b^2-c^2)(4SA^2-b^2c^2)] : : = X(14559).
The isoconjugate of X(523) is Y = a^2 / [(b^2-c^2)(4SA^2-b^2c^2)] : : = X(14560).
K396 is also Kc1(X523) in CL053.