X(1), X(2), X(6), X(75), X(239), X(291), X(366), X(518), X(673), X(1575), X(2319), X(2669), X(3212), X(3226), X(7061), X(8301), X(9278)
isogonal conjugates of all the points of K155
tX726 = isotomic conjugate of X(726) = X(3226)
harmonic associates of X(366)
infinite points of the Steiner ellipse
A1 = - bc : b^2 : c^2 on AK, B1 and C1 similarly
A2 = - a : c : b on AX(75), B2 and C2 similarly
It meets the line at infinity at the same points as the Steiner ellipse and has only one real asymptote.
See a generalization in CL041.
K323 is the cornerstone of a group of 12 cubics all related between themselves under isogonal, isotomic, G-Hirst conjugations – denoted g, t, h in the following diagram – or a product of these such as e = gtg which is X(32)-isoconjugation. All these cubics are weak cubics and contain a good number of ETC centers.
A similar group of strong cubics is obtained when K323 is replaced with K718.