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X(2), X(6), X(13), X(14), X(30), X(3070), X(3071), X(41107), X(41108)

Geometric properties :

K1198 is a KHO-cubic. See K1191 for explanations and also CL075. See K1197, K1199, other Cullen cubics.

Its KHO-equation is : x^2 (2y + 5z) - 3 (2y - z) (y + z)^2 = 0.

The KHO-equation of its Hessian is : x^2 (10y + 7z) - 3 (2y + 5z) (y + z)^2 = 0, an analogous cubic passing through X(6), X(13), X(14), X(30), X(3543), X(41945), X(41946). The last two remaining points on the Evans conic lie on the line X(6)X(1657) and their KHO-coordinates are (±√33, 2, -3).

K1198 is an acnodal cubic with an isolated point X(30) at infinity. The tangents at X(30) are imaginary and meet the Brocard axis at the imaginary foci of the Brocard inellipse. These foci also lie on the Kiepert hyperbola and their KHO-coordinates are (±i √3, 0, 1).

X(6), X(13), X(14) are three points of inflexion on K1198.

The inflexional tangent at X(6) meets the Euler line (which is the harmonic polar) at X(3543).

The inflexional tangents at X(13), X(14) concur at X(549) on the Euler line. They are the tangents at X(13), X(14) to the Evans conic. The harmonic polars are the parallels at X(62), X(61) respectively to the Euler line.