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X(2), X(6), X(13), X(14), X(15), X(16), X(30), X(376)

other points below

Geometric properties :

K1219 is the KHO-cubic obtained when P = X(376). See K1191 for explanations and also CL075.

Its KHO-equation is : x^2 (5 y - z) - (2 y - z) (y + z) (4 y + z) = 0

K1219 meets the Kiepert hyperbola at X(2) which is quadruple and X(13), X(14).

K1219 meets the Evans conic at X(13), X(14), X(15), X(16) and two other real points Q1, Q2 on the line X(6)X(547) with KHO-coordinates (±3√6,5,7).

K1219 also contains (±2√6,5,-2), (±3√6,-2,14), (±6√6,1,8).