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X(2), X(4), X(94), X(253), X(311), X(328), X(1141), X(3153), X(3260), X(5627), X(18815), X(52344), X(52409), X(52504), X(73145), X(73146), X(73147), X(73148), X(73149), X(73150)

Q1, Q2 on the circumcircle and on the de Longchamps axis, see Table 82

vertices of the cevian triangle of X(328)

Geometric properties :

K1457 is the isotomic transform of K499 and also its barycentric product by X(94).

Its isogonal transform is pK(X19627, X3) where X(19627) is the barycentric products X(6) x X(50) and X(1399) x X(2361).

Both cubics K499 and K1457 and also K1455, K1456 pass through Q1, Q2 on the circumcircle and on the de Longchamps axis.

Q2, Q1 are the bicentric pair PU(240) in ETC. See Table 82 for further properties.