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on both curves : X(2), X(3), X(4), X(13), X(14), X(15), X(16), X(17), X(18) on K1214a : N1 = X(42784), T1 = X(42647) on K1214b : N2 = X(42783), T2 = X(42648) see below |
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Geometric properties : |
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K1214a and K1214b are the nodal KHO-cubics with respective KHO-equations : √6 x (x^2 - 3 y^2 + 2 y z - z^2) +8 y (x^2 - 6 y z + 3 z^2) = 0 √6 x (x^2 - 3 y^2 + 2 y z - z^2) - 8 y (x^2 - 6 y z + 3 z^2) = 0 See K1191 for explanations and also CL075. These two cubics K1214a, K1214b meet the line through X(5), X(6) at their nodes N1, N2 and remaining points T1, T2 respectively. The KHO-coordinates of these points are : N1 = (- √6,1,1), N2 = (√6,1,1) and T1 = (4,√6,√6), T2 = (- 4,√6,√6). For each cubic, the nodal tangents pass through X(371), X(372), two points on the Brocard axis. |
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