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K1209

too complicated to be written here. Click on the link to download a text file.

X(2), X(5), X(13), X(14), X(15), X(16), X(17), X(18), X(140), X(262), X(511), X(42785), X(42786), X(42787), X(42788)

further details and other points below

Geometric properties :

K1209 is another Evans cubic sharing the points X(13), X(14), X(15), X(16), X(17), X(18) with the Evans conic. It is not a KHO-curve.

Other points on the curve :

T1 = X(42786), the tangential of X(2), on the Napoleon line and on the lines {2, 1495}, {5, 3098}, {141, 547}, {156, 182}, {511, 3090}, {542, 15703}, {575, 40330}, {576, 3631}, etc.

T2 = X(42785), the tangential of X(140), on the Fermat axis and on the lines {5, 3631}, {20, 5092}, {140, 3098}, {141, 10109}, {182, 3627}, {193, 25561}, {262, 8782}, {511, 3090}, etc.

Note that the tangential of X(5) is X(511).

Q1 = X(42788) on the lines {5, 99}, {30, 1506}, {83, 549}, {140, 143}, {547, 7789}, {550, 7608}, etc.

Q2 = X(42787) on the lines {3, 147}, {5, 3098}, {30, 3096}, {32, 549}, {140, 262}, {376, 18503}, {548, 9873}, {550, 9996}, etc.

Q3 on the lines {5, 15}, {17, 262}.

Q4 on the lines {5, 16}, {18, 262}.

K1209a