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X(6), X(25), X(69), X(111), X(2393), X(5913), X(11744), X(40228), X(40229), X(40230), X(40231), X(40232), X(40233), X(40234)

Geometric properties :

K1163 is introduced at the bottom of page K1162. It is a member of a pencil of cubics containing three pKs namely K169, K1164 = pK(X32, X6353) and K1165 = pK(X1196, X4).

K1163 is actually the only circular cubic of the pencil and its singular focus is F = X(40235) on the lines {3, 126}, {235, 1560}, {2373, 37201}, {3542, 30247}, {5656, 9968}.

All these cubics pass through A, B, C, X(6), X(25), X(69) and the three singular points Q1, Q2, Q3 of the transformation 𝛍 mentioned in page K1162.

Remark : the points labelled P1, ... , P7 are now X(40228), ... , X(40234) in ETC.