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on both curves :

X(2), X(4), X(69)

vertices of the antimedial triangle

on K1053a :

X(616), X(621), X(628), X(2992), X(3180), X(11121), X(16770)

on K1053b :

X(617), X(622), X(627), X(2993), X(3181), X(11122), X(16771)

Geometric properties :

K1053a = pK(X2, X621) and K1053b = pK(X2, X622) are the anticomplements of K341a and K341b respectively hence they are both anharmonically equivalent to the Neuberg cubic K001. See Table 20.

K1053a and K1053b are two members of the pencil of isotomic pKs generated by the Lucas cubic K007 and the Droussent cubic K008. See Table 35.