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X(6), X(111), X(187), X(232), X(248), X(385) O1, O2 cited in CL051 

See the notations and the general properties at CL030. See here for a family of related cubics. (Comments below by Wilson Stothers) K222 is
R* = X(110) so T(R*) is the Brocard Axis. K222 contains :
The nodal tangents are the tripolars of the intersections of C(K) and T(R*). These are the points X(1379) and X(1380). Their isoconjugates must be the intersections of T(K) and C(R). The Lemoine Axis is an asymptote of the pivotal conic as it "meets" it at R. This identifies the conic as it is an inconic of the tangential triangle with center a^2(b^2c^2)(b^2+c^23a^2) : : . Note that the centre of the pivotal conic then lies on the Lemoine Axis. 
