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X(7), X(40), X(46), X(84), X(90), X(999)
X3-OAP points, see Table 53
other points below
(Peter Moses, private message 2016-09-12)
K815 is a weak cubic passing through the X3-OAP points as in Table 53.
It is spK(P, X1158) where P= X(14646) is the homothetic of X(1158) under h(X4, 4/3).
K815 contains Q1 = X(14647), the reflection of P about X(1158) and the common points of (O) with pK(X6, Q1).
The third point Q2 = X(14648) on the line X(40), X(84) also lies on the line X(109), X(3241).
Note that X(40), X(84) are the real foci of the inconic with center X(1158) hence K815 must also contain the imaginary foci on the line X(522), X(1158).
K815 contains the isogonal conjugate P* of P with SEARCH = 10.9691906660951.