ETC

X(67263) = EULER LINE INTERCEPT OF X(141)X(18390)

Barycentrics    -2*a^10 + 12*a^2*b^2*c^2*(b^2 - c^2)^2 + 3*a^8*(b^2 + c^2) + (b^2 - c^2)^4*(b^2 + c^2) - 4*a^4*(b^2 + c^2)^3 + 2*a^6*(b^4 + c^4) : :

As a point on the Euler line, X(67263) has Shinagawa coefficients: {1/3 (2 e + f), -f}

See David Nguyen, euclid 7991.

X(67263) lies on these lines: {2, 3}, {141, 18390}, {206, 51737}, {542, 13562}, {569, 61607}, {800, 7753}, {1216, 13142}, {1353, 58891}, {1568, 37649}, {2883, 37515}, {3564, 5891}, {3589, 18388}, {3917, 16657}, {5065, 5309}, {5562, 61658}, {5650, 61744}, {5907, 18914}, {7687, 34573}, {10170, 44665}, {10605, 54012}, {10733, 59776}, {11202, 61507}, {11245, 11459}, {11430, 53415}, {11487, 12429}, {11591, 13292}, {11695, 13568}, {11793, 12241}, {12293, 33540}, {13394, 61606}, {13567, 44683}, {13570, 29317}, {13599, 54798}, {13754, 45298}, {14128, 31831}, {14216, 33537}, {15087, 63069}, {15311, 16836}, {15606, 40240}, {15740, 48672}, {15873, 46728}, {17712, 46852}, {17814, 31804}, {18358, 18474}, {18445, 26206}, {18451, 48906}, {18918, 40330}, {19139, 50979}, {23039, 34380}, {25406, 32063}, {29181, 40670}, {30308, 34657}, {34817, 45088}, {35254, 64095}, {35512, 44750}, {37506, 59553}, {37513, 51425}, {37648, 63425}, {39571, 64060}, {40448, 54922}, {41465, 62209}, {43273, 64719}, {44862, 44870}, {47354, 51756}, {50955, 63703}, {59659, 61681}, {63128, 64729}, {64100, 64730}

X(67263) = midpoint of X(i) and X(j) for these {i,j}: {4, 7667}, {3917, 16657}, {5562, 61658}, {11245, 11459}
X(67263) = reflection of X(i) in X(j) for these {i,j}: {3, 7734}, {9825, 13361}, {10127, 547}
X(67263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6816, 16072}, {2, 16072, 5}, {3, 5, 21841}, {3, 6677, 37935}, {3, 18537, 1596}, {4, 7667, 30}, {5, 140, 63667}, {5, 549, 10201}, {5, 550, 13861}, {5, 6676, 37942}, {5, 7502, 44233}, {5, 7514, 6676}, {5, 11819, 23411}, {5, 12362, 6756}, {140, 547, 34330}, {140, 18570, 16976}, {235, 7509, 16197}, {403, 7550, 7499}, {549, 10201, 6676}, {1368, 9818, 64474}, {1656, 12605, 9825}, {2043, 2044, 1598}, {5907, 64038, 18914}, {6643, 11479, 1595}, {6816, 7395, 5}, {7395, 16072, 2}, {7514, 10201, 549}, {15765, 18585, 6823}, {18586, 18587, 7401}

---