ETC

X(68177) = EULER LINE INTERCEPT OF X(76)X(3793)

Barycentrics    -6 a^4+a^2 (b^2+c^2)+b^4-6 b^2 c^2+c^4 : :

As a point on the Euler line, X(68177) has Shinagawa coefficients: {2 (E+F)^2-3 S^2,7 S^2}

See Juan José Isach Mayo, euclid 8245.

X(68177) lies on these lines: {2, 3}, {32, 63923}, {76, 3793}, {698, 5052}, {736, 15480}, {1506, 32459}, {1975, 18907}, {3053, 64093}, {3589, 7756}, {3734, 7767}, {3788, 53418}, {3933, 7737}, {3972, 5305}, {5034, 42421}, {5215, 12815}, {5475, 59545}, {5503, 60146}, {5943, 58211}, {6337, 15484}, {6390, 7745}, {6392, 21309}, {6645, 15172}, {6680, 53419}, {7747, 7789}, {7753, 59546}, {7760, 52229}, {7768, 63945}, {7783, 53489}, {7784, 43618}, {7787, 63633}, {7794, 63941}, {7804, 63548}, {7812, 32820}, {7839, 47287}, {7858, 59634}, {7863, 14537}, {15491, 15515}, {15513, 58446}, {17130, 63928}, {18501, 39141}, {18844, 60262}, {19661, 34505}, {22253, 32822}, {22331, 63955}, {30103, 65632}, {30104, 65631}, {30435, 32815}, {31664, 31665}, {32520, 61624}, {32836, 63936}, {39590, 44377}, {40894, 40895}, {53106, 60186}, {60209, 62912}

X(68177) = midpoint of X(i) and X(j) for these {i,j}: {384, 19687}, {6656, 6658}, {6661, 66328}, {19686, 66319}, {19695, 19696}
X(68177) = reflection of X(i) in X(j) for these {i,j}: {6655, 8364}, {6656, 19697}, {7819, 384}, {8357, 7819}, {19695, 66347}, {66318, 66321}, {66321, 66319}, {66326, 66318}, {66335, 6661}, {66349, 66340}
X(68177) = complement of X(19695)
X(68177) = anticomplement of X(66347)
X(68177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 19695, 66347}, {2, 19696, 19695}, {2, 33250, 548}, {3, 32981, 66391}, {4, 8361, 37350}, {4, 8369, 8361}, {4, 33181, 11318}, {4, 33201, 32954}, {5, 14035, 66409}, {20, 8362, 8354}, {20, 11286, 8362}, {140, 3552, 27088}, {382, 14001, 33184}, {384, 6655, 6661}, {384, 6656, 19697}, {384, 6658, 6656}, {384, 7819, 66318}, {384, 7924, 19692}, {384, 7948, 66317}, {384, 19686, 19687}, {384, 19688, 19677}, {384, 19691, 19702}, {384, 19693, 66319}, {384, 19696, 2}, {384, 33256, 19689}, {384, 66328, 6655}, {439, 32983, 3526}, {546, 66393, 7807}, {550, 7770, 8359}, {1003, 14035, 5}, {1656, 32979, 3363}, {3146, 7866, 66392}, {3146, 14039, 7866}, {3529, 33198, 11287}, {3530, 66412, 32992}, {3552, 8370, 140}, {3552, 14034, 8370}, {3830, 33242, 14064}, {3853, 8368, 5025},{3972, 32819, 5305}, {5025, 66408, 3853}, {5059, 32956, 5077}, {5073, 33237, 32974}, {6655, 6661, 8364}, {6655, 8364, 66335}, {6655, 19694, 6656}, {6655, 66320, 384}, {6655, 66335, 8357}, {6656, 6661, 19694}, {6656, 7819, 66343}, {6656, 19687, 6658}, {6656, 19689, 66344}, {6656, 19694, 8364}, {6656, 19697, 7819}, {6656, 66343, 66326}, {6658, 19689, 33256}, {6661, 8364, 7819}, {6661, 66319, 66320}, {7439, 21490, 19280},{7745, 7816, 6390}, {7770, 33007, 550}, {7791, 66387, 15704}, {7807, 11361, 546}, {7819, 8357, 66326}, {7819, 66321, 384}, {7819, 66335, 8364}, {7824, 8598, 33923}, {7841, 14037, 33185}, {7841, 33280, 62036}, {7887, 14068, 3845}, {7892, 33229, 8360}, {7892, 66419, 33229}, {7924, 19692, 66342}, {7924, 66342, 66346}, {7948, 19691, 66349}, {7948, 19702, 66340}, {7948, 66317, 19702}, {8356, 33257, 12103}, {8357, 66318, 7819}, {8357, 66343, 6656}, {8358, 62123, 33260}, {8360, 62026, 33229}, {8363, 33019, 66394}, {8363, 66423, 33019}, {8366, 33283, 33212}, {8367, 33923, 7824}, {11285, 33244, 8703}, {11317, 32961, 3858}, {13586, 32992, 3530}, {14031, 33007, 7770}, {14033, 32981, 3}, {14033, 33239, 32971}, {14033, 66391, 66415}, {14036, 33019, 8363}, {14036, 66423, 66394}, {14037, 33280, 7841}, {14038, 66405, 7933}, {14042, 33225, 33228}, {14042, 33228, 3861}, {14063, 33220, 33186}, {14068, 33255, 7887}, {15687, 33186, 14063}, {16044, 35297, 3628}, {16898, 33193, 33234}, {16924, 33187, 33235}, {16924, 33235, 549}, {16925, 33016, 33270}, {16925, 33270, 33233}, {19670, 66320, 19696}, {19686, 19693, 384}, {19686, 66320, 66328}, {19687, 66319, 384}, {19687, 66320, 8364}, {19687, 66321, 8357}, {19689, 33256, 6656}, {19689, 66344, 7819}, {19690, 66322, 66341}, {19690, 66341, 66334}, {19691, 66317, 7948}, {19692, 66346, 7819}, {19697, 66344, 19689}, {19702, 66340, 7819}, {19702, 66349, 7948}, {32954, 33201, 8369}, {32964, 44543, 632}, {32968, 35927, 3}, {32971, 32981, 33239}, {32971, 33239, 3}, {32975, 35287, 15720}, {32979, 32985, 1656}, {32991, 33216, 5070}, {32997, 66395, 62159}, {33016, 33233, 5}, {33018, 33246, 33249}, {33018, 33249, 5066}, {33019, 66423, 62034}, {33183, 50687, 33292}, {33185, 62036, 7841}, {33193, 33234, 62155}, {33214, 35955, 550}, {33229, 35954, 7892}, {33229, 66419, 62026}, {35954, 66419, 8360}, {37060, 38071, 32963}, {62034, 66394, 33019}, {66317, 66349, 66340}, {66320, 66328, 6661}

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