ETC

X(66603) = X(5)X(1614)∩X(157)X(1656)

Barycentrics    -a^14 (b^2 + c^2) + (b^2 - c^2)^6 (b^4 + c^4) + a^12 (5 b^4 + 8 b^2 c^2 + 5 c^4) - a^2 (b^2 - c^2)^4 (5 b^6 + 2 b^4 c^2 + 2 b^2 c^4 + 5 c^6) - a^10 (11 b^6 + 16 b^4 c^2 + 16 b^2 c^4 + 11 c^6) + a^4 (b^2 - c^2)^2 (11 b^8 + 2 b^6 c^2 + 2 b^4 c^4 + 2 b^2 c^6 + 11 c^8) + a^8 (15 b^8 + 10 b^6 c^2 + 8 b^4 c^4 + 10 b^2 c^6 + 15 c^8) + a^6 (-15 b^10 + 7 b^8 c^2 + 2 b^6 c^4 + 2 b^4 c^6 + 7 b^2 c^8 - 15 c^10), a^16 - a^14 (5 b^2 + 6 c^2) + c^2 (-b^2 + c^2)^5 (b^4 + c^4) + a^12 (11 b^4 + 18 b^2 c^2 + 16 c^4) - a^10 (15 b^6 + 20 b^4 c^2 + 24 b^2 c^4 + 26 c^6) - a^2 (b^2 - c^2)^3 (b^8 - 5 b^6 c^2 - 2 b^4 c^4 - 6 c^8) + a^8 (15 b^8 + 7 b^6 c^2 + 9 b^4 c^4 + 11 b^2 c^6 + 30 c^8) + a^6 (-11 b^10 + 10 b^8 c^2 + 2 b^6 c^4 + 11 b^2 c^8 - 26 c^10) + a^4 (5 b^12 - 16 b^10 c^2 + 8 b^8 c^4 + 2 b^6 c^6 + 9 b^4 c^8 - 24 b^2 c^10 + 16 c^12), a^16 - a^14 (6 b^2 + 5 c^2) + b^2 (b^2 - c^2)^5 (b^4 + c^4) + a^12 (16 b^4 + 18 b^2 c^2 + 11 c^4) - a^10 (26 b^6 + 24 b^4 c^2 + 20 b^2 c^4 + 15 c^6) - a^2 (b^2 - c^2)^3 (6 b^8 + 2 b^4 c^4 + 5 b^2 c^6 - c^8) + a^8 (30 b^8 + 11 b^6 c^2 + 9 b^4 c^4 + 7 b^2 c^6 + 15 c^8) + a^6 (-26 b^10 + 11 b^8 c^2 + 2 b^4 c^6 + 10 b^2 c^8 - 11 c^10) + a^4 (16 b^12 - 24 b^10 c^2 + 9 b^8 c^4 + 2 b^6 c^6 + 8 b^4 c^8 - 16 b^2 c^10 + 5 c^12) : :

See Antreas Hatzipolakis, David Nguyen and Francisco Javier García Capitán, euclid 7572.

X(66603) lies on these lines: {5, 1614}, {140, 14769}, {157, 1656}, {570, 1506}, {1594, 13856}, {2165, 25738}, {6146, 15367}, {16837, 39504}, {21975, 37938}, {32551, 34826}

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X(66604) = X(4)X(94)∩X(185)X(973)

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

See Antreas Hatzipolakis, Antonio Roberto Martínez Fernández and Francisco Javier García Capitán, euclid 7573.

X(66604) lies on these lines: {3, 6403}, {4, 94}, {24, 12006}, {25, 5946}, {30, 47328}, {51, 1596}, {52, 1595}, {74, 7730}, {185, 973}, {186, 13339}, {235, 10095}, {378, 13391}, {389, 1503}, {403, 13364}, {427, 1154}, {428, 52000}, {468, 13363}, {511, 44683}, {542, 51994}, {1593, 10263}, {1594, 11591}, {1597, 3060}, {1598, 3567}, {1843, 9730}, {1906, 58533}, {3088, 6243}, {3515, 34513}, {3517, 6800}, {3520, 6152}, {3541, 6101}, {3542, 15026}, {3575, 13630}, {5094, 15067}, {5446, 13488}, {5462, 21841}, {5562, 45303}, {5876, 7507}, {5889, 61700}, {5890, 18494}, {5892, 37935}, {5943, 37942}, {6240, 11576}, {6242, 35482}, {7487, 37481}, {7505, 32205}, {7545, 16222}, {7547, 45958}, {8541, 13352}, {8705, 16836}, {8889, 23039}, {9826, 12106}, {10110, 43392}, {11411, 31810}, {11430, 44668}, {11438, 16270}, {11561, 12140}, {11808, 17855}, {12173, 13491}, {12233, 32364}, {12235, 13142}, {13321, 18535}, {13416, 18281}, {13474, 32392}, {14708, 38322}, {15037, 19128}, {15074, 37506}, {16982, 35502}, {18369, 22750}, {19124, 37478}, {23047, 45959}, {27371, 53493}, {32136, 52432}, {32142, 37119}, {35503, 55286}, {37460, 40280}, {37475, 54183}, {37933, 43584}, {39871, 63475}, {44413, 61724}, {61749, 63659}

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