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Label Polynomial Discriminant Galois group Class group
8.0.1763584.1 x8 - 2x7 + x6 + 2x5 - 3x4 + 2x3 + x2 - 2x + 1 \( 2^{8}\cdot 83^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.3207681.1 x8 - 3x7 + 4x6 - 3x5 + 2x4 - x2 + 1 \( 3^{4}\cdot 199^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.4247721.1 x8 - 2x5 - x4 + x2 + x + 1 \( 3^{4}\cdot 229^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.4626801.1 x8 - 3x7 + 3x6 + 3x5 - 7x4 + 3x3 + 3x2 - 3x + 1 \( 3^{4}\cdot 239^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.5349969.1 x8 - x6 - 2x5 + x3 + x + 1 \( 3^{4}\cdot 257^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.5607424.1 x8 - 2x5 - 2x4 + 2x2 + 2x + 1 \( 2^{12}\cdot 37^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.5817744.1 x8 - 2x7 + 2x5 - x4 + 2x3 - 2x + 1 \( 2^{4}\cdot 3^{4}\cdot 67^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.6487209.1 x8 - 2x5 + x4 + x2 - x + 1 \( 3^{4}\cdot 283^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.7485696.1 x8 - 2x7 + 2x6 - 2x5 - 3x4 + 6x3 - 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 19^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.7573504.1 x8 - 2x7 + 2x6 + 2x4 - 6x3 + 8x2 - 4x + 1 \( 2^{12}\cdot 43^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.7634169.1 x8 - 3x7 + 5x6 - 6x5 + 5x4 - 2x2 + 1 \( 3^{4}\cdot 307^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.8346321.1 x8 + x6 - 3x3 + 4x2 - 3x + 1 \( 3^{6}\cdot 107^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.8661249.1 x8 - 3x7 + x6 + 3x5 - 3x4 + 3x3 + x2 - 3x + 1 \( 3^{6}\cdot 109^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.8667136.1 x8 - 2x7 + 2x6 + 2x5 - 4x4 + 2x3 + 2x2 - 2x + 1 \( 2^{14}\cdot 23^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.8874441.1 x8 - x7 - 3x5 + 3x4 - x3 + 2x2 - x + 1 \( 3^{4}\cdot 331^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.10909809.1 x8 - 4x7 + 6x6 - 4x5 + 2x3 + 2x2 - 3x + 1 \( 3^{4}\cdot 367^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.11029041.1 x8 - x7 - 2x6 + x5 + 5x4 + x3 - 2x2 - x + 1 \( 3^{8}\cdot 41^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.11397376.1 x8 - 2x7 + 2x6 + 3x4 - 4x3 + 2x2 + 2x + 1 \( 2^{8}\cdot 211^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.11505664.1 x8 - 2x7 + 2x6 - 2x5 + 3x4 - 2x3 + 1 \( 2^{12}\cdot 53^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.11634921.1 x8 - 3x7 + 4x6 - 3x5 - x4 + 3x3 + 2x2 - 3x + 1 \( 3^{4}\cdot 379^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.12730624.2 x8 - 2x7 + x6 + x2 + 2x + 1 \( 2^{8}\cdot 223^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.13220496.1 x8 - 3x7 + 4x6 - 3x5 + 2x4 - 3x3 + 5x2 - 6x + 4 \( 2^{4}\cdot 3^{4}\cdot 101^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.13424896.3 x8 + 2x4 + x2 + 1 \( 2^{8}\cdot 229^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.13690000.1 x8 - x7 + x6 + x2 + x + 1 \( 2^{4}\cdot 5^{4}\cdot 37^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.14070001.1 x8 - x7 - x6 + x5 + x4 + x3 - x2 - x + 1 \( 11^{4}\cdot 31^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.14220441.1 x8 - x7 + x6 - x5 - 3x4 + x3 + x2 + x + 1 \( 3^{4}\cdot 419^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.14258176.1 x8 - 2x7 + 3x4 - 2x + 1 \( 2^{12}\cdot 59^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.14258176.2 x8 - 2x7 + x6 + x4 + x2 - 2x + 1 \( 2^{12}\cdot 59^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.14561856.1 x8 - x7 + 6x6 - 3x5 + 12x4 - x3 + 11x2 + 2x + 4 \( 2^{6}\cdot 3^{4}\cdot 53^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.15241216.1 x8 - 2x5 - x4 - 2x3 + 2x2 + 2x + 1 \( 2^{12}\cdot 61^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.15610401.1 x8 + 5x6 + 11x4 + 10x2 + 1 \( 3^{4}\cdot 439^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.15745024.1 x8 - 2x7 + 4x5 - 4x3 + 4x + 2 \( 2^{14}\cdot 31^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.16908544.2 x8 - x6 + 3x4 - 2x2 + 1 \( 2^{8}\cdot 257^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.16916769.1 x8 - 2x6 - 2x5 + 5x4 + 2x3 + 3x2 - x + 1 \( 3^{4}\cdot 457^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.18122049.1 x8 - 2x7 + x6 - x5 + x3 + x2 + 2x + 1 \( 3^{4}\cdot 11^{2}\cdot 43^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.19527561.1 x8 - x7 + 2x6 - 5x5 + 5x4 - 5x3 + 8x2 - 3x + 1 \( 3^{4}\cdot 491^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.20169081.1 x8 + x4 + 3x2 - 3x + 1 \( 3^{4}\cdot 499^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.20493729.1 x8 - x7 - 2x6 + 5x5 + 3x4 - 5x3 - 2x2 + x + 1 \( 3^{4}\cdot 503^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.20502784.2 x8 - 2x4 + x2 + 1 \( 2^{8}\cdot 283^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.20647936.1 x8 - 2x7 + x6 - 2x5 + 4x4 + 2x3 + x2 + 2x + 1 \( 2^{12}\cdot 71^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.21818241.1 x8 + 2x6 + 3x4 + 5x2 + 1 \( 3^{6}\cdot 173^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.22838841.1 x8 - x7 - 5x6 + x5 + 11x4 + x3 - 5x2 - x + 1 \( 3^{8}\cdot 59^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.24255625.2 x8 + 2x6 - x5 - 2x4 + 4x3 + x2 - x + 1 \( 5^{4}\cdot 197^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.25563136.1 x8 - 2x5 - x4 + 2x3 + 2x2 + 2x + 1 \( 2^{12}\cdot 79^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.25674489.1 x8 - x7 + x5 + x4 - 3x3 + 2x2 + x + 1 \( 3^{4}\cdot 563^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.25765776.1 x8 - 2x7 + 2x6 - 2x5 + x4 + 2x3 + 2x2 + 2x + 1 \( 2^{4}\cdot 3^{6}\cdot 47^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.27489049.1 x8 - x7 - 2x6 + x5 + 3x4 + x3 - 2x2 - x + 1 \( 7^{4}\cdot 107^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.28047616.2 x8 - x6 + x4 + 3x2 + 1 \( 2^{8}\cdot 331^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.28387584.3 x8 - 2x7 + 2x6 - 2x4 + 4x3 - 4x + 4 \( 2^{8}\cdot 3^{4}\cdot 37^{2} \) $S_4\times C_2$ (as 8T24) Trivial
8.0.31719424.1 x8 - 4x5 + 8x4 - 4x3 + 1 \( 2^{18}\cdot 11^{2} \) $S_4\times C_2$ (as 8T24) Trivial

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