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Label Polynomial Discriminant Galois group Class group
8.4.54828125.1 x8 - 3x7 + 2x5 + 4x4 + 3x3 - 10x2 + 3x + 1 \( 5^{6}\cdot 11^{2}\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.60765625.1 x8 - x7 + x5 - x4 + 6x3 - 5x2 - x + 1 \( 5^{6}\cdot 3889 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.70140625.1 x8 - 2x6 - x4 - 3x2 + 1 \( 5^{6}\cdot 67^{2} \) $S_4\times C_2$ (as 8T24) trivial
8.4.80453125.1 x8 - 2x7 + x6 - x5 - x4 + 2x3 - x2 + x + 1 \( 5^{6}\cdot 19\cdot 271 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.81000000.1 x8 - 3x7 + 6x6 - 9x5 + 14x4 - 27x3 + 39x2 - 36x + 16 \( 2^{6}\cdot 3^{4}\cdot 5^{6} \) $D_4\times C_2$ (as 8T9) $[2]$
8.4.106703125.1 x8 - 3x7 + x6 + 6x5 - 11x4 + 8x3 - x2 - x + 1 \( 5^{6}\cdot 6829 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.107750000.1 x8 - 2x7 + 6x6 - 6x5 + 9x4 - 8x3 + 4x2 - 4x + 1 \( -\,2^{4}\cdot 5^{6}\cdot 431 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.109234375.1 x8 + 2x6 - 5x5 + 4x4 - 10x3 + 3x2 - 5x + 1 \( -\,5^{6}\cdot 6991 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.111390625.1 x8 - x7 - x6 - 2x5 + 4x4 + x3 - 4x2 + 2x + 1 \( 5^{6}\cdot 7129 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.124000000.2 x8 - 4x7 + 9x6 - 8x5 - x4 + 14x3 - 14x2 + 8x - 4 \( -\,2^{8}\cdot 5^{6}\cdot 31 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.132250000.1 x8 - x7 + x5 - 6x4 + x3 - x + 1 \( 2^{4}\cdot 5^{6}\cdot 23^{2} \) $S_4\times C_2$ (as 8T24) trivial
8.2.134234375.1 x8 - x7 + 4x6 - 2x5 - x4 - 4x3 - 4x2 - 3x - 9 \( -\,5^{6}\cdot 11^{2}\cdot 71 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.6.144546875.1 x8 - 3x7 + x6 + 6x5 - 11x4 + 3x3 + 9x2 - 6x + 1 \( -\,5^{6}\cdot 11\cdot 29^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.151000000.1 x8 - 3x7 + 5x6 - 3x5 - 6x4 + 13x3 - 5x2 - 2x + 1 \( 2^{6}\cdot 5^{6}\cdot 151 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.155140625.1 x8 - 3x7 + 7x5 - 6x4 - 2x3 - 2x + 1 \( 5^{6}\cdot 9929 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.157984375.1 x8 - 2x7 + 3x5 - x4 + 2x3 - 5x2 + 2x + 1 \( -\,5^{6}\cdot 10111 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.165765625.1 x8 - 3x6 + 9x4 - 7x2 + 1 \( 5^{6}\cdot 103^{2} \) $S_4\times C_2$ (as 8T24) trivial
8.6.168296875.1 x8 - 2x7 - 4x6 + 9x5 + 4x4 - 13x3 - x2 + 6x + 1 \( -\,5^{6}\cdot 10771 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.177015625.1 x8 - x7 - x6 + 3x5 - x4 + x3 - 4x2 - 3x + 1 \( 5^{6}\cdot 11329 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.182250000.1 x8 - 3x7 + x6 + 6x5 - 6x4 - 12x3 + 4x2 + 24x + 16 \( 2^{4}\cdot 3^{6}\cdot 5^{6} \) $D_4\times C_2$ (as 8T9) $[2]$
8.4.186078125.1 x8 - x7 + 6x5 - 11x4 + 11x3 - 5x2 - x + 1 \( 5^{6}\cdot 11909 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.191703125.1 x8 - 3x7 + 6x6 - 9x5 + 4x4 + 8x3 - 6x2 - x + 1 \( 5^{6}\cdot 12269 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.196000000.1 x8 - 2x7 - 2x5 + 9x4 + 2x3 - 10x2 + 2x + 1 \( 2^{8}\cdot 5^{6}\cdot 7^{2} \) $S_4\times C_2$ (as 8T24) trivial
8.2.199234375.1 x8 - 3x7 + 7x5 - x4 - 12x3 + 5x2 + 8x - 4 \( -\,5^{6}\cdot 41\cdot 311 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.213890625.1 x8 - x7 + 10x6 - 9x5 + 34x4 - 29x3 + 45x2 - 36x + 16 \( 3^{4}\cdot 5^{6}\cdot 13^{2} \) $Q_8:C_2$ (as 8T11) $[2]$
8.4.220765625.1 x8 - 2x7 - 2x5 + 4x4 + 2x3 - 3x + 1 \( 5^{6}\cdot 71\cdot 199 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.223578125.1 x8 - 3x7 + x6 + x5 + 4x4 - 7x3 + 9x2 - 6x + 1 \( 5^{6}\cdot 41\cdot 349 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.232671875.1 x8 + 3x6 - 5x5 + 4x4 - 5x3 + 7x2 - 5x + 1 \( -\,5^{6}\cdot 14891 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.239828125.1 x8 - 3x7 + 5x6 - 3x5 - x4 + 8x3 - 5x2 - 2x + 1 \( 5^{6}\cdot 15349 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.240250000.1 x8 - 3x7 + 7x5 - 6x4 + 3x3 - 5x2 + 8x - 4 \( -\,2^{4}\cdot 5^{6}\cdot 31^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.245796875.1 x8 - x7 - x6 + 3x5 - 6x4 + 11x3 - 9x2 + 2x + 1 \( -\,5^{6}\cdot 15731 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.247328125.1 x8 - 2x7 + x6 - 6x5 + 4x4 + 7x3 - x2 - 4x + 1 \( 5^{6}\cdot 11\cdot 1439 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.247359375.1 x8 - 3x7 + 6x6 - 9x5 + 14x4 - 12x3 + 9x2 - 6x + 1 \( -\,3^{2}\cdot 5^{6}\cdot 1759 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.247671875.1 x8 - 3x7 + x6 + 6x5 + 4x4 + 3x3 - 11x2 - 21x - 9 \( -\,5^{6}\cdot 11^{2}\cdot 131 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.257750000.2 x8 - 3x7 + x6 + 6x5 - 6x4 - 2x3 + 4x2 + 4x - 4 \( -\,2^{4}\cdot 5^{6}\cdot 1031 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.269859375.1 x8 - 3x7 + 5x6 - 8x5 + 9x4 - 7x3 + 10x2 - 17x + 11 \( -\,3^{2}\cdot 5^{6}\cdot 19\cdot 101 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.274515625.1 x8 - x7 + x5 - 6x4 - 14x3 - 5x2 + 4x + 1 \( 5^{6}\cdot 17569 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.281000000.1 x8 - 2x7 + 3x5 - 6x4 + 2x3 - 3x + 1 \( 2^{6}\cdot 5^{6}\cdot 281 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.284000000.1 x8 - 2x7 - 4x6 + 4x5 + 9x4 + 12x3 - 16x2 - 14x - 19 \( -\,2^{8}\cdot 5^{6}\cdot 71 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.285484375.1 x8 - x7 + 5x6 - 4x5 - x4 + 6x3 - 20x2 - 6x - 9 \( -\,5^{6}\cdot 11^{2}\cdot 151 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.289828125.1 x8 - x7 - 4x5 - x4 + 16x3 + 10x2 - 51x + 31 \( 3^{4}\cdot 5^{6}\cdot 229 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$
8.4.292953125.1 x8 - 3x7 + x6 + x5 - x4 + 3x3 + 4x2 + 4x + 1 \( 5^{6}\cdot 18749 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.299515625.1 x8 - 2x6 - 6x4 - 5x3 + 2x2 + 5x + 1 \( 5^{6}\cdot 29\cdot 661 \) $S_4\wr C_2$ (as 8T47) trivial
8.6.304234375.1 x8 - x7 - 6x6 + 3x5 + 14x4 - 4x3 - 9x2 + 2x + 1 \( -\,5^{6}\cdot 19471 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.320171875.1 x8 - x7 - 5x6 + 11x5 - x4 - 9x3 + 4x + 1 \( -\,5^{6}\cdot 31\cdot 661 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.323296875.1 x8 - x7 + x5 - 11x4 - 4x3 - 36x - 29 \( -\,3^{2}\cdot 5^{6}\cdot 11^{2}\cdot 19 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.323296875.2 x8 - 4x7 + 7x6 - 7x5 + 5x4 - 3x3 - 8x2 + 9x - 19 \( -\,3^{2}\cdot 5^{6}\cdot 11^{2}\cdot 19 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.4.327953125.2 x8 - 2x7 + x6 + 4x5 - 6x4 - 3x3 - x2 + 6x + 1 \( 5^{6}\cdot 139\cdot 151 \) $S_4\wr C_2$ (as 8T47) trivial
8.4.329750000.1 x8 - 2x7 - 4x6 + 9x5 + 4x4 - 8x3 - 6x2 + x + 1 \( 2^{4}\cdot 5^{6}\cdot 1319 \) $S_4\wr C_2$ (as 8T47) trivial
8.2.330250000.1 x8 - 2x7 + 5x6 - 7x5 + 4x4 + 7x3 - 5x2 - 3x + 1 \( -\,2^{4}\cdot 5^{6}\cdot 1321 \) $S_4\wr C_2$ (as 8T47) trivial
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