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Label Polynomial Discriminant Galois group Class group
8.0.111411200.2 x8 - 4x6 + 6x4 - 12x2 + 17 \( 2^{18}\cdot 5^{2}\cdot 17 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.337903616.2 x8 - 2x6 - 8x5 + 12x3 + 16x2 + 8x + 2 \( 2^{18}\cdot 1289 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.398721024.1 x8 - 4x6 + 14x4 - 12x2 + 9 \( 2^{18}\cdot 3^{2}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.425984000.4 x8 + 2x6 - 12x5 - 4x4 - 20x3 + 36x2 + 24x + 58 \( 2^{18}\cdot 5^{3}\cdot 13 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.478412800.1 x8 - 2x6 - 8x5 + 28x4 - 28x3 + 34x2 - 36x + 13 \( 2^{18}\cdot 5^{2}\cdot 73 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.478412800.2 x8 - 4x7 + 6x6 - 4x5 + 4x4 - 4x3 + 4x2 + 2 \( 2^{18}\cdot 5^{2}\cdot 73 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.528744448.2 x8 - 2x6 - 8x5 + 8x4 + 4x3 + 8x2 - 8x + 2 \( 2^{18}\cdot 2017 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.583270400.1 x8 - 4x7 + 6x6 + 12x4 - 44x3 + 24x2 + 10 \( 2^{18}\cdot 5^{2}\cdot 89 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.583270400.2 x8 - 6x4 - 32x2 + 89 \( 2^{18}\cdot 5^{2}\cdot 89 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.591659008.2 x8 - 4x7 + 10x6 - 12x5 + 8x4 + 4x3 - 4x2 + 2 \( 2^{18}\cdot 37\cdot 61 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.635699200.2 x8 - 2x6 - 8x5 - 20x4 + 4x3 + 74x2 + 92x + 37 \( 2^{18}\cdot 5^{2}\cdot 97 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.736362496.3 x8 - 4x7 + 6x6 - 8x4 + 8x3 - 2x2 - 4x + 5 \( 2^{18}\cdot 53^{2} \) $V_4^2:(S_3\times C_2)$ (as 8T41) trivial
8.0.792985600.1 x8 + 6x6 - 12x5 + 8x4 - 52x3 + 38x2 - 32x + 101 \( 2^{18}\cdot 5^{2}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.950272000.5 x8 - 10x6 - 4x5 + 32x4 + 4x3 - 28x2 + 48x + 58 \( 2^{18}\cdot 5^{3}\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.975437824.3 x8 + 6x6 - 4x5 + 8x4 - 12x3 + 6x2 - 8x + 5 \( 2^{18}\cdot 61^{2} \) $V_4^2:(S_3\times C_2)$ (as 8T41) trivial
8.0.979632128.1 x8 - 4x7 + 14x6 - 28x5 + 44x4 - 44x3 + 28x2 - 8x + 2 \( 2^{18}\cdot 37\cdot 101 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.994312192.2 x8 - 8x5 + 4x4 + 16x3 + 40x2 + 16x + 4 \( 2^{18}\cdot 3793 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.1189347328.1 x8 + 2x6 - 8x5 - 4x4 - 12x3 + 16x2 + 16x + 26 \( 2^{18}\cdot 13\cdot 349 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.1264844800.2 x8 - 8x6 + 34x4 - 104x2 + 193 \( 2^{18}\cdot 5^{2}\cdot 193 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.1327759360.3 x8 - 2x6 - 8x5 - 4x4 + 12x3 + 18x2 + 12x + 5 \( 2^{18}\cdot 5\cdot 1013 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.1526988800.3 x8 - 4x7 + 10x6 - 16x4 + 36x3 + 48x2 - 40x + 50 \( 2^{18}\cdot 5^{2}\cdot 233 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.1736704000.4 x8 + 2x6 - 16x5 - 4x4 - 20x3 + 86x2 + 84x + 157 \( 2^{18}\cdot 5^{3}\cdot 53 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2248409088.2 x8 - 4x7 + 10x6 - 8x5 + 12x3 + 2 \( 2^{18}\cdot 3^{2}\cdot 953 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2284060672.1 x8 - 4x6 - 8x5 + 18x4 + 16x3 - 4x2 - 40x + 25 \( 2^{18}\cdot 8713 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2365849600.1 x8 - 4x7 + 6x6 - 8x4 + 24x3 + 78x2 + 92x + 37 \( 2^{18}\cdot 5^{2}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.2470707200.3 x8 - 4x7 + 6x6 + 8x5 - 12x4 + 4x3 + 88x2 + 96x + 34 \( 2^{18}\cdot 5^{2}\cdot 13\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2470707200.9 x8 - 4x7 + 18x6 - 32x5 + 80x4 - 56x3 + 114x2 - 28x + 53 \( 2^{18}\cdot 5^{2}\cdot 13\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2627993600.1 x8 - 4x7 + 10x6 - 16x5 + 16x4 + 40x3 - 94x2 + 52x + 173 \( 2^{18}\cdot 5^{2}\cdot 401 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2627993600.2 x8 - 4x7 - 2x6 + 4x5 + 52x4 - 28x3 - 68x2 - 104x + 178 \( 2^{18}\cdot 5^{2}\cdot 401 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2785280000.5 x8 - 6x6 + 12x4 - 20x3 + 126x2 - 300x + 221 \( 2^{18}\cdot 5^{4}\cdot 17 \) $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.2837708800.5 x8 - 4x7 + 14x6 - 12x5 + 12x4 + 32x3 + 50x2 - 32x + 101 \( 2^{18}\cdot 5^{2}\cdot 433 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2879651840.4 x8 + 10x6 - 12x5 + 40x4 - 44x3 + 42x2 - 24x + 5 \( 2^{18}\cdot 5\cdot 13^{3} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.2885943296.2 x8 - 4x7 + 6x6 - 4x4 - 4x3 + 8x2 + 8x + 2 \( 2^{18}\cdot 101\cdot 109 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2906914816.1 x8 + 2x6 - 8x5 + 12x4 - 4x3 + 8x2 - 8x + 2 \( 2^{18}\cdot 13\cdot 853 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2913206272.1 x8 - 4x7 + 2x6 + 4x5 + 4x3 + 4x2 + 2 \( 2^{18}\cdot 11113 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2913206272.2 x8 + 2x6 - 8x5 + 4x4 - 4x3 + 6x2 - 4x + 5 \( 2^{18}\cdot 11113 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2925789184.2 x8 - 4x7 + 2x6 + 4x5 + 8x4 - 20x3 + 20x2 - 40x + 34 \( 2^{18}\cdot 11161 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.2942566400.2 x8 - 4x7 + 14x6 - 24x5 + 32x4 - 24x3 + 14x2 - 12x + 5 \( 2^{18}\cdot 5^{2}\cdot 449 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.3152281600.3 x8 + 14x6 - 16x5 + 80x4 - 68x3 + 168x2 - 80x + 130 \( 2^{18}\cdot 5^{2}\cdot 13\cdot 37 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.3152281600.4 x8 - 14x6 - 8x5 + 52x4 + 28x3 - 16x2 + 200x + 250 \( 2^{18}\cdot 5^{2}\cdot 13\cdot 37 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.3229876224.1 x8 + 4x4 - 24x2 + 36 \( 2^{18}\cdot 3^{2}\cdot 37^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.3234070528.1 x8 - 4x7 + 2x6 - 8x5 + 24x4 + 16x3 + 34x2 + 12x + 5 \( 2^{18}\cdot 13^{2}\cdot 73 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.3309568000.2 x8 - 6x6 - 12x4 - 52x3 + 88x2 + 296x + 178 \( 2^{18}\cdot 5^{3}\cdot 101 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.3747872768.1 x8 - 8x6 + 36x4 - 72x2 + 68 \( 2^{18}\cdot 17\cdot 29^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.3942907904.2 x8 - 4x6 + 30x4 - 76x2 + 89 \( 2^{18}\cdot 13^{2}\cdot 89 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.4043571200.1 x8 + 6x6 - 20x5 - 84x3 + 108x2 + 80x + 370 \( 2^{18}\cdot 5^{2}\cdot 617 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.4297326592.1 x8 + 10x6 - 12x5 + 36x4 - 68x3 + 92x2 - 96x + 90 \( 2^{18}\cdot 13^{2}\cdot 97 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.4410572800.1 x8 - 4x7 + 14x6 - 16x5 + 52x4 + 20x3 + 128x2 + 48x + 74 \( 2^{18}\cdot 5^{2}\cdot 673 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.5511577600.4 x8 - 4x6 - 2x4 + 20x2 + 25 \( 2^{18}\cdot 5^{2}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.5511577600.11 x8 - 10x6 - 16x5 + 28x4 + 68x3 + 66x2 + 28x + 5 \( 2^{18}\cdot 5^{2}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
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