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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 8.2.4286875.1 | x8 - x7 + x5 - 2x4 - x3 + 2x2 + 2x - 1 | \( -\,5^{4}\cdot 19^{3} \) | $D_{8}$ (as 8T6) | Trivial |
| 8.2.4296211.1 | x8 - x7 + 3x5 - 4x4 + 2x3 + 2x2 - 3x + 1 | \( -\,199\cdot 21589 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4297507.1 | x8 - x7 - 2x6 + x5 + x3 + 2x2 - 1 | \( -\,2011\cdot 2137 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4364587.1 | x8 - x7 + 2x6 - 3x5 + 3x4 - 4x3 + 2x2 - 2x + 1 | \( -\,29\cdot 150503 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4386467.1 | x8 - x7 - x6 + 3x5 - x4 - 2x3 + 2x2 + x - 1 | \( -\,41\cdot 83\cdot 1289 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4421387.1 | x8 - 2x7 + 2x6 + x5 - 2x4 + x3 + x2 - 1 | \( -\,1321\cdot 3347 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4461875.1 | x8 - x7 + x6 + 2x5 - 2x4 + 2x2 - x - 1 | \( -\,5^{4}\cdot 11^{2}\cdot 59 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.4570723.1 | x8 - 2x7 + 3x6 - 3x5 + 2x3 - 4x2 + 3x - 1 | \( -\,4570723 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4584491.1 | x8 - x7 + 2x6 - 2x5 + 4x4 - 5x3 + 4x2 - 3x + 1 | \( -\,19\cdot 101\cdot 2389 \) | $S_8$ (as 8T50) | Trivial |
| 8.2.4616192.1 | x8 - 2x7 + 3x6 - 4x5 + 3x4 - 4x3 + 3x2 - 2x + 1 | \( -\,2^{12}\cdot 7^{2}\cdot 23 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.4711123.1 | x8 - x7 - x5 + 2x3 + x - 1 | \( -\,43\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.4725251.1 | x8 - 4x6 - 2x5 + 7x4 + 5x3 - 3x2 - 4x - 1 | \( -\,59\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.4960000.1 | x8 - 2x7 + 4x5 - 8x4 + 10x3 - 7x2 + 4x - 1 | \( -\,2^{8}\cdot 5^{4}\cdot 31 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.5149367.1 | x8 - x6 - x5 - x3 + x2 + x - 1 | \( -\,47\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.5365963.1 | x8 - x7 + x6 - 2x5 + 5x4 - 5x3 + 3x2 - 1 | \( -\,67\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.5365963.2 | x8 - 2x5 + x4 - x3 - 2x2 + 3x + 1 | \( -\,67\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.5369375.1 | x8 - 2x7 + 2x6 - 4x3 + 5x2 - 4x + 1 | \( -\,5^{4}\cdot 11^{2}\cdot 71 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.5756875.1 | x8 - x7 - 2x6 + 3x5 - 3x3 + 2x2 - 1 | \( -\,5^{4}\cdot 61\cdot 151 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.5781875.1 | x8 - x7 + x6 - 2x5 + x4 - 2x3 + x2 - x + 1 | \( -\,5^{4}\cdot 11\cdot 29^{2} \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.5856875.1 | x8 - x7 - x6 + 2x5 - 3x3 + x2 + x - 1 | \( -\,5^{4}\cdot 9371 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.6022411.1 | x8 - x7 + x5 + x4 + x3 - 5x2 + 4x - 1 | \( -\,19\cdot 563^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.6464099.1 | x8 - 3x7 + 3x6 + x5 - 4x4 + 5x2 - 5x + 1 | \( -\,59\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.6647387.1 | x8 + x6 - x5 - 4x4 - 4x3 - 5x2 - 4x - 1 | \( -\,83\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.6647387.2 | x8 - 2x6 - x5 + 5x4 + 7x3 + 3x2 - x - 1 | \( -\,83\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.6668032.1 | x8 + x6 - 2x5 - x4 - 2x3 + x2 + 1 | \( -\,2^{8}\cdot 7\cdot 61^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.7288099.1 | x8 - 3x7 + 4x6 + x5 - 9x4 + 13x3 - 9x2 + 4x - 1 | \( -\,7\cdot 13\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.7290287.1 | x8 - x7 - 3x6 + 4x5 + 3x4 - 4x3 - 2x2 + 1 | \( -\,23\cdot 563^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.7356875.1 | x8 - 3x7 + 6x6 - 7x5 + 5x4 - 3x3 + x2 - 2x + 1 | \( -\,5^{4}\cdot 79\cdot 149 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.7473511.1 | x8 - x7 + x6 - x5 - 2x4 + x3 - x2 + 2x + 1 | \( -\,31\cdot 491^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.7486875.1 | x8 - 2x7 - x6 + 6x5 - 2x4 - 5x3 + 3x2 + 2x - 1 | \( -\,3^{2}\cdot 5^{4}\cdot 11^{3} \) | $(C_4^2 : C_2):C_2$ (as 8T26) | Trivial |
| 8.2.8249167.1 | x8 - x6 - 3x5 - 2x4 + x3 - 3x2 - 3x - 1 | \( -\,103\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.8406875.1 | x8 - x7 + 2x6 - 2x4 + 4x3 - 5x2 + 3x - 1 | \( -\,5^{4}\cdot 13451 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.8454607.1 | x8 - x6 - 2x5 + 3x4 - 2x3 - x2 + 1 | \( -\,7^{3}\cdot 157^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.8569523.1 | x8 - 2x6 - 2x5 + x4 + 3x3 + x2 - 1 | \( -\,107\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.8655319.1 | x8 - 2x7 + x6 - x5 + 4x4 - 3x3 + x2 - x - 1 | \( -\,79\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.8906875.1 | x8 - x6 - x5 + x4 + 3x3 - 2x2 - x + 1 | \( -\,5^{4}\cdot 14251 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.9344375.1 | x8 - 3x7 + 3x6 - x5 - x4 + 3x3 - 3x2 + x - 1 | \( -\,5^{4}\cdot 14951 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.9461875.1 | x8 - x7 + x6 + x5 - x4 - x - 1 | \( -\,5^{4}\cdot 15139 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.9530591.1 | x8 + 2x6 - x4 - 2x3 - x2 + 3x - 1 | \( -\,7\cdot 17\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.9610000.1 | x8 + x6 + 3x2 - 1 | \( -\,2^{4}\cdot 5^{4}\cdot 31^{2} \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.9906875.1 | x8 - 2x7 + 2x6 + x5 - 4x4 + 7x3 - 7x2 + 4x - 1 | \( -\,5^{4}\cdot 11^{2}\cdot 131 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.9986875.1 | x8 - 2x7 + 2x6 - 3x5 + 3x4 - 3x3 + 2x2 - 2x + 1 | \( -\,5^{4}\cdot 19\cdot 29^{2} \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.10136875.1 | x8 - x7 + x6 + x5 - 4x4 + 4x3 - 3x2 + x - 1 | \( -\,5^{4}\cdot 7^{2}\cdot 331 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.10366483.1 | x8 - x7 + x6 - 3x5 + 3x4 - x3 + 2x2 - 2x - 1 | \( -\,43\cdot 491^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.10408295.1 | x8 - 3x7 + 5x6 - 4x5 + x4 + 4x3 - 6x2 + 4x - 1 | \( -\,5\cdot 19\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.10491659.1 | x8 - x7 - x6 + 4x4 - 4x3 + x - 1 | \( -\,131\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.10511875.1 | x8 - x7 + 2x6 - 3x5 + 2x4 - 3x3 + 2x - 1 | \( -\,5^{4}\cdot 11^{2}\cdot 139 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.2.10744375.1 | x8 - x7 - x6 + x5 - 2x4 + 2x3 - x2 - 2x - 1 | \( -\,5^{4}\cdot 17191 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.2.10886912.1 | x8 - 2x7 + 2x5 - 2x3 - 2x - 1 | \( -\,2^{8}\cdot 23\cdot 43^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.2.10961875.1 | x8 - 3x7 + 6x6 - 7x5 + 4x4 + x3 - 4x2 + 4x - 1 | \( -\,5^{4}\cdot 17539 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
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