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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 8.4.15243125.1 | x8 - x7 - 3x6 + 3x5 + 3x4 - 6x3 - 2x2 + 3x + 1 | \( 5^{4}\cdot 29^{3} \) | $C_4\wr C_2$ (as 8T17) | Trivial |
| 8.4.15297613.1 | x8 - 2x7 - x6 + 5x5 - 2x4 - 6x3 + 3x2 + 2x - 1 | \( 37\cdot 643^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.15908237.1 | x8 - x6 - x5 - 3x4 + 4x2 - 1 | \( 43\cdot 369959 \) | $S_8$ (as 8T50) | Trivial |
| 8.4.16324589.1 | x8 - 5x6 - x5 + 7x4 + 4x3 - 2x2 - 4x - 1 | \( 149\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.16374773.1 | x8 - x7 - x6 - 2x4 + 2x3 + 4x2 - x - 1 | \( 1753\cdot 9341 \) | $S_8$ (as 8T50) | Trivial |
| 8.4.16526789.1 | x8 - 3x6 - x3 + 3x2 - 1 | \( 19\cdot 607\cdot 1433 \) | $S_8$ (as 8T50) | Trivial |
| 8.4.16643125.1 | x8 - x7 - 2x6 + 2x5 - x3 + x + 1 | \( 5^{4}\cdot 31\cdot 859 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.17025973.1 | x8 - 3x7 + 2x6 + 4x5 - 8x4 + 3x3 + 3x2 - 4x + 1 | \( 67\cdot 254119 \) | $S_8$ (as 8T50) | Trivial |
| 8.4.17238125.1 | x8 - x7 - 2x6 + x5 + 3x4 - 3x3 - 3x2 + 2x + 1 | \( 5^{4}\cdot 27581 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.17318125.1 | x8 - 2x7 + x6 + 3x5 - 7x4 + 4x3 - 4x2 + 4x - 1 | \( 5^{4}\cdot 11^{2}\cdot 229 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.17383253.1 | x8 - x6 - x5 - 2x4 + x2 + 2x + 1 | \( 17383253 \) | $S_8$ (as 8T50) | Trivial |
| 8.4.18340381.1 | x8 - 4x6 - x5 + 5x4 + x3 - 4x2 + 1 | \( 229\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.18660737.1 | x8 - 3x6 - 4x5 + 5x4 + 4x3 - 3x2 + 1 | \( 233\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.19268125.1 | x8 - 2x7 + x6 + x5 - 5x4 + 4x3 + 4x2 - 2x - 1 | \( 5^{4}\cdot 30829 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.19360000.1 | x8 - 3x6 + 3x4 - 3x2 + 1 | \( 2^{8}\cdot 5^{4}\cdot 11^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | Trivial |
| 8.4.20262517.1 | x8 - 2x6 - 3x5 - x4 + 9x3 + x2 - 5x + 1 | \( 11\cdot 23\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.20268125.1 | x8 - x7 - x6 + 2x5 - 3x4 - 4x3 + x2 + 3x + 1 | \( 5^{4}\cdot 32429 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.20493125.1 | x8 - x7 + 3x5 - 3x4 + 2x2 - 2x - 1 | \( 5^{4}\cdot 32789 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.20502784.1 | x8 - x6 + 4x4 - 4x2 + 1 | \( 2^{8}\cdot 283^{2} \) | $C_2^3:S_4$ (as 8T39) | Trivial |
| 8.4.20993125.1 | x8 - x7 - 2x5 + x3 + x2 + 2x - 1 | \( 5^{4}\cdot 33589 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.21543941.1 | x8 - x7 + 2x6 - 7x5 + 4x4 - 5x3 + 6x2 + 2x - 1 | \( 269\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.21550625.1 | x8 - x7 - x6 - 2x5 + 3x4 + 4x3 - 4x2 - 2x + 1 | \( 5^{4}\cdot 29^{2}\cdot 41 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.22974464.1 | x8 - 2x7 + x6 - 4x4 + 6x3 - 6x2 + 4x - 1 | \( 2^{12}\cdot 71\cdot 79 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.23040000.1 | x8 - 2x7 - x6 - 5x4 - x2 - 2x + 1 | \( 2^{12}\cdot 3^{2}\cdot 5^{4} \) | $Q_8:C_2$ (as 8T11) | Trivial |
| 8.4.23643125.1 | x8 - 2x7 + x6 + 2x5 - 5x4 + 3x3 + x2 - 3x + 1 | \( 5^{4}\cdot 11\cdot 19\cdot 181 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.24212981.1 | x8 - x7 - 3x6 + 4x5 + 3x4 - 4x3 - 3x2 + x + 1 | \( 13\cdot 17\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.25338125.1 | x8 - 3x7 + 3x6 - x5 - 3x4 + 6x3 - 5x2 + 4x - 1 | \( 5^{4}\cdot 71\cdot 571 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.25388213.1 | x8 - 3x7 + 3x6 + 4x5 - 7x4 - 4x3 + 3x2 + 3x + 1 | \( 283^{2}\cdot 317 \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.25755625.1 | x8 - x7 + 3x5 - 5x4 + x3 + 6x2 - 3x - 1 | \( 5^{4}\cdot 7^{2}\cdot 29^{2} \) | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) | Trivial |
| 8.4.25961949.1 | x8 - 2x7 + 3x5 - 3x4 - 3x3 + 2x + 1 | \( 3^{2}\cdot 13^{4}\cdot 101 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.26277829.1 | x8 - 2x7 - x6 + 5x5 - 4x4 - 4x3 + 6x2 + x - 1 | \( 109\cdot 491^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.26393125.1 | x8 - x7 - x6 - 2x4 + 6x3 - 5x + 1 | \( 5^{4}\cdot 11^{2}\cdot 349 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.27300625.1 | x8 - 2x7 - 3x6 + 2x5 + 3x4 + 2x3 - 3x2 - 2x + 1 | \( 5^{4}\cdot 11^{2}\cdot 19^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | Trivial |
| 8.4.27496448.1 | x8 - 2x7 - 3x6 + 8x5 + 2x4 - 10x3 + 4x - 1 | \( 2^{12}\cdot 7^{2}\cdot 137 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.27905625.1 | x8 - x7 - 4x6 + 5x5 + 5x4 - 5x3 - 4x2 + x + 1 | \( 3^{2}\cdot 5^{4}\cdot 11^{2}\cdot 41 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.28047616.1 | x8 + x6 - 2x4 - 2x2 + 1 | \( 2^{8}\cdot 331^{2} \) | $C_2^3:S_4$ (as 8T39) | Trivial |
| 8.4.28157177.1 | x8 - 3x7 + 5x5 - x4 - 5x3 + 3x + 1 | \( 257\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.29043125.1 | x8 - x7 - 4x6 + 3x5 + 5x4 - 4x3 + 2x - 1 | \( 5^{4}\cdot 31\cdot 1499 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.29305625.1 | x8 - 2x7 + 4x5 - 3x4 + 3x2 - x - 1 | \( 5^{4}\cdot 46889 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.29483264.1 | x8 - 4x7 + 6x6 - 4x5 + 2x3 - 3x2 + 2x + 1 | \( 2^{8}\cdot 41\cdot 53^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.29918125.1 | x8 - x7 + x5 - 5x4 + 3x3 + 3x2 - 4x + 1 | \( 5^{4}\cdot 47869 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.30348397.1 | x8 - 3x7 + 4x6 - 5x5 + 11x3 - 12x2 + 6x - 1 | \( 277\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.30348397.2 | x8 - 2x7 - x6 + 8x5 - 8x4 - x3 + 7x2 - 6x + 1 | \( 277\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.31218125.1 | x8 - x7 - 2x4 + 5x3 - 3x + 1 | \( 5^{4}\cdot 199\cdot 251 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.31518125.1 | x8 - 2x7 + x6 + x5 - 3x4 + 2x3 - x2 - x + 1 | \( 5^{4}\cdot 211\cdot 239 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.4.31878125.1 | x8 - 3x7 + x6 + 2x5 - x4 + 2x3 + x2 - 3x + 1 | \( 5^{5}\cdot 101^{2} \) | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) | Trivial |
| 8.4.32063125.1 | x8 - 2x7 + 4x6 - 3x5 + 2x4 - x3 - 6x2 + 5x - 1 | \( 5^{4}\cdot 29^{2}\cdot 61 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.4.32115689.1 | x8 - 4x7 + 2x6 + 8x5 - 7x4 - 4x3 + 3x2 + x + 1 | \( 283^{2}\cdot 401 \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.32596021.1 | x8 - 2x6 - x5 - 2x4 - x3 + 4x2 + x - 1 | \( 17^{2}\cdot 43^{2}\cdot 61 \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.4.32756401.1 | x8 - 6x6 - 2x5 + 11x4 + 8x3 - 5x2 - 7x - 1 | \( 283^{2}\cdot 409 \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
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