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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 8.0.1257728.1 | x8 - 2x7 + 4x5 - 4x4 + 3x2 - 2x + 1 | \( 2^{8}\cdot 17^{3} \) | $C_4\wr C_2$ (as 8T17) | Trivial |
| 8.0.1265625.1 | x8 - x7 + x5 - x4 + x3 - x + 1 | \( 3^{4}\cdot 5^{6} \) | $C_4\times C_2$ (as 8T2) | Trivial |
| 8.0.1282789.1 | x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 3x2 - 2x + 1 | \( 1103\cdot 1163 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1327833.1 | x8 - x7 + x6 - 2x5 + 3x4 - 4x3 + 4x2 - 2x + 1 | \( 3^{4}\cdot 13^{2}\cdot 97 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.1342413.1 | x8 - x7 + x6 + x4 - 2x3 + 3x2 - 3x + 1 | \( 3^{4}\cdot 16573 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.1361513.1 | x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 2x2 - x + 1 | \( 17\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.1385533.1 | x8 - 2x7 + 3x6 - 3x5 + x4 + 1 | \( 29\cdot 47777 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1424293.1 | x8 - 2x7 + 2x6 - x5 + x4 - x3 + 2x2 - 2x + 1 | \( 13\cdot 331^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.1474013.1 | x8 - x7 + x6 - x4 + x3 - x2 + 1 | \( 617\cdot 2389 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1492101.1 | x8 - x7 + x6 - 3x5 + x4 - 2x3 + 3x2 + 1 | \( 3^{4}\cdot 13^{2}\cdot 109 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.1513728.1 | x8 - 2x7 + x6 + 2x5 - 3x4 - 2x3 + x2 + 2x + 1 | \( 2^{8}\cdot 3^{4}\cdot 73 \) | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) | Trivial |
| 8.0.1520789.1 | x8 - x7 - x6 + x4 - x2 + x + 1 | \( 29\cdot 229^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.1578125.1 | x8 - 2x7 + 3x5 - x4 - 3x3 + 2x + 1 | \( 5^{6}\cdot 101 \) | $((C_8 : C_2):C_2):C_2$ (as 8T27) | Trivial |
| 8.0.1590773.1 | x8 - x7 + 2x5 - 2x4 + x3 + x2 - 2x + 1 | \( 179\cdot 8887 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1601613.1 | x8 - 2x6 - 3x5 + 3x4 + 3x3 - 2x2 + 1 | \( 3^{6}\cdot 13^{3} \) | $C_4\wr C_2$ (as 8T17) | Trivial |
| 8.0.1740113.1 | x8 - 2x7 + 3x6 - 4x5 + 4x4 - 4x3 + 3x2 - x + 1 | \( 1740113 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1750329.1 | x8 - 3x7 + 4x6 - 3x5 + 3x4 - 3x3 + 4x2 - 3x + 1 | \( 3^{6}\cdot 7^{4} \) | $D_4$ (as 8T4) | Trivial |
| 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 |
| 8.0.1797309.1 | x8 - 3x7 + 6x6 - 8x5 + 10x4 - 9x3 + 7x2 - 4x + 1 | \( 3^{4}\cdot 22189 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.1820637.1 | x8 - x7 + x5 - x4 - 2x3 + 2x + 1 | \( 3^{4}\cdot 7\cdot 13^{2}\cdot 19 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.1867553.1 | x8 - x7 + x5 - 2x4 + x3 + x2 - x + 1 | \( 1867553 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.1890625.1 | x8 - 3x7 + 6x6 - 9x5 + 9x4 - 7x3 + 4x2 - x + 1 | \( 5^{6}\cdot 11^{2} \) | $C_2^2:C_4$ (as 8T10) | Trivial |
| 8.0.2067245.1 | x8 - x7 + x6 - x4 + x2 - x + 1 | \( 5\cdot 643^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.2105893.1 | x8 - x7 + 2x6 - x5 + x4 - x3 + x2 - 2x + 1 | \( 29\cdot 72617 \) | $S_8$ (as 8T50) | Trivial |
| 8.0.2118069.1 | x8 - x7 - x3 + 2x2 - x + 1 | \( 3^{4}\cdot 79\cdot 331 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2149173.1 | x8 - x7 - 2x6 + 2x5 + x3 + x2 - 2x + 1 | \( 3^{4}\cdot 13^{2}\cdot 157 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.2178981.1 | x8 - x7 - x6 + 2x5 + x4 - 2x3 - x2 + x + 1 | \( 3^{6}\cdot 7^{2}\cdot 61 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.2193125.1 | x8 - 2x7 + 4x6 - 5x5 + 5x4 - 5x3 + 4x2 - 2x + 1 | \( 5^{4}\cdot 11^{2}\cdot 29 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.2217213.1 | x8 - x7 - x6 - x5 + 3x4 - x + 1 | \( 3^{4}\cdot 31\cdot 883 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2313441.1 | x8 - x7 + 2x6 + 3x5 - x4 + 3x3 + 2x2 - x + 1 | \( 3^{4}\cdot 13^{4} \) | $D_4$ (as 8T4) | Trivial |
| 8.0.2314413.1 | x8 - x6 - x5 - x3 + 2x + 1 | \( 3^{4}\cdot 28573 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2477709.1 | x8 - x7 + 3x5 - x3 + 2x2 + 2x + 1 | \( 3^{4}\cdot 13^{2}\cdot 181 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.2560000.1 | x8 - 2x7 + 2x6 + 2x5 - 2x4 + 2x3 + 2x2 - 2x + 1 | \( 2^{12}\cdot 5^{4} \) | $D_4$ (as 8T4) | Trivial |
| 8.0.2671805.1 | x8 - x5 + x4 - x3 + 1 | \( 5\cdot 17^{2}\cdot 43^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.2708009.1 | x8 - x7 - x6 + x5 + x4 - x3 - x2 + x + 1 | \( 41\cdot 257^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.2712933.1 | x8 - 3x7 + 3x6 - x5 + x4 - 2x2 + x + 1 | \( 3^{4}\cdot 33493 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2824713.1 | x8 - 3x7 + 2x6 + 3x5 - 4x4 + x2 + 1 | \( 3^{4}\cdot 43\cdot 811 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2828125.1 | x8 - x7 - x6 - 2x5 + 4x4 + x3 + x2 - 3x + 1 | \( 5^{6}\cdot 181 \) | $((C_8 : C_2):C_2):C_2$ (as 8T27) | Trivial |
| 8.0.2844928.1 | x8 - 2x7 + 2x6 - 2x4 + 2x3 + x2 - 2x + 1 | \( 2^{8}\cdot 11113 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.2963293.1 | x8 - 3x7 + 5x6 - 6x5 + 7x4 - 6x3 + 5x2 - 3x + 1 | \( 37\cdot 283^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.2970513.1 | x8 - 2x7 + 2x6 - 2x5 + 3x4 - 3x2 + x + 1 | \( 3^{4}\cdot 7\cdot 13^{2}\cdot 31 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | Trivial |
| 8.0.2985984.1 | x8 - 2x7 + 2x6 - 2x5 + 7x4 - 10x3 + 8x2 - 4x + 1 | \( 2^{12}\cdot 3^{6} \) | $D_4$ (as 8T4) | Trivial |
| 8.0.3057993.1 | x8 - 2x7 + 3x6 - 2x5 + x3 + 2x2 - 3x + 1 | \( 3^{4}\cdot 19\cdot 1987 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.3134053.1 | x8 - x7 + x6 - 2x5 + 3x4 - 2x3 + x2 - x + 1 | \( 13\cdot 491^{2} \) | $C_2 \wr S_4$ (as 8T44) | Trivial |
| 8.0.3167829.1 | x8 - 3x7 + 4x6 - 4x4 + 3x3 + 2x2 - 3x + 1 | \( 3^{4}\cdot 7\cdot 37\cdot 151 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.3198933.1 | x8 - x7 - x6 + 4x4 - x3 - 3x2 + x + 1 | \( 3^{4}\cdot 73\cdot 541 \) | $S_4\wr C_2$ (as 8T47) | Trivial |
| 8.0.3203125.1 | x8 - x7 + 2x6 + 2x5 + 3x3 + 2x2 + x + 1 | \( 5^{7}\cdot 41 \) | $((C_8 : C_2):C_2):C_2$ (as 8T27) | 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 |
| 8.0.3211264.1 | x8 - 4x7 + 8x6 - 8x5 + 7x4 - 8x3 + 8x2 - 4x + 1 | \( 2^{16}\cdot 7^{2} \) | $D_4\times C_2$ (as 8T9) | Trivial |
| 8.0.3240000.1 | x8 - 3x7 + 3x6 + x5 - 2x4 - 3x3 + 7x2 - 4x + 1 | \( 2^{6}\cdot 3^{4}\cdot 5^{4} \) | $Q_8:C_2$ (as 8T11) | Trivial |
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