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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 8.0.64000000.3 | x8 - 4x7 + 8x6 - 10x5 + 11x4 - 10x3 + 2x2 + 2x + 1 | \( 2^{12}\cdot 5^{6} \) | $D_4$ (as 8T4) | $[2]$ |
| 8.0.76488065.1 | x8 - 4x7 + 8x6 - 10x5 + 7x4 - 2x3 + x2 - x + 1 | \( 5\cdot 37\cdot 643^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 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) | $[2]$ |
| 8.0.81450625.1 | x8 - x7 + 8x6 + 7x5 + 19x4 + 7x3 + 8x2 - x + 1 | \( 5^{4}\cdot 19^{4} \) | $D_4$ (as 8T4) | $[2]$ |
| 8.0.93000677.1 | x8 - 3x7 + 4x6 - 3x5 + 5x4 - 7x3 + 7x2 - 4x + 1 | \( 7^{3}\cdot 11\cdot 157^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.96059601.1 | x8 - x7 - 2x6 - 5x5 + 11x4 + x3 + 4x2 - x + 1 | \( 3^{8}\cdot 11^{4} \) | $S_4$ (as 8T14) | $[2]$ |
| 8.0.97831881.1 | x8 - 2x7 + x6 - 2x5 + 6x4 - 13x3 + 16x2 - 7x + 1 | \( 3^{4}\cdot 7^{2}\cdot 157^{2} \) | $A_4\wr C_2$ (as 8T42) | $[2]$ |
| 8.0.100618240.2 | x8 - 2x7 + 8x6 - 4x5 + 13x4 + 8x3 + 10x2 + 6x + 1 | \( 2^{12}\cdot 5\cdot 17^{3} \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.101875968.1 | x8 - 2x7 + 4x6 - 8x4 + 8x3 + 15x2 + 6x + 1 | \( 2^{8}\cdot 3^{4}\cdot 17^{3} \) | $C_4\wr C_2$ (as 8T17) | $[2]$ |
| 8.0.102468645.1 | x8 - 2x7 + 3x6 - 3x5 + 4x4 + 3x2 + 2x + 1 | \( 3^{4}\cdot 5\cdot 503^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.104934441.1 | x8 - 3x7 + 4x6 - 10x5 + 21x4 - 20x3 + 20x2 - 27x + 15 | \( 3\cdot 23\cdot 29\cdot 229^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.106172416.1 | x8 - 2x7 + 3x6 - 2x5 + 8x4 + 2x3 + 3x2 + 2x + 1 | \( 2^{12}\cdot 7^{2}\cdot 23^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.106770069.1 | x8 - 2x7 + 7x5 - 11x4 - 3x3 + 30x2 - 42x + 21 | \( 3^{6}\cdot 7^{4}\cdot 61 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.110502144.1 | x8 - 4x7 + 11x6 - 14x5 + 7x4 + 18x3 - 18x2 - 36x + 36 | \( 2^{8}\cdot 3^{4}\cdot 73^{2} \) | $D_4\times C_2$ (as 8T9) | $[2]$ |
| 8.0.110502144.2 | x8 - 9x6 + 29x4 - 36x2 + 16 | \( 2^{8}\cdot 3^{4}\cdot 73^{2} \) | $D_4\times C_2$ (as 8T9) | $[2]$ |
| 8.0.110502144.3 | x8 + x6 - 8x5 - 4x4 - 4x3 + 21x2 + 20x + 25 | \( 2^{8}\cdot 3^{4}\cdot 73^{2} \) | $D_4\times C_2$ (as 8T9) | $[2]$ |
| 8.0.111017597.1 | x8 - 5x6 - 2x5 + 12x4 + 5x3 - 9x2 - 10x + 9 | \( 29\cdot 73\cdot 229^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.112021056.1 | x8 - x7 - x6 - 7x5 + 22x4 - 23x3 + 11x2 - 2x + 1 | \( 2^{6}\cdot 3^{6}\cdot 7^{4} \) | $Q_8:C_2$ (as 8T11) | $[2]$ |
| 8.0.113396024.1 | x8 - 3x7 + 8x6 - 10x5 + 12x4 - 10x3 + 8x2 - 3x + 1 | \( 2^{3}\cdot 7\cdot 1423^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.119771136.5 | x8 - 2x7 + 2x6 + 2x4 - 6x3 + 8x2 + 4x + 1 | \( 2^{12}\cdot 3^{4}\cdot 19^{2} \) | $S_4\times C_2$ (as 8T24) | $[2]$ |
| 8.0.121999616.1 | x8 - 4x7 + 7x6 - 6x5 - 4x4 + 4x3 + 11x2 + 6x + 1 | \( 2^{8}\cdot 17^{3}\cdot 97 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.123183909.1 | x8 - 3x7 + 6x6 - 4x5 + 5x4 - 15x3 + 25x2 - x + 1 | \( 3^{4}\cdot 29\cdot 229^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.125333229.1 | x8 + 4x6 - 3x5 + 5x4 - 3x3 + 4x2 + 1 | \( 3\cdot 7^{3}\cdot 349^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.126376848.1 | x8 - 2x7 - 4x6 + 8x5 + 5x4 - 10x3 + 2x2 + 1 | \( 2^{4}\cdot 3^{4}\cdot 13^{2}\cdot 577 \) | $S_4\wr C_2$ (as 8T47) | $[2]$ |
| 8.0.126773829.1 | x8 - x7 - 2x6 - 4x5 + 7x4 + 5x3 + 7x2 + 2x + 1 | \( 3^{7}\cdot 7^{3}\cdot 13^{2} \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.127828125.1 | x8 - 2x7 + 12x6 - 20x5 + 51x4 - 65x3 + 83x2 - 66x + 31 | \( 3^{4}\cdot 5^{6}\cdot 101 \) | $((C_8 : C_2):C_2):C_2$ (as 8T27) | $[2]$ |
| 8.0.128307240.1 | x8 - 3x7 + 6x6 - 6x5 + 8x4 - 6x3 + 6x2 - 3x + 1 | \( 2^{3}\cdot 3^{4}\cdot 5\cdot 199^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.128777104.2 | x8 - x7 + 2x6 - x5 + 6x4 + x3 + 2x2 + x + 1 | \( 2^{4}\cdot 2837^{2} \) | $C_2^3:S_4$ (as 8T39) | $[2]$ |
| 8.0.128799801.1 | x8 - 2x7 - 4x6 + 29x4 + 6x3 - 43x2 - 35x + 49 | \( 3^{4}\cdot 13^{2}\cdot 97^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.129267065.1 | x8 - x7 + x6 + 3x5 + 2x4 + 3x3 + 13x2 + 20x + 9 | \( 5\cdot 17\cdot 29\cdot 229^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.131974144.1 | x8 + x6 + 4x4 - 3x2 + 1 | \( 2^{10}\cdot 359^{2} \) | $C_2^3:S_4$ (as 8T39) | $[2]$ |
| 8.0.132710400.3 | x8 - 4x5 + 13x4 - 24x3 + 22x2 - 8x + 1 | \( 2^{16}\cdot 3^{4}\cdot 5^{2} \) | $Q_8:C_2$ (as 8T11) | $[2]$ |
| 8.0.132917841.2 | x8 - x7 - 6x6 + 11x5 + 37x4 + 9x3 - 30x2 - 9x + 9 | \( 3^{6}\cdot 7^{2}\cdot 61^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.135644301.1 | x8 - x7 + x6 - 8x5 + 5x4 - 2x3 + 7x2 + 5x + 1 | \( 3^{7}\cdot 13^{2}\cdot 367 \) | $S_4\wr C_2$ (as 8T47) | $[2]$ |
| 8.0.138515453.1 | x8 - 3x7 + 5x6 - 4x5 + 4x4 - 4x3 + 4x2 + 5x + 1 | \( 19\cdot 23\cdot 563^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.140955633.1 | x8 - x7 - 5x6 + 10x5 - 19x3 + 22x2 - 8x + 1 | \( 3^{4}\cdot 7\cdot 13^{2}\cdot 1471 \) | $S_4\wr C_2$ (as 8T47) | $[2]$ |
| 8.0.142850304.2 | x8 + 3x6 - 4x5 + 8x4 - 6x3 + 7x2 + 2x + 1 | \( 2^{8}\cdot 3^{4}\cdot 83^{2} \) | $S_4\times C_2$ (as 8T24) | $[2]$ |
| 8.0.144733797.1 | x8 - 4x7 + 7x6 - 7x5 - 3x4 + 13x3 - 2x2 - 5x + 43 | \( 3^{4}\cdot 13^{2}\cdot 97\cdot 109 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.144733797.2 | x8 - 2x6 - 5x5 - 7x4 + 41x3 - 76x + 49 | \( 3^{4}\cdot 13^{2}\cdot 97\cdot 109 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.146313216.1 | x8 - 2x7 + 4x5 + 10x4 - 48x3 + 72x2 - 48x + 12 | \( 2^{12}\cdot 3^{6}\cdot 7^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.146313216.2 | x8 - 2x7 - 4x6 + 16x5 - 14x4 - 16x3 + 56x2 - 64x + 28 | \( 2^{12}\cdot 3^{6}\cdot 7^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.148777965.1 | x8 + 2x6 - 3x5 + 6x4 - 3x3 + 2x2 + 3x + 1 | \( 3^{6}\cdot 5\cdot 7^{4}\cdot 17 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
| 8.0.151253973.1 | x8 - 3x7 + 3x6 - x4 + 3x2 - 3x + 1 | \( 3^{4}\cdot 13\cdot 379^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.151725312.1 | x8 - 4x7 + 13x6 - 22x5 + 28x4 - 16x3 - 2x2 + 2x + 1 | \( 2^{8}\cdot 3^{7}\cdot 271 \) | $S_4\wr C_2$ (as 8T47) | $[2]$ |
| 8.0.151807041.1 | x8 - 5x6 + 28x4 + 15x2 + 9 | \( 3^{4}\cdot 37^{4} \) | $D_4$ (as 8T4) | $[2]$ |
| 8.0.153140625.1 | x8 - x7 - 9x5 + 9x4 - 4x3 + 20x2 - 16x + 16 | \( 3^{4}\cdot 5^{6}\cdot 11^{2} \) | $D_4\times C_2$ (as 8T9) | $[2]$ |
| 8.0.153140625.2 | x8 - 3x7 - x6 + 13x5 + 6x4 - 35x3 - 15x2 + 25x + 25 | \( 3^{4}\cdot 5^{6}\cdot 11^{2} \) | $C_2^2:C_4$ (as 8T10) | $[2]$ |
| 8.0.153364736.1 | x8 - 4x7 + 10x6 - 16x5 + 16x4 - 10x3 + 5x2 - 2x + 1 | \( 2^{8}\cdot 7\cdot 23\cdot 61^{2} \) | $C_2 \wr S_4$ (as 8T44) | $[2]$ |
| 8.0.153760000.1 | x8 + 7x6 + 18x4 + 17x2 + 1 | \( 2^{8}\cdot 5^{4}\cdot 31^{2} \) | $C_2^2 \wr C_2$ (as 8T18) | $[2]$ |
| 8.0.155356461.1 | x8 - 2x7 - 7x6 + 16x5 + 22x4 - 43x3 - 37x2 + 44x + 37 | \( 3^{6}\cdot 13^{3}\cdot 97 \) | $C_2 \wr C_2\wr C_2$ (as 8T35) | $[2]$ |
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