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Label Polynomial Discriminant Galois group Class group
8.0.4000000.2 x8 - 2x6 + 4x4 - 3x2 + 1 \( 2^{8}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) 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
8.2.6668032.1 x8 + x6 - 2x5 - x4 - 2x3 + x2 + 1 \( -\,2^{8}\cdot 7\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.9144576.1 x8 + x6 - 2x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 7^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.0.9144576.2 x8 - x6 + 2x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 7^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.0.10637568.1 x8 - 4x7 + 7x6 - 4x5 - 2x4 + 2x3 + 4x2 - 4x + 1 \( 2^{8}\cdot 3^{7}\cdot 19 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.11360000.1 x8 - 4x7 + 9x6 - 12x5 + 10x4 - 2x3 - 4x2 + 4x - 1 \( -\,2^{8}\cdot 5^{4}\cdot 71 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.12224768.1 x8 - 2x7 + 3x6 - 4x5 + 6x4 - 4x3 + 4x2 - 2x + 1 \( 2^{8}\cdot 17\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.12640000.1 x8 - 2x7 - x6 + 2x5 + 2x4 - 6x3 + 4x2 - 1 \( -\,2^{8}\cdot 5^{4}\cdot 79 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.14240000.1 x8 + 3x6 - 4x5 + 3x4 - 6x3 + 7x2 - 4x + 1 \( 2^{8}\cdot 5^{4}\cdot 89 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.16539392.1 x8 - 4x7 + 8x6 - 10x5 + 6x4 - 5x2 + 4x - 1 \( -\,2^{8}\cdot 23\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.19360000.1 x8 + 3x6 + 3x4 + 3x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 11^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.4.19360000.1 x8 - 3x6 + 3x4 - 3x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 11^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.0.22581504.1 x8 - 2x7 - x6 - 2x5 + 7x4 + 2x3 - x2 + 2x + 1 \( 2^{8}\cdot 3^{6}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.2.28045056.1 x8 - x6 - 4x5 - 5x4 - 4x3 - x2 + 1 \( -\,2^{8}\cdot 3\cdot 13\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) 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
8.2.30416640.1 x8 - 2x7 + 3x6 - 6x5 + 3x4 - 6x3 + 3x2 - 2x + 1 \( -\,2^{8}\cdot 3\cdot 5\cdot 89^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.31539456.1 x8 + 3x6 + 12x4 + 18x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 13^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.0.31539456.2 x8 - 3x6 + 12x4 - 18x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 13^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.2.31840000.2 x8 + 3x6 - 4x5 + 4x4 - 6x3 + 6x2 - 6x + 1 \( -\,2^{8}\cdot 5^{4}\cdot 199 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.32993536.1 x8 - 2x7 + 4x6 - 8x5 + 6x4 - 4x3 + 3x2 + 2x + 1 \( 2^{8}\cdot 359^{2} \) $C_2^3:S_4$ (as 8T39) trivial
8.4.32993536.1 x8 - 4x7 + 10x6 - 16x5 + 14x4 - 6x3 - 3x2 + 4x - 1 \( 2^{8}\cdot 359^{2} \) $C_2^3:S_4$ (as 8T39) trivial
8.4.33440000.1 x8 - 2x7 - 3x6 + 10x5 - 5x4 - 4x3 + 5x2 - 4x + 1 \( 2^{8}\cdot 5^{4}\cdot 11\cdot 19 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.33797888.2 x8 - 2x7 + 2x5 + 2x4 - 4x3 - x2 + 4x - 1 \( -\,2^{8}\cdot 47\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.34472192.1 x8 - 2x7 + 3x6 - 2x5 + x4 - 2x3 + 3x2 - 2x + 1 \( 2^{8}\cdot 17\cdot 89^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.36018432.2 x8 - 4x7 + 2x6 + 8x5 - 8x4 - 2x3 + 5x2 - 2x + 1 \( 2^{8}\cdot 3^{6}\cdot 193 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.37511424.2 x8 - 2x7 + 7x6 - 14x5 + 19x4 - 14x3 + 7x2 - 2x + 1 \( 2^{8}\cdot 3^{7}\cdot 67 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.38240000.1 x8 - 4x7 + 6x6 - 4x5 + 2x4 - 2x3 + x2 - 1 \( -\,2^{8}\cdot 5^{4}\cdot 239 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.39055616.1 x8 - 4x7 + 8x6 - 10x5 + 10x4 - 8x3 + 7x2 - 4x + 1 \( 2^{8}\cdot 41\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.40497408.2 x8 - 2x7 + 3x6 - 8x5 + 4x4 + 6x2 + 3 \( 2^{8}\cdot 3^{6}\cdot 7\cdot 31 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.40988928.1 x8 - 2x7 + 3x6 - 2x5 + 3x4 - 2x3 + 3x2 - 2x + 1 \( 2^{8}\cdot 3\cdot 19\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.43360000.1 x8 - 4x7 + 6x6 - 4x5 + 2x3 - x2 - 1 \( -\,2^{8}\cdot 5^{4}\cdot 271 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.44771072.1 x8 - 4x7 + 7x6 - 6x5 + 2x4 + 4x3 - 6x2 + 4x - 1 \( -\,2^{8}\cdot 47\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.44771072.2 x8 - x6 - 2x5 + 2x4 + 2x3 - 4x + 1 \( -\,2^{8}\cdot 47\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.4.46240000.1 x8 - 4x7 + 5x6 + 2x5 - 8x4 + 2x2 + 2x - 1 \( 2^{8}\cdot 5^{4}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.47997184.1 x8 - x6 - 2x5 + 5x4 - 2x3 - x2 + 1 \( 2^{8}\cdot 433^{2} \) $C_2^3:S_4$ (as 8T39) trivial
8.0.47997184.2 x8 - 2x7 - x6 + 2x5 + x4 + 2x3 - x2 - 2x + 1 \( 2^{8}\cdot 433^{2} \) $C_2^3:S_4$ (as 8T39) trivial
8.0.49787136.2 x8 - 2x7 - 4x5 + 2x4 + 8x3 + 9x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 7^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.2.51040000.1 x8 - 4x7 + 5x6 + 4x5 - 17x4 + 16x3 - 3x2 - 2x - 1 \( -\,2^{8}\cdot 5^{4}\cdot 11\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.51040000.2 x8 - 4x7 + 10x6 - 16x5 + 18x4 - 14x3 + 7x2 - 2x - 1 \( -\,2^{8}\cdot 5^{4}\cdot 11\cdot 29 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.52391680.1 x8 + x6 - 4x5 - x4 - 4x3 + x2 + 1 \( -\,2^{8}\cdot 5\cdot 11\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.52723968.1 x8 - 4x7 + 8x6 - 10x5 + 10x4 - 8x3 + 3x2 + 1 \( 2^{8}\cdot 3\cdot 11\cdot 79^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.52723968.2 x8 - 2x7 + 4x6 - 4x5 + 2x4 - x2 + 2x + 1 \( 2^{8}\cdot 3\cdot 11\cdot 79^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.56809216.1 x8 - 4x7 + 9x6 - 10x5 + 4x4 + 4x3 - 6x2 + 4x - 1 \( -\,2^{8}\cdot 53^{2}\cdot 79 \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.57760000.1 x8 + 5x6 + 7x4 + 5x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 19^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.4.57760000.1 x8 - 5x6 + 7x4 - 5x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 19^{2} \) $C_2^2 \wr C_2$ (as 8T18) trivial
8.0.58413312.3 x8 - 4x7 + 5x6 + 2x5 - 5x4 - 2x3 + 5x2 + 4x + 1 \( 2^{8}\cdot 3^{6}\cdot 313 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.2.62562048.1 x8 - 2x7 + 3x6 - 6x5 + 5x4 - 6x3 + 3x2 - 2x + 1 \( -\,2^{8}\cdot 3\cdot 29\cdot 53^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.62861056.1 x8 - 4x7 + 8x6 - 10x5 + 6x4 - x2 - 1 \( -\,2^{8}\cdot 31\cdot 89^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.64160000.2 x8 - 2x7 + x6 - 6x5 + 3x4 + 8x3 + 9x2 + 4x + 1 \( 2^{8}\cdot 5^{4}\cdot 401 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
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