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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
8.0.1601613.1 x8 - 2x6 - 3x5 + 3x4 + 3x3 - 2x2 + 1 \( 3^{6}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.4917248.1 x8 - 3x7 + 6x6 - 8x5 + 10x4 - 9x3 + 6x2 - 2x + 1 \( 2^{11}\cdot 7^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.8192000.1 x8 - 2x4 + 5 \( 2^{16}\cdot 5^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.8719893.1 x8 - 3x7 - x6 + 11x5 - 6x4 - 10x3 + 9x2 - x + 1 \( 3^{4}\cdot 7^{2}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.8719893.2 x8 - 3x7 + 5x5 + x4 - 3x3 - 5x2 - 2x + 7 \( 3^{4}\cdot 7^{2}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
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
8.0.16471125.1 x8 - x7 + 5x6 - 2x5 + 9x4 - 2x3 + 5x2 - x + 1 \( 3^{2}\cdot 5^{3}\cdot 11^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.16471125.2 x8 - x7 + x6 + 2x5 - 3x4 - 2x3 + x2 + x + 1 \( 3^{2}\cdot 5^{3}\cdot 11^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.20123648.1 x8 - 2x7 + 3x6 - 4x4 + 2x3 + 4x2 - 4x + 1 \( 2^{12}\cdot 17^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.31510377.1 x8 + 2x6 - 2x5 - 6x4 - 2x3 + 9x2 + 10x + 4 \( 3^{4}\cdot 73^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.32768000.1 x8 + 2x4 + 5 \( 2^{18}\cdot 5^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.36926037.1 x8 - x7 + 6x6 - x5 + 10x4 + 6x3 + 6x2 + 9x + 3 \( 3^{6}\cdot 37^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.45556992.2 x8 - 7x6 + 20x4 - 26x2 + 13 \( 2^{8}\cdot 3^{4}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.45556992.3 x8 + 7x6 + 20x4 + 26x2 + 13 \( 2^{8}\cdot 3^{4}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.64242477.1 x8 - 3x7 + 11x6 - 22x5 + 42x4 - 52x3 + 66x2 - 43x + 37 \( 3^{4}\cdot 13^{3}\cdot 19^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.64242477.2 x8 - 3x7 - 3x6 + 10x5 + 16x4 - 36x3 - 2x2 + 17x + 7 \( 3^{4}\cdot 13^{3}\cdot 19^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.70304000.3 x8 - 2x7 - 2x6 + 11x4 - 2x2 - 2x + 1 \( 2^{8}\cdot 5^{3}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.70304000.4 x8 - 2x7 + 4x6 - 8x5 + 10x4 - 12x3 + 19x2 - 8x + 1 \( 2^{8}\cdot 5^{3}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.73926513.1 x8 - x7 + 3x6 + 6x5 + 3x4 + 8x3 + 20x2 + 8x + 1 \( 3^{4}\cdot 97^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.78675968.2 x8 + 3x6 + 3x4 + 2x2 + 2 \( 2^{15}\cdot 7^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
8.4.88410125.1 x8 - 4x7 + 5x6 - x5 - 7x4 + 11x3 - 6x2 + x + 1 \( 5^{3}\cdot 29^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
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) $[2]$
8.0.131072000.1 x8 - 2x6 + 8x4 - 10x2 + 5 \( 2^{20}\cdot 5^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.131072000.2 x8 - 6x6 + 12x4 - 10x2 + 5 \( 2^{20}\cdot 5^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.134217728.2 x8 + 2x4 + 2 \( 2^{27} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.134217728.3 x8 - 2x4 + 2 \( 2^{27} \) $C_4\wr C_2$ (as 8T17) Trivial (GRH)
8.0.143982592.1 x8 + 6x4 + 13 \( 2^{16}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.165469149.1 x8 - 3x7 + 2x6 - 6x5 + 30x4 - 63x3 + 71x2 - 36x + 7 \( 3^{6}\cdot 61^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.171016677.1 x8 - 3x7 + 14x6 - 23x5 + 57x4 - 59x3 + 99x2 - 62x + 43 \( 3^{4}\cdot 13^{3}\cdot 31^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.171016677.2 x8 - 9x6 - 5x5 + 37x4 + 24x3 - 71x2 - 25x + 67 \( 3^{4}\cdot 13^{3}\cdot 31^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.201041757.1 x8 - x7 + 7x6 - 13x5 + 24x4 - 32x3 + 43x2 - 29x + 19 \( 3^{4}\cdot 7^{2}\cdot 37^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.201041757.2 x8 - 2x7 + 11x6 - 14x5 + 32x4 - 23x3 + 31x2 - 12x + 3 \( 3^{4}\cdot 7^{2}\cdot 37^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.204800000.1 x8 + 2x6 - 12x5 + 4x4 + 8x3 + 14x2 - 8x + 1 \( 2^{16}\cdot 5^{5} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.0.221445125.1 x8 - 3x7 + 7x6 - 15x5 + 18x4 - 16x3 + 13x2 - 5x + 3 \( 5^{3}\cdot 11^{6} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.233644288.1 x8 - 4x7 + 8x6 - 10x5 + 13x4 - 10x3 - 4x2 + 6x + 5 \( 2^{8}\cdot 97^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.240945152.1 x8 - 3x7 + 11x6 - 23x5 + 42x4 - 55x3 + 57x2 - 39x + 11 \( 2^{11}\cdot 7^{6} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.270672597.1 x8 - 3x7 - 5x6 + 15x5 + 15x4 - 6x3 - 71x2 - 36x + 133 \( 3^{6}\cdot 13^{5} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.8.282300416.1 x8 - 4x7 + 14x5 - 8x4 - 12x3 + 7x2 + 2x - 1 \( 2^{12}\cdot 41^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.282300416.2 x8 - 4x7 + 8x6 - 10x5 + 11x4 - 6x3 - 4x2 + 4x + 2 \( 2^{12}\cdot 41^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.282300416.3 x8 - 2x7 + 3x6 + 4x5 - 5x4 - 4x3 + 13x2 - 10x + 3 \( 2^{12}\cdot 41^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.314703872.3 x8 - 2x6 + 6x4 - 12x2 + 8 \( 2^{17}\cdot 7^{4} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.0.314703872.4 x8 + 2x6 + 6x4 + 12x2 + 8 \( 2^{17}\cdot 7^{4} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.321978368.5 x8 + 2x4 + 17 \( 2^{16}\cdot 17^{3} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.0.321978368.6 x8 - 4x7 + 6x6 - 6x4 + 4x3 + 2x2 + 9 \( 2^{16}\cdot 17^{3} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.0.329042493.2 x8 - 3x7 + 3x6 - x5 + 25x4 - 30x3 - 26x2 + 97x + 67 \( 3^{4}\cdot 13^{3}\cdot 43^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.329042493.3 x8 - 3x7 - 7x6 + 19x5 + 33x4 - 50x3 - 84x2 + 19x + 139 \( 3^{4}\cdot 13^{3}\cdot 43^{2} \) $C_4\wr C_2$ (as 8T17) Trivial
8.0.363483392.1 x8 - 2x7 + 10x5 - 6x4 - 20x3 + 55x2 - 62x + 25 \( 2^{8}\cdot 17^{5} \) $C_4\wr C_2$ (as 8T17) $[2]$
8.0.369381632.2 x8 - 4x7 + 8x6 - 10x5 + 5x4 - 6x3 + 14x2 - 8x + 8 \( 2^{8}\cdot 113^{3} \) $C_4\wr C_2$ (as 8T17) Trivial
8.4.381078125.1 x8 - 3x7 + x6 + 11x5 - 26x4 + 28x3 - 21x2 + 9x + 1 \( 5^{6}\cdot 29^{3} \) $C_4\wr C_2$ (as 8T17) Trivial

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