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Label Polynomial Discriminant Galois group Class group
8.2.21434375.1 x8 - x7 + 2x6 - 5x5 + x4 - 5x3 + 2x2 - x + 1 \( -\,5^{5}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.107171875.2 x8 - x7 + 6x5 - 11x4 + 6x3 - x + 1 \( -\,5^{6}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.0.215378125.1 x8 - 3x7 + 2x6 + 4x5 - x4 - 4x3 + 2x2 + 3x + 1 \( 5^{5}\cdot 41^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.363483392.1 x8 - 4x7 + 9x6 - 12x5 + 7x4 + 10x3 - 22x2 + 16x - 4 \( -\,2^{8}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.363483392.2 x8 - 2x6 - 4x5 + 4x4 + 4x3 + x2 - 6x - 2 \( -\,2^{8}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.536870912.1 x8 + 4x6 + 4x4 - 2 \( -\,2^{29} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.536870912.2 x8 - 4x6 + 4x4 - 2 \( -\,2^{29} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.641809375.1 x8 - 2x7 + 3x6 + 4x5 - 4x4 + 10x3 + 10x2 + 18x + 9 \( -\,5^{5}\cdot 59^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.0.643956736.1 x8 - 2x7 + 5x6 - 8x5 + 7x4 - 6x3 + 5x2 + 4x + 2 \( 2^{17}\cdot 17^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.0.709315625.1 x8 - x7 + 4x6 - 9x5 - x4 + 9x3 + 4x2 + x + 1 \( 5^{5}\cdot 61^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1050284375.1 x8 - 3x6 - 2x5 - 22x3 + 50x2 - 24x - 1 \( -\,5^{5}\cdot 7^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$
8.2.1050284375.2 x8 - x7 - 5x6 + 12x5 + 5x4 - 38x3 + 18x2 + 40x - 31 \( -\,5^{5}\cdot 7^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$
8.2.1050284375.3 x8 - 2x7 + x6 + 3x5 - 16x4 + 33x3 - 59x2 + 63x - 29 \( -\,5^{5}\cdot 7^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1050284375.4 x8 - 2x7 - x6 + 2x5 - 6x4 - 18x3 + 2x2 - 19 \( -\,5^{5}\cdot 7^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1073741824.2 x8 + 4x6 + 6x4 + 4x2 - 1 \( -\,2^{30} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1073741824.3 x8 - 4x6 + 6x4 - 4x2 - 1 \( -\,2^{30} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.4.1076890625.1 x8 - 4x6 - 9x4 - 20x3 - 9x2 - 5x + 1 \( 5^{6}\cdot 41^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1331000000.1 x8 - 2x7 - x6 + 7x5 - 4x4 - 5x3 - 5x2 + 15x - 5 \( -\,2^{6}\cdot 5^{6}\cdot 11^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1331000000.2 x8 - 2x7 + 6x6 - 16x5 + 24x4 - 38x3 + 49x2 - 44x + 16 \( -\,2^{6}\cdot 5^{6}\cdot 11^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1453933568.1 x8 + x6 - 6x5 - 12x4 - 20x3 - 29x2 - 10x - 1 \( -\,2^{10}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1453933568.2 x8 - 4x7 + 6x6 + 6x5 - 30x4 + 32x3 - 3x2 - 4x - 8 \( -\,2^{10}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1540746875.1 x8 - 2x7 + 2x6 - 11x5 + 19x4 - 15x3 + 35x2 - 50x + 20 \( -\,5^{5}\cdot 79^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1736184375.1 x8 - x7 - 9x6 + 15x5 + 24x4 - 67x3 + 5x2 + 98x - 71 \( -\,3^{4}\cdot 5^{5}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.1872286839.1 x8 + 5x6 - 10x5 + 2x4 + 12x3 - 18x2 + 12x - 3 \( -\,3^{3}\cdot 37^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.0.2575826944.1 x8 - 2x6 - 5x4 + 34 \( 2^{19}\cdot 17^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$
8.2.2593559375.1 x8 - x7 + 6x6 - 16x4 - 7x3 - 40x2 + 8x - 31 \( -\,5^{5}\cdot 11^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.2593559375.2 x8 - 2x7 - 5x6 + 5x5 + 10x4 + 13x3 + 29x2 - 85x - 25 \( -\,5^{5}\cdot 11^{2}\cdot 19^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$
8.2.3209046875.1 x8 - x7 - 4x5 - 21x4 + x3 + 15x2 - 16x - 19 \( -\,5^{6}\cdot 59^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.4.3219690625.1 x8 - 2x7 + 5x6 - 20x5 + 4x4 + 4x3 + 32x2 - 12x - 1 \( 5^{5}\cdot 101^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.4.3219690625.2 x8 - 2x7 + 4x6 - 8x5 + 4x4 + 2x3 - 13x2 + 1 \( 5^{5}\cdot 101^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.4.3219690625.3 x8 - x7 - 5x6 + 12x5 - x4 - 20x3 + 30x2 - 20x + 5 \( 5^{5}\cdot 101^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3258096075.1 x8 - 3x7 + 4x6 - 10x5 + 15x4 - 4x3 + 10x2 - 3x - 23 \( -\,3^{3}\cdot 5^{2}\cdot 13^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3258096075.2 x8 - x7 - 4x6 + 2x5 + 4x4 - 3x3 - 9x2 + 18x - 12 \( -\,3^{3}\cdot 5^{2}\cdot 13^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3276800000.1 x8 + 2x6 + x4 - 10x2 - 5 \( -\,2^{20}\cdot 5^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3276800000.2 x8 - 4x6 + 4x4 - 5 \( -\,2^{20}\cdot 5^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3276800000.3 x8 + 4x6 + 4x4 - 5 \( -\,2^{20}\cdot 5^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3276800000.4 x8 - 2x6 + x4 + 10x2 - 5 \( -\,2^{20}\cdot 5^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3514671875.1 x8 - 8x6 - 5x5 - x4 - 25x3 - 27x2 - 20x - 4 \( -\,5^{6}\cdot 11^{3}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3514671875.2 x8 - 2x7 - 3x6 + 5x5 + x4 + 10x3 - 7x2 - 6x - 4 \( -\,5^{6}\cdot 11^{3}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.4.3546578125.1 x8 - 2x7 - 7x5 - 6x4 + 17x3 - 8x + 1 \( 5^{6}\cdot 61^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3641573376.1 x8 - 2x7 + x6 + 6x5 - 17x4 + 20x3 - 18x2 + 12x - 2 \( -\,2^{17}\cdot 3^{4}\cdot 7^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3641573376.2 x8 + 6x6 + 11x4 - 14 \( -\,2^{17}\cdot 3^{4}\cdot 7^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3904765952.1 x8 - 2x7 - x6 - 8x5 - 13x4 - 14x3 - 17x2 - 12x - 2 \( -\,2^{17}\cdot 31^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3904765952.2 x8 - 2x7 + 5x6 + 2x5 - 17x4 - 4x3 - 2x2 - 12x - 2 \( -\,2^{17}\cdot 31^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.3904765952.3 x8 - 2x7 - 7x6 + 6x5 + 26x4 + 10x3 - 29x2 - 38x - 17 \( -\,2^{17}\cdot 31^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.4096000000.4 x8 - 2x6 - 6x4 - 8x2 - 4 \( -\,2^{18}\cdot 5^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.4096000000.5 x8 - 4x6 + 6x4 - 4x2 - 4 \( -\,2^{18}\cdot 5^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.4096000000.7 x8 + 4x6 + 6x4 + 4x2 - 4 \( -\,2^{18}\cdot 5^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.4096000000.8 x8 + 2x6 - 6x4 + 8x2 - 4 \( -\,2^{18}\cdot 5^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
8.2.4517521931.1 x8 - 4x7 + x6 + 11x5 - 14x4 + 5x3 + x2 - x - 1 \( -\,13^{5}\cdot 23^{3} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) Trivial
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