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Label Polynomial Discriminant Galois group Class group
8.0.1262025625.2 x8 - 2x7 - 4x5 + 12x4 + 2x3 - 14x2 - 5x + 11 \( 5^{4}\cdot 7^{4}\cdot 29^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.1480325625.1 x8 - 3x7 + x6 + 7x5 - 3x4 - 5x3 + 11x2 + 15x + 5 \( 3^{8}\cdot 5^{4}\cdot 19^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.2338399449.1 x8 - 3x7 - 3x6 + 17x5 - 3x4 - 27x3 + 10x2 + 9x + 3 \( 3^{10}\cdot 199^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.4.2522550625.1 x8 - 3x7 - x6 + 9x5 - 11x4 + 11x3 - 13x2 + 21x - 9 \( 5^{4}\cdot 7^{4}\cdot 41^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.4.6146560000.1 x8 - 4x7 + 6x6 - 8x4 - 4x3 - 2x2 + 8x - 1 \( 2^{12}\cdot 5^{4}\cdot 7^{4} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.6146560000.8 x8 - 2x7 - 2x6 - 2x5 + 4x4 + 22x3 + 38x2 + 30x + 11 \( 2^{12}\cdot 5^{4}\cdot 7^{4} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.6332339776.1 x8 - x7 + 4x6 - x5 + 9x4 - 11x3 + 22x2 - 7x + 2 \( 2^{6}\cdot 7^{6}\cdot 29^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.6332339776.3 x8 - x7 + 7x5 + 28x2 + 6x + 8 \( 2^{6}\cdot 7^{6}\cdot 29^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.6371392041.3 x8 - x7 - 4x6 + 3x5 + 18x4 - 2x3 + 7x2 + 84x + 63 \( 3^{4}\cdot 7^{4}\cdot 181^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.6720228529.1 x8 - 3x6 - 2x5 + 15x4 - 4x3 - 12x2 + 10x + 11 \( 7^{6}\cdot 239^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.7564650625.2 x8 - x7 + 8x6 - 14x5 + 31x4 - 37x3 + 33x2 - 16x + 4 \( 5^{4}\cdot 7^{4}\cdot 71^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.4.7766544384.2 x8 + 4x6 - 2x5 - 15x4 - 14x3 + x2 + 6x + 1 \( 2^{12}\cdot 3^{8}\cdot 17^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.8414025984.10 x8 - 2x7 + 7x6 - 18x5 + 26x4 - 26x3 + 21x2 - 12x + 4 \( 2^{8}\cdot 3^{4}\cdot 7^{4}\cdot 13^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.8481857409.1 x8 - 3x6 - x5 - 6x4 - 9x3 + 19x2 + 30x + 12 \( 3^{10}\cdot 379^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.9855525625.4 x8 - 3x7 + 7x6 - 6x5 + 8x4 - 5x3 + 14x2 - 6x + 9 \( 5^{4}\cdot 11^{2}\cdot 19^{4} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.10144316961.1 x8 - x7 - 9x6 + x5 + 19x4 + 27x3 + 53x2 + 37x + 19 \( 3^{4}\cdot 19^{4}\cdot 31^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.4.12834170944.2 x8 - 4x7 + 9x6 - 5x5 - 12x3 + 5x2 + 3x - 1 \( 2^{6}\cdot 7^{4}\cdot 17^{4} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.13558506481.3 x8 - x6 - 2x5 + 17x4 - 25x3 + 30x2 - 20x + 9 \( 13^{6}\cdot 53^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.13922112064.2 x8 - x7 + x6 - x5 + 8x4 - 8x3 - 6x2 - 14x + 28 \( 2^{6}\cdot 7^{6}\cdot 43^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.13922112064.5 x8 - 3x7 + 2x6 + 11x5 - 20x4 - 12x3 + 88x2 - 120x + 64 \( 2^{6}\cdot 7^{6}\cdot 43^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.14438185281.4 x8 - x7 - 7x6 + 10x5 + 5x4 - 83x3 + 242x2 - 216x + 61 \( 3^{4}\cdot 13^{4}\cdot 79^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.16019205489.1 x8 - 3x7 + 7x5 - 7x4 + 7x2 + 4x + 16 \( 3^{4}\cdot 7^{6}\cdot 41^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.16151613921.1 x8 - 9x6 - 10x5 + 60x4 + 3x3 - 98x2 - 21x + 93 \( 3^{10}\cdot 523^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.16531787776.6 x8 - 2x7 - 3x6 + 14x5 - 8x4 - 16x3 + 35x2 - 28x + 14 \( 2^{12}\cdot 7^{4}\cdot 41^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.16796160000.4 x8 - 2x7 - 4x6 + 27x4 - 12x3 - 20x2 + 10x + 11 \( 2^{12}\cdot 3^{8}\cdot 5^{4} \) $C_2^4:C_6$ (as 8T33) Trivial
8.4.16796160000.6 x8 - 2x7 + 2x6 + 8x5 - 46x4 + 88x3 - 64x2 + 8x + 4 \( 2^{12}\cdot 3^{8}\cdot 5^{4} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.16899220009.1 x8 - 2x7 + 14x5 - 28x4 + 14x3 + 56x2 - 107x + 74 \( 7^{6}\cdot 379^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.17282520369.1 x8 - x7 + 4x6 - 22x5 + 40x4 - 34x3 + 94x2 - 184x + 133 \( 3^{10}\cdot 541^{2} \) $C_2^4:C_6$ (as 8T33) $[4]$
8.0.17620173081.2 x8 - x7 + 2x6 + 4x5 + 8x4 + 16x3 + 11x2 + 6x + 4 \( 3^{4}\cdot 7^{6}\cdot 43^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.4.19770609664.2 x8 - 4x7 + 6x6 - 2x5 - 15x4 + 26x3 - 24x2 + 14x - 3 \( 2^{12}\cdot 13^{6} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.19770609664.6 x8 - 2x7 - 4x6 - 4x5 + 17x4 + 24x3 + 24x2 + 10x + 3 \( 2^{12}\cdot 13^{6} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.20136745216.2 x8 - 2x7 - 7x6 + 24x5 - 9x4 - 58x3 + 108x2 - 80x + 25 \( 2^{8}\cdot 7^{4}\cdot 181^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.20671250625.1 x8 - 3x7 + 7x6 - 22x5 + 36x4 - 49x3 + 76x2 - 60x + 25 \( 3^{8}\cdot 5^{4}\cdot 71^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.20694548736.3 x8 - 3x6 - 2x5 + 6x4 + 6x3 + x2 - 6x + 6 \( 2^{8}\cdot 3^{10}\cdot 37^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.25329359104.7 x8 - 2x7 + 4x6 - 4x5 - 3x4 + 10x3 + 11x2 - 10x + 2 \( 2^{8}\cdot 7^{6}\cdot 29^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.26155945984.5 x8 - 4x7 + 4x6 - 6x5 + 29x4 - 42x3 + 19x2 - 14x + 17 \( 2^{12}\cdot 7^{2}\cdot 19^{4} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.27935445321.2 x8 - x7 + 14x6 - 14x5 + 56x4 - 98x3 + 98x2 - 48x + 13 \( 3^{4}\cdot 7^{4}\cdot 379^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.28362938569.1 x8 + 2x6 - 2x5 + 2x4 + 12x3 + 16x2 - x + 2 \( 7^{6}\cdot 491^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.28993575625.3 x8 - 3x7 + 8x6 - 22x5 + 22x4 + 6x3 - 6x2 + 5 \( 5^{4}\cdot 7^{4}\cdot 139^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.29182547241.1 x8 - x7 - 8x6 + 2x5 + 16x4 + 20x3 + 58x2 + 50x + 13 \( 3^{10}\cdot 19^{2}\cdot 37^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.29182547241.2 x8 - 3x7 - 6x6 + 33x5 - 27x4 - 117x3 + 279x2 - 135x + 27 \( 3^{10}\cdot 19^{2}\cdot 37^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.30124114969.1 x8 - 4x6 - 3x5 - x4 + 6x3 + 35x2 + 14x + 3 \( 13^{6}\cdot 79^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.32247898929.1 x8 - x7 + 10x6 + 2x5 + 25x4 + 29x3 + 31x2 - 22x + 4 \( 3^{10}\cdot 739^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.32481050625.3 x8 - 2x6 - 6x5 + 6x4 + 21x3 + 34x2 + 45x + 25 \( 3^{8}\cdot 5^{4}\cdot 89^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.33837970401.1 x8 - x7 + 7x6 - 8x5 + 14x4 - 11x3 + 10x2 + 20x + 7 \( 3^{10}\cdot 757^{2} \) $C_2^4:C_6$ (as 8T33) $[2]$
8.0.33890232649.2 x8 - 6x6 - 8x5 + 18x4 + 58x3 + 74x2 + 49x + 16 \( 7^{4}\cdot 13^{2}\cdot 17^{4} \) $C_2^4:C_6$ (as 8T33) $[4]$
8.0.35201639641.1 x8 - x7 - 5x6 - 17x5 + 36x4 + 44x3 - 17x2 - 15x + 18 \( 7^{6}\cdot 547^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.37956390976.3 x8 - x7 + x6 - 4x5 + 9x4 - 8x3 + 4x2 - 12x + 18 \( 2^{6}\cdot 7^{6}\cdot 71^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.0.37956390976.4 x8 - x7 - 3x6 + 2x5 + 15x4 + 4x3 - 12x2 + 4x + 22 \( 2^{6}\cdot 7^{6}\cdot 71^{2} \) $C_2^4:C_6$ (as 8T33) Trivial
8.4.39033114624.6 x8 - 4x7 + 2x6 + 6x5 - 17x4 + 26x3 - 6x2 - 14x + 7 \( 2^{12}\cdot 3^{4}\cdot 7^{6} \) $C_2^4:C_6$ (as 8T33) Trivial
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