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Label Polynomial Discriminant Galois group Class group
8.0.1142440000.2 x8 + x6 + 3x2 + 4 \( 2^{6}\cdot 5^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.1142440000.3 x8 - 6x6 + 15x4 - 13x2 + 4 \( 2^{6}\cdot 5^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.1662029824.1 x8 - 2x7 + 2x5 + 4x4 - 6x3 + 14x + 7 \( 2^{12}\cdot 7^{4}\cdot 13^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.1662029824.2 x8 - 2x7 + 4x6 - x4 + 6x3 - 2x2 - 4x + 2 \( 2^{12}\cdot 7^{4}\cdot 13^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.2924646400.1 x8 - 2x7 + 6x6 - 4x5 + 13x4 + 4x3 + 6x2 + 2x + 1 \( 2^{12}\cdot 5^{2}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.2924646400.2 x8 - 2x7 + 8x6 - 16x5 + 11x4 + 2x3 + 6x2 - 8x + 2 \( 2^{12}\cdot 5^{2}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.4388797504.1 x8 + 5x6 + 12x4 + 3x2 + 4 \( 2^{6}\cdot 7^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.4388797504.2 x8 + 3x6 + 8x4 + 7x2 + 4 \( 2^{6}\cdot 7^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.4569760000.5 x8 - x6 - 3x2 + 4 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.4569760000.6 x8 + 6x6 + 15x4 + 13x2 + 4 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.6648119296.1 x8 - 2x7 - 2x6 + 10x5 + 8x4 + 14x3 + 22x2 - 10x + 1 \( 2^{14}\cdot 7^{4}\cdot 13^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.6648119296.2 x8 - 2x7 + 2x6 - 10x5 + 4x4 + 2x3 + 26x2 + 14x + 25 \( 2^{14}\cdot 7^{4}\cdot 13^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.7766544384.1 x8 - 4x7 + 4x6 + 2x5 + 13x4 - 34x3 + 54x2 - 36x + 18 \( 2^{12}\cdot 3^{8}\cdot 17^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.7766544384.2 x8 - 2x7 - 4x6 + 14x5 - 4x4 - 38x3 + 80x2 - 70x + 31 \( 2^{12}\cdot 3^{8}\cdot 17^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.8270811136.1 x8 - 2x7 + 10x6 - 24x5 + 41x4 - 52x3 + 42x2 - 6x + 1 \( 2^{12}\cdot 7^{4}\cdot 29^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.8270811136.2 x8 - 2x7 + 4x6 + 10x5 + 10x3 + 80x2 - 2x + 27 \( 2^{12}\cdot 7^{4}\cdot 29^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.9701462016.1 x8 - 2x7 + 8x6 - 10x5 + 20x4 - 14x3 + 20x2 - 22x + 7 \( 2^{12}\cdot 3^{8}\cdot 19^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.9701462016.2 x8 - 2x7 - 2x6 - 16x5 + 14x4 + 32x3 + 108x2 + 72x + 36 \( 2^{12}\cdot 3^{8}\cdot 19^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.11698585600.1 x8 - 2x7 + 10x6 - 6x5 + 24x4 + 6x3 + 10x2 + 2x + 1 \( 2^{14}\cdot 5^{2}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.11698585600.2 x8 - 8x6 + 18x4 + 25 \( 2^{14}\cdot 5^{2}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.15130968064.2 x8 + 2x6 + 18x4 - 6x2 + 1 \( 2^{14}\cdot 31^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[8]$
8.0.15130968064.3 x8 - 2x6 + 18x4 + 6x2 + 1 \( 2^{14}\cdot 31^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[8]$
8.0.15130968064.5 x8 + 5x4 - 8x2 + 16 \( 2^{14}\cdot 31^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.15130968064.6 x8 + 5x4 + 8x2 + 16 \( 2^{14}\cdot 31^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.16531787776.1 x8 - 2x7 + 10x6 - 24x5 + 49x4 - 64x3 + 58x2 - 26x + 5 \( 2^{12}\cdot 7^{4}\cdot 41^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.16531787776.2 x8 - 2x7 + 4x6 + 6x5 - 16x4 + 18x3 + 36x2 + 2x + 11 \( 2^{12}\cdot 7^{4}\cdot 41^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.17555190016.2 x8 - 3x6 + 8x4 - 7x2 + 4 \( 2^{8}\cdot 7^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.17555190016.3 x8 - 5x6 + 12x4 - 3x2 + 4 \( 2^{8}\cdot 7^{4}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.18183983104.1 x8 - 4x7 + 14x5 + 9x4 - 46x3 + 16x2 + 10x + 3 \( 2^{12}\cdot 7^{4}\cdot 43^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.18183983104.2 x8 - 2x7 - 2x6 + 12x5 - 22x4 + 8x3 + 56x2 - 96x + 56 \( 2^{12}\cdot 7^{4}\cdot 43^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.20025646144.1 x8 - 3x6 + 9x4 - 4x2 + 1 \( 2^{6}\cdot 7^{4}\cdot 19^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.20025646144.2 x8 + 3x4 + 7x2 + 4 \( 2^{6}\cdot 7^{4}\cdot 19^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.26155945984.1 x8 - 4x7 + 12x6 - 8x5 - 2x4 + 20x3 + 12x2 - 32x + 13 \( 2^{12}\cdot 7^{2}\cdot 19^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.26155945984.2 x8 - 2x7 + 12x6 - 18x5 + 52x4 - 54x3 + 92x2 - 54x + 47 \( 2^{12}\cdot 7^{2}\cdot 19^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.28561000000.1 x8 - x7 + 9x6 - 2x5 + 9x4 - 9x3 - 24x2 + 7x + 11 \( 2^{6}\cdot 5^{6}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.28561000000.2 x8 - x7 + 9x6 - 17x5 + 34x4 - 64x3 + 81x2 - 53x + 16 \( 2^{6}\cdot 5^{6}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.28561000000.3 x8 + 5x6 + 5x4 + 25 \( 2^{6}\cdot 5^{6}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.28561000000.4 x8 + 5x4 + 25x2 + 25 \( 2^{6}\cdot 5^{6}\cdot 13^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$
8.0.31066177536.1 x8 - 2x7 + 6x6 - 14x5 + 4x4 - 18x3 + 66x2 - 42x + 9 \( 2^{14}\cdot 3^{8}\cdot 17^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.31066177536.2 x8 - 2x7 + 10x6 - 26x5 + 52x4 - 86x3 + 134x2 - 94x + 29 \( 2^{14}\cdot 3^{8}\cdot 17^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.33083244544.1 x8 - 2x7 + 4x6 + 4x4 + 4x3 - 16x2 - 28x + 34 \( 2^{14}\cdot 7^{4}\cdot 29^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.33083244544.2 x8 - 2x7 + 14x6 - 26x5 + 60x4 - 90x3 + 98x2 - 98x + 49 \( 2^{14}\cdot 7^{4}\cdot 29^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.35070801984.1 x8 - 3x6 + 9x4 - 8x2 + 9 \( 2^{6}\cdot 3^{8}\cdot 17^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.35070801984.2 x8 + 8x6 + 27x4 + 27x2 + 9 \( 2^{6}\cdot 3^{8}\cdot 17^{4} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.36790308864.1 x8 - 2x7 - 4x6 + 22x5 - 17x4 - 10x3 + 116x2 - 136x + 55 \( 2^{12}\cdot 3^{8}\cdot 37^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.36790308864.2 x8 - 2x7 + 2x6 - 8x5 - 2x4 + 8x3 + 8x2 + 80x + 112 \( 2^{12}\cdot 3^{8}\cdot 37^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) Trivial
8.0.38805848064.1 x8 - 2x7 - 8x5 + 28x4 - 24x3 + 12x2 - 24x + 18 \( 2^{14}\cdot 3^{8}\cdot 19^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.38805848064.2 x8 - 2x7 + 4x6 - 20x5 + 28x4 + 4x3 + 128x2 + 32x + 86 \( 2^{14}\cdot 3^{8}\cdot 19^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.39432030625.1 x8 - 2x7 - 2x6 + 5x5 + 13x4 - 2x3 - 5x2 + 4x + 9 \( 5^{4}\cdot 13^{4}\cdot 47^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
8.0.39432030625.2 x8 - x7 + 5x5 + 3x4 + 15x3 + 20x2 - 43x + 16 \( 5^{4}\cdot 13^{4}\cdot 47^{2} \) $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$
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