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Label Polynomial Discriminant Galois group Class group
8.0.1890625.1 x8 - 3x7 + 6x6 - 9x5 + 9x4 - 7x3 + 4x2 - x + 1 \( 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.4000000.2 x8 - 2x6 + 4x4 - 3x2 + 1 \( 2^{8}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.5640625.1 x8 - x7 - 2x6 + 5x5 + x4 - 5x3 + 2x2 + 3x + 1 \( 5^{6}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.13140625.1 x8 - 3x7 + 5x6 - 3x5 + 4x4 + 3x3 + 5x2 + 3x + 1 \( 5^{6}\cdot 29^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.15015625.1 x8 - 3x7 + x6 + 6x5 - x4 - 12x3 + 4x2 + 4x + 1 \( 5^{6}\cdot 31^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.26265625.1 x8 - 3x7 + 2x6 + x4 + 8x2 - 24x + 16 \( 5^{6}\cdot 41^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.43441281.1 x8 - 3x7 + 6x6 - 8x5 + 7x4 - 2x3 + 2x2 + 3x + 3 \( 3^{2}\cdot 13^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.54390625.1 x8 - 3x7 + 9x6 - 17x5 + 26x4 - 35x3 + 35x2 - 25x + 25 \( 5^{6}\cdot 59^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.58140625.2 x8 - 3x7 + 4x6 - 7x5 + 11x4 + 5x3 - 10x2 - 25x + 25 \( 5^{6}\cdot 61^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.64000000.1 x8 - 2x7 - 4x6 + 4x5 + 14x4 - 8x3 - 16x2 + 16x - 4 \( 2^{12}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.64000000.4 x8 - 4x6 + 16x4 - 24x2 + 16 \( 2^{12}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.67108864.1 x8 + 4x6 - 2x4 + 4x2 + 1 \( 2^{26} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.67108864.1 x8 - 4x6 - 2x4 - 4x2 + 1 \( 2^{26} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.78765625.1 x8 - x7 - 5x6 + 11x5 + 9x4 - 24x3 + 24x + 16 \( 5^{6}\cdot 71^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.97515625.1 x8 - x7 - 4x6 + 9x5 + 11x4 - 15x3 - 10x2 + 25x + 25 \( 5^{6}\cdot 79^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.123765625.1 x8 - 3x7 + 6x6 - 4x5 + 9x4 + 8x3 + 24x2 + 24x + 16 \( 5^{6}\cdot 89^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.153140625.1 x8 - x7 + x6 + 4x5 - 9x4 - 10x3 + 10x2 + 10x - 5 \( 3^{4}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.153140625.2 x8 - 3x7 - x6 + 13x5 + 6x4 - 35x3 - 15x2 + 25x + 25 \( 3^{4}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.4.153140625.2 x8 - 3x7 + x6 + 11x5 - 16x4 - 17x3 + 9x2 + 4x + 1 \( 3^{4}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.159390625.1 x8 - x7 + 6x6 - 11x5 + 21x4 - 5x3 + 10x2 + 25x + 25 \( 5^{6}\cdot 101^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.185640625.1 x8 - 3x7 + x6 + x5 + 4x4 + 3x3 + 9x2 - 81x + 81 \( 5^{6}\cdot 109^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.205520896.3 x8 - 4x6 + 6x4 - 8x2 + 4 \( 2^{22}\cdot 7^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.205520896.5 x8 + 4x6 + 6x4 + 8x2 + 4 \( 2^{22}\cdot 7^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.228765625.1 x8 - x7 - 6x6 + 8x5 - x4 + 16x3 - 24x2 - 8x + 16 \( 5^{6}\cdot 11^{4} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.268140625.1 x8 - 2x7 - 5x6 + 3x5 + 34x4 - 33x3 - 45x2 + 27x + 81 \( 5^{6}\cdot 131^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.301890625.1 x8 - 3x7 + 12x6 - 25x5 + 51x4 - 85x3 + 108x2 - 99x + 121 \( 5^{6}\cdot 139^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.324000000.2 x8 - 2x6 - 16x4 - 13x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.324000000.3 x8 - x6 - 9x4 - x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.324000000.5 x8 - 6x6 + 36x4 - 81x2 + 81 \( 2^{8}\cdot 3^{4}\cdot 5^{6} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.346890625.1 x8 - x7 + x5 + 9x4 + 31x3 - 50x2 - 11x + 121 \( 5^{6}\cdot 149^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.356265625.1 x8 - 2x7 - 4x6 + 4x5 + 29x4 - 28x3 - 61x2 + 11x + 121 \( 5^{6}\cdot 151^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.386201104.1 x8 - 4x6 - 11x4 - 4x2 + 1 \( 2^{4}\cdot 17^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.390971529.1 x8 - 3x7 + 12x5 - 25x4 + 24x3 - 24x + 16 \( 3^{4}\cdot 13^{6} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.456890625.1 x8 - x7 - 2x6 + 15x5 - 29x4 - 5x3 + 12x2 + 3x + 1 \( 3^{4}\cdot 5^{6}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.4.456890625.2 x8 - x7 - x6 - 2x5 - 11x4 + 6x3 + 6x2 - 18x - 9 \( 3^{4}\cdot 5^{6}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.456890625.2 x8 - x7 - 6x6 + 13x5 + 29x4 - 29x3 - 54x2 + 77x + 121 \( 3^{4}\cdot 5^{6}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.4.484000000.4 x8 - 3x6 + 4x4 - 7x2 + 1 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.484000000.5 x8 - 7x6 + 34x4 - 88x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.4.484000000.5 x8 - 5x6 + 5x4 - 25x2 + 25 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.484000000.6 x8 - x6 + 16x4 - 66x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.484000000.9 x8 + x6 + 16x4 + 66x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.500640625.1 x8 - x7 - 7x6 + 15x5 + 26x4 - 45x3 - 43x2 + 88x + 121 \( 5^{6}\cdot 179^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.511890625.1 x8 - 3x7 + 7x6 - 5x5 + 16x4 + 15x3 + 63x2 + 81x + 81 \( 5^{6}\cdot 181^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.570015625.1 x8 - 3x7 - 5x6 + 22x5 + 19x4 - 102x3 + 108x + 81 \( 5^{6}\cdot 191^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.618765625.1 x8 - 3x7 - 3x6 + 20x5 + 21x4 - 70x3 - 72x2 + 66x + 121 \( 5^{6}\cdot 199^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.682515625.4 x8 - 3x7 + 2x5 + 9x4 + 8x3 - 192x + 256 \( 5^{6}\cdot 11^{2}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.682515625.5 x8 - 3x7 + 5x6 + 2x5 + 19x4 + 28x3 + 100x2 + 88x + 121 \( 5^{6}\cdot 11^{2}\cdot 19^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$
8.0.695640625.1 x8 - 3x7 - 4x6 + 21x5 + 19x4 - 87x3 - 46x2 + 99x + 121 \( 5^{6}\cdot 211^{2} \) $C_2^2:C_4$ (as 8T10) Trivial
8.0.819390625.1 x8 - 3x7 + 10x6 - 13x5 + 29x4 - 7x3 + 80x2 + 143x + 121 \( 5^{6}\cdot 229^{2} \) $C_2^2:C_4$ (as 8T10) $[3]$
8.0.822083584.2 x8 + 4x4 + 8x2 + 1 \( 2^{24}\cdot 7^{2} \) $C_2^2:C_4$ (as 8T10) $[2]$

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