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Label Polynomial Discriminant Galois group Class group
8.0.25401600.1 x8 - 2x7 + 4x6 - 10x5 + 9x4 - 14x3 + 16x2 - 4x + 13 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.39690000.1 x8 - 3x7 - x6 + 10x5 - 20x3 + 9x2 + 7x + 1 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.51840000.1 x8 - 3x6 + 5x4 - 6x2 + 4 \( 2^{10}\cdot 3^{4}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.62726400.1 x8 + 5x6 - 2x5 + 18x4 - 14x3 + 30x2 - 14x + 13 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.77792400.1 x8 - x7 - 2x6 + 8x5 - 6x4 - 5x3 + 16x2 - 14x + 7 \( 2^{4}\cdot 3^{4}\cdot 5^{2}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.87609600.1 x8 - 2x7 - 6x6 + 12x5 + 24x4 - 14x3 - 31x2 + 4x + 13 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.122943744.1 x8 - 4x7 + 9x6 - 4x5 - 16x4 + 34x3 - 20x2 - 24x + 37 \( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.132710400.1 x8 - 4x6 - 8x5 + x4 + 16x3 + 22x2 + 12x + 3 \( 2^{16}\cdot 3^{4}\cdot 5^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.132710400.2 x8 - 8x6 + 33x4 - 50x2 + 25 \( 2^{16}\cdot 3^{4}\cdot 5^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.138297600.1 x8 - 2x7 + 7x6 - 2x5 - 4x3 + 3x2 + 4x + 1 \( 2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.158760000.1 x8 - 3x7 - 2x6 + 8x5 + 11x4 - 20x3 - 12x2 + 7x + 19 \( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.171714816.5 x8 - 4x7 - x6 + 16x5 + x4 - 24x3 - 12x2 + 36 \( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.171714816.6 x8 - 5x6 - 8x5 - 4x4 + 26x3 + 60x2 + 62x + 37 \( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.187142400.1 x8 - 2x7 + 7x6 - 18x5 + 34x4 - 64x3 + 78x2 - 84x + 61 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 19^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.199148544.1 x8 - 7x6 + 17x4 - 14x2 + 4 \( 2^{10}\cdot 3^{4}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.216090000.1 x8 - x7 + x6 + 5x5 - 5x3 + x2 + x + 1 \( 2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.235929600.1 x8 - 12x6 - 12x5 + 36x4 + 72x3 + 40x2 + 12x + 9 \( 2^{20}\cdot 3^{2}\cdot 5^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.260112384.1 x8 + 8x6 - 4x5 + 15x4 - 16x3 + 12x2 - 16x + 7 \( 2^{16}\cdot 3^{4}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.292410000.1 x8 - 3x7 + 14x6 - 32x5 + 69x4 - 92x3 + 102x2 - 65x + 31 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 19^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.311169600.1 x8 - 2x7 + 10x6 - 15x5 + 28x4 - 34x3 + 30x2 - 21x + 7 \( 2^{6}\cdot 3^{4}\cdot 5^{2}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.321126400.1 x8 - 4x7 - 2x6 + 16x5 + 8x4 - 28x3 - 16x2 + 24x + 18 \( 2^{18}\cdot 5^{2}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.354041856.1 x8 - 2x6 + 2x4 + 6x2 + 9 \( 2^{14}\cdot 3^{2}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.368640000.1 x8 - 2x6 + 2x4 - 6x2 + 9 \( 2^{16}\cdot 3^{2}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.4.368640000.1 x8 - 2x6 - 8x5 - 5x4 + 8x3 + 12x2 + 4x - 1 \( 2^{16}\cdot 3^{2}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.368640000.2 x8 - 4x6 + 13x4 - 18x2 + 9 \( 2^{16}\cdot 3^{2}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.392040000.1 x8 - 9x6 - 8x5 + 31x4 + 36x3 - 23x2 - 28x + 16 \( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.406425600.1 x8 - 2x7 - 3x6 - 4x5 + 3x4 + 28x3 + 37x2 + 18x + 3 \( 2^{12}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.406425600.2 x8 - 2x7 + 7x6 - 20x5 + 42x4 - 58x3 + 52x2 - 28x + 7 \( 2^{12}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.424030464.1 x8 - 2x7 - 5x6 + 10x5 + 15x4 - 46x3 - 17x2 + 68x + 73 \( 2^{8}\cdot 3^{4}\cdot 11^{2}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.462422016.1 x8 - 4x6 - 12x5 + 22x4 + 16x3 + 8x2 - 80x + 50 \( 2^{20}\cdot 3^{2}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.466560000.1 x8 - 6x6 + 27x4 - 54x2 + 36 \( 2^{10}\cdot 3^{6}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.498182400.1 x8 - 2x7 + 7x6 + 2x5 + 9x4 + 52x3 + 28x2 + 80x + 100 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 31^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.530841600.1 x8 - 10x6 + 62x4 - 140x2 + 100 \( 2^{18}\cdot 3^{4}\cdot 5^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.4.530841600.1 x8 - 4x7 + 6x6 - 4x5 - 4x4 + 4x3 + 4x2 - 2 \( 2^{18}\cdot 3^{4}\cdot 5^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.547560000.1 x8 - 7x6 - 10x5 + 3x4 + 20x3 + 63x2 + 110x + 76 \( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.588305025.1 x8 - 3x7 + 6x6 - x5 + 19x4 + 9x3 + 22x2 + 7x + 7 \( 3^{4}\cdot 5^{2}\cdot 7^{4}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.635040000.1 x8 - 2x7 - 4x5 - 12x4 + 16x3 + 43x2 + 30x + 9 \( 2^{8}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.4.635040000.1 x8 - 2x7 - 3x6 + 10x5 - 10x4 - 4x3 + 10x2 + 6x + 1 \( 2^{8}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.642318336.1 x8 + 4x6 - 8x5 + 5x4 - 16x3 + 18x2 - 4x + 7 \( 2^{16}\cdot 3^{4}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.642318336.2 x8 - 10x6 + 50x4 - 110x2 + 121 \( 2^{16}\cdot 3^{4}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.700131600.1 x8 - x7 - 4x6 - x5 - 2x4 + x3 + 29x2 + 40x + 16 \( 2^{4}\cdot 3^{6}\cdot 5^{2}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.709689600.1 x8 - 6x6 - 14x5 + 46x4 + 30x3 - 29x2 - 172x + 157 \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 37^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.778410000.1 x8 - 3x7 - 7x6 + 20x5 + 21x4 - 55x3 - 27x2 + 98x + 76 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 31^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.788486400.1 x8 - 4x7 + 5x6 + 8x5 - 41x4 + 70x3 - 22x2 - 164x + 244 \( 2^{8}\cdot 3^{6}\cdot 5^{2}\cdot 13^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.829440000.1 x8 + x4 + 4 \( 2^{14}\cdot 3^{4}\cdot 5^{4} \) $C_2^3 : D_4 $ (as 8T22) $[2]$
8.0.843321600.5 x8 + 3x6 - 12x5 + 8x4 - 18x3 + 35x2 - 18x + 5 \( 2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 11^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.843321600.6 x8 - 4x7 + 5x6 + 4x5 - 12x4 - 2x3 + 24x2 - 20x + 5 \( 2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 11^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.854509824.1 x8 - 2x7 - 9x6 + 24x5 + 36x4 - 110x3 - 109x2 + 184x + 193 \( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 29^{2} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.864360000.1 x8 - x7 + x6 - x5 + 4x4 + x3 + 3x2 + 10x + 11 \( 2^{6}\cdot 3^{2}\cdot 5^{4}\cdot 7^{4} \) $C_2^3 : D_4 $ (as 8T22) Trivial
8.0.882090000.1 x8 - 3x7 + 4x6 - 9x5 + 30x4 - 27x3 + 25x2 - 126x + 124 \( 2^{4}\cdot 3^{6}\cdot 5^{4}\cdot 11^{2} \) $C_2^3 : D_4 $ (as 8T22) $[2]$

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