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Label Polynomial Discriminant Galois group Class group
8.0.3504384.1 x8 - x6 - x4 + x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.6906384.1 x8 - x7 + x6 + x5 - x3 + x2 - 2x + 1 \( 2^{4}\cdot 3^{4}\cdot 73^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.12278016.1 x8 - x6 - 2x5 - x4 + 2x3 + 3x2 + 2x + 1 \( 2^{8}\cdot 3^{2}\cdot 73^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.16842816.1 x8 - x7 - x6 - x5 + 4x4 - 5x3 + 5x2 - 2x + 1 \( 2^{6}\cdot 3^{6}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.18939904.1 x8 + x4 - 2x2 + 1 \( 2^{16}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.22581504.1 x8 - 2x7 - x6 - 2x5 + 7x4 + 2x3 - x2 + 2x + 1 \( 2^{8}\cdot 3^{6}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.24920064.1 x8 - 2x7 + 2x5 - 2x3 + 4x2 - 2x + 1 \( 2^{14}\cdot 3^{2}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.25310961.1 x8 - x7 + 6x6 + 9x4 + 8x3 + 8x2 + 5x + 7 \( 3^{4}\cdot 13^{2}\cdot 43^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.4.25755625.1 x8 - x7 + 3x5 - 5x4 + x3 + 6x2 - 3x - 1 \( 5^{4}\cdot 7^{2}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.26708224.1 x8 - 2x7 + 3x6 - 10x5 + 15x4 - 10x3 + 7x2 - 4x + 1 \( 2^{8}\cdot 17^{2}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.27040000.1 x8 - 2x7 + x6 + 4x5 - 5x4 - 4x3 + 14x2 - 12x + 4 \( 2^{8}\cdot 5^{4}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.27541504.1 x8 - 4x6 + 9x4 - 8x2 + 4 \( 2^{14}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.28387584.1 x8 - 3x6 + x4 + 3x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 37^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.31539456.3 x8 - 9x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.35605089.1 x8 - x7 + 2x6 + 5x5 + x4 + 7x3 + 8x2 + 13x + 13 \( 3^{6}\cdot 13^{2}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.38440000.1 x8 - x7 - x6 + 2x5 + 2x4 - 4x3 + x2 + 3x + 1 \( 2^{6}\cdot 5^{4}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.38452401.1 x8 - x7 - 3x6 + 3x5 - 13x3 + 5x2 + 26x + 13 \( 3^{4}\cdot 13^{2}\cdot 53^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.39337984.1 x8 - x6 + x2 + 1 \( 2^{14}\cdot 7^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.4.46240000.1 x8 - 4x7 + 5x6 + 2x5 - 8x4 + 2x2 + 2x - 1 \( 2^{8}\cdot 5^{4}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.47155689.1 x8 - x7 + x5 + 5x4 + x3 - x + 1 \( 3^{4}\cdot 7^{2}\cdot 109^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.48274704.1 x8 - x7 - 3x6 + 3x5 + 4x4 - 3x3 + 3x2 - 2x + 1 \( 2^{4}\cdot 3^{4}\cdot 193^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.48776256.1 x8 + 3x6 - x4 - 6x2 + 4 \( 2^{6}\cdot 3^{4}\cdot 97^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.49561600.1 x8 - 2x7 + 6x6 - 4x5 + 6x4 + 4x3 + 4x + 2 \( 2^{14}\cdot 5^{2}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.49787136.2 x8 - 2x7 - 4x5 + 2x4 + 8x3 + 9x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 7^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.50481025.1 x8 - 3x7 + 2x6 + x5 - 2x4 + 4x3 - x + 2 \( 5^{2}\cdot 7^{4}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.50694400.1 x8 - 2x7 + 5x6 - 2x5 + 2x4 + 4x3 + 10x2 + 6x + 1 \( 2^{8}\cdot 5^{2}\cdot 89^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.51380224.2 x8 + 2x6 - 4x5 + 12x4 - 16x3 + 16x2 - 8x + 2 \( 2^{20}\cdot 7^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.52301824.1 x8 - 3x6 - 2x5 + 2x4 + 4x3 + 5x2 + 2x + 1 \( 2^{12}\cdot 113^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.56070144.1 x8 - 2x6 - 4x4 + 8x2 + 16 \( 2^{12}\cdot 3^{4}\cdot 13^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.65173329.1 x8 - 3x7 - 2x6 + 6x5 + 15x4 - 12x3 - 26x2 - 3x + 31 \( 3^{6}\cdot 13^{2}\cdot 23^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.65205625.1 x8 - 3x7 + 3x6 - 2x5 + 5x4 - 6x3 + 2x2 + 4x + 1 \( 5^{4}\cdot 17^{2}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.66341025.1 x8 - x7 - 3x6 - 2x5 + 5x4 + 4x3 + 6x2 + 2x + 1 \( 3^{4}\cdot 5^{2}\cdot 181^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.67240000.1 x8 - x6 + 3x4 - 2x2 + 4 \( 2^{6}\cdot 5^{4}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.67765824.1 x8 - x7 - x6 - x5 + 2x4 + x3 - x2 + x + 1 \( 2^{6}\cdot 3^{2}\cdot 7^{6} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.67815225.1 x8 - 3x7 + 8x6 - 15x5 + 21x4 - 15x3 + 8x2 - 3x + 1 \( 3^{6}\cdot 5^{2}\cdot 61^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.75272976.1 x8 - x7 - 3x6 + x5 + 8x4 + x3 - 3x2 - x + 1 \( 2^{4}\cdot 3^{4}\cdot 241^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.75759616.3 x8 - 2x6 - 2x4 + 4x2 + 4 \( 2^{18}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.77158656.1 x8 - 3x6 + 10x4 - 6x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 61^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.78907689.1 x8 - x7 + 2x6 - x5 + x4 - 5x3 + 20x2 - 23x + 13 \( 3^{6}\cdot 7^{2}\cdot 47^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.4.79210000.1 x8 - 4x6 - 3x4 + 4x2 + 1 \( 2^{4}\cdot 5^{4}\cdot 89^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.81288256.1 x8 - x7 + 2x6 - 3x5 + 2x4 + 5x3 - 3x2 - 6x + 4 \( 2^{6}\cdot 7^{4}\cdot 23^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.84768849.1 x8 - x7 - 4x6 + 11x5 - 5x4 - 17x3 + 32x2 - 23x + 7 \( 3^{6}\cdot 11^{2}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.85821696.1 x8 - 3x6 - 4x5 + 3x4 + 4x3 + 5x2 + 2x + 1 \( 2^{8}\cdot 3^{2}\cdot 193^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.86266944.1 x8 - 3x7 + 5x6 - 3x5 + 3x3 + 5x2 + 3x + 1 \( 2^{6}\cdot 3^{6}\cdot 43^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.4.88830625.1 x8 - x7 - x6 + 2x5 - 3x4 + 6x3 - 4x2 - 2x + 1 \( 5^{4}\cdot 13^{2}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.93702400.1 x8 - x6 + x4 + x2 + 1 \( 2^{8}\cdot 5^{2}\cdot 11^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.98406400.1 x8 - 2x7 + 5x6 - 6x5 + 10x4 - 6x3 + 3x2 + 2x + 1 \( 2^{12}\cdot 5^{2}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.98406400.2 x8 - 6x5 + 7x4 + 6x3 + 10x2 + 6x + 1 \( 2^{12}\cdot 5^{2}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.0.98724096.1 x8 - 2x7 + 9x6 - 14x5 + 25x4 - 24x3 + 21x2 - 12x + 3 \( 2^{8}\cdot 3^{6}\cdot 23^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial
8.4.103530625.1 x8 - 3x7 + 3x6 - 2x5 - 7x4 + 12x3 + 8x - 1 \( 5^{4}\cdot 11^{2}\cdot 37^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) Trivial

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