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Label Polynomial Discriminant Galois group Class group
8.0.1513728.1 x8 - 2x7 + x6 + 2x5 - 3x4 - 2x3 + x2 + 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 73 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.4002048.1 x8 - 4x7 + 10x6 - 16x5 + 18x4 - 14x3 + 7x2 - 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 193 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.4313088.1 x8 - 2x7 - 2x6 + 6x5 + x4 - 10x3 + 6x2 + 1 \( 2^{12}\cdot 3^{4}\cdot 13 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.4997376.1 x8 - x6 - 2x5 + 4x3 + 6x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 241 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.7405568.1 x8 - 4x7 + 10x6 - 16x5 + 21x4 - 20x3 + 12x2 - 4x + 1 \( 2^{16}\cdot 113 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.8481024.1 x8 - 3x6 - 2x5 + 4x4 + 6x3 + x2 - 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 409 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.9163125.1 x8 - x7 - 2x6 + 4x5 + 3x4 - 4x3 - 2x2 + x + 1 \( 3^{4}\cdot 5^{4}\cdot 181 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.9476352.1 x8 - 4x7 + 12x6 - 22x5 + 33x4 - 34x3 + 26x2 - 12x + 4 \( 2^{8}\cdot 3^{4}\cdot 457 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.9974016.1 x8 - 4x7 + 2x6 + 8x5 - 6x4 - 6x3 + 3x2 + 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 37 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.9974016.2 x8 - 2x7 + 3x6 + 2x5 - 4x4 - 4x3 + 3x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 37 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.10747904.1 x8 - 4x7 + 10x6 - 16x5 + 20x4 - 16x3 + 10x2 - 4x + 1 \( 2^{18}\cdot 41 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.11593125.1 x8 - 4x7 + 5x6 - x5 - 3x3 + 3x2 - x + 1 \( 3^{4}\cdot 5^{4}\cdot 229 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.12275712.1 x8 - 2x7 + 4x6 - 8x5 + 18x4 - 28x3 + 28x2 - 16x + 4 \( 2^{12}\cdot 3^{4}\cdot 37 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.12462336.1 x8 - 4x7 + 4x6 + 2x5 - 8x3 + x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 601 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.14240000.3 x8 - 2x7 + x6 - 4x5 + 11x4 - 12x3 + 9x2 - 4x + 1 \( 2^{8}\cdot 5^{4}\cdot 89 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.15390000.1 x8 - 3x7 + 9x6 - 15x5 + 20x4 - 15x3 + 9x2 - 3x + 1 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 19 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.15390000.2 x8 - 3x7 + 2x6 - x5 + 6x4 - 7x3 + 3x2 - 4x + 4 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 19 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.15945984.1 x8 - 2x7 + 2x6 + 8x4 + 6x3 + 5x2 + 4x + 1 \( 2^{8}\cdot 3^{4}\cdot 769 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.16443648.1 x8 - 2x7 + 9x6 - 10x5 + 17x4 - 10x3 + 9x2 - 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 61 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.16443648.2 x8 - 2x7 - x6 + 4x5 + 3x4 - 6x3 - 6x2 + 4x + 4 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 61 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.16842752.1 x8 + x4 - 4x3 + 6x2 - 4x + 1 \( 2^{16}\cdot 257 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.17668125.1 x8 - 2x7 + 4x6 - 5x5 + 6x4 - x3 - 2x2 + 2x + 1 \( 3^{4}\cdot 5^{4}\cdot 349 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.17825792.1 x8 - 4x5 + 2x4 + 8x2 - 8x + 2 \( 2^{20}\cdot 17 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.18102528.1 x8 + 4x6 - 6x5 + 9x4 - 6x3 + 10x2 - 12x + 4 \( 2^{8}\cdot 3^{6}\cdot 97 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.18911232.1 x8 - 2x7 + 5x6 - 12x5 + 17x4 - 12x3 + 5x2 - 2x + 1 \( 2^{12}\cdot 3^{5}\cdot 19 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.20238336.1 x8 - 4x7 + 6x6 + 2x5 - 7x4 - 2x3 + 10x2 + 6x + 1 \( 2^{12}\cdot 3^{4}\cdot 61 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.21198429.1 x8 - 3x7 + 2x6 - 2x5 + 3x4 + x3 + 3x2 - 2x + 1 \( 3^{4}\cdot 7^{4}\cdot 109 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.21781872.1 x8 - x7 + 3x6 - 5x5 + 8x4 - 5x3 + 3x2 - x + 1 \( 2^{4}\cdot 3^{4}\cdot 7^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.22085632.1 x8 - 4x7 + 10x6 - 16x5 + 19x4 - 16x3 + 10x2 - 4x + 2 \( 2^{16}\cdot 337 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.23134208.1 x8 - 4x6 - 4x5 + 3x4 + 12x3 + 12x2 + 4x + 1 \( 2^{16}\cdot 353 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.23908608.1 x8 - 7x6 - 4x5 + 15x4 + 14x3 - 6x2 - 4x + 4 \( 2^{8}\cdot 3^{4}\cdot 1153 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.25110000.1 x8 - 3x7 + 4x6 + 2x5 - 7x4 + 4x3 + 6x2 + x + 1 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.25110000.2 x8 - 3x7 + 8x6 - 16x5 + 27x4 - 34x3 + 30x2 - 16x + 4 \( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.26894592.1 x8 - 2x7 - x6 - x4 + 18x3 - 7x2 - 20x + 13 \( 2^{8}\cdot 3^{4}\cdot 1297 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.27388125.1 x8 - 4x7 + 11x6 - 19x5 + 27x4 - 27x3 + 21x2 - 10x + 4 \( 3^{4}\cdot 5^{4}\cdot 541 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.27392256.1 x8 - 4x7 + 4x6 + 2x5 - 3x4 - 2x3 - 2x2 + 4x + 4 \( 2^{8}\cdot 3^{4}\cdot 1321 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.27793125.1 x8 - x7 + 5x6 - 7x5 + 10x4 - 14x3 + 11x2 - 8x + 4 \( 3^{6}\cdot 5^{4}\cdot 61 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.29382912.1 x8 - 4x6 - 6x5 + 13x4 + 6x3 - 18x + 9 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 109 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.29382912.3 x8 - 2x7 + x6 + 4x5 - 12x4 - 4x3 + 16x2 + 8x + 1 \( 2^{8}\cdot 3^{4}\cdot 13\cdot 109 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.29818125.2 x8 - x7 + 6x6 - 2x5 + 11x4 - 2x3 + 6x2 - x + 1 \( 3^{4}\cdot 5^{4}\cdot 19\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.29818125.3 x8 - x7 - 3x6 - x5 + 8x4 + 4x3 - 5x2 - 6x + 4 \( 3^{4}\cdot 5^{4}\cdot 19\cdot 31 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.32182272.1 x8 - 2x7 + 15x4 - 44x3 + 56x2 - 38x + 13 \( 2^{12}\cdot 3^{4}\cdot 97 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.32182272.2 x8 - 2x7 + 3x6 + 4x4 - 6x3 + 6x2 - 4x + 1 \( 2^{12}\cdot 3^{4}\cdot 97 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.34359552.2 x8 - 4x7 + x6 + 8x5 + 3x4 - 14x3 - 2x2 + 4x + 4 \( 2^{8}\cdot 3^{4}\cdot 1657 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.35893125.1 x8 - 4x7 + 9x6 - 13x5 + 15x4 - 13x3 + 11x2 - 6x + 4 \( 3^{4}\cdot 5^{4}\cdot 709 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.35913728.2 x8 + 2x6 - 8x5 + 16x4 - 20x3 + 16x2 - 8x + 2 \( 2^{18}\cdot 137 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.36163584.1 x8 - 2x7 - 6x4 + 4x3 + 20x2 + 16x + 4 \( 2^{12}\cdot 3^{4}\cdot 109 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.36847872.1 x8 - 2x7 - 3x6 + 8x5 + 5x4 - 16x3 - 12x2 + 16x + 16 \( 2^{8}\cdot 3^{4}\cdot 1777 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.37345536.1 x8 - 4x7 + 11x6 - 18x5 + 29x4 - 36x3 + 41x2 - 28x + 13 \( 2^{8}\cdot 3^{4}\cdot 1801 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
8.0.37814272.1 x8 + 6x6 - 8x5 + 11x4 - 12x3 + 6x2 - 4x + 2 \( 2^{16}\cdot 577 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) Trivial
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