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Label Polynomial Discriminant Galois group Class group
8.0.1817487424.1 x8 - x7 + 6x6 - 2x5 + 12x4 + 4x3 + 14x2 + 2 \( 2^{6}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.9597924961.1 x8 - x7 + x6 + 3x5 + 5x4 - 5x3 + 7x + 9 \( 313^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.9597924961.2 x8 - x7 - x6 - 4x5 + x4 + 11x3 + 16x2 + 5x + 1 \( 313^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.18078415936.1 x8 - x7 + 7x6 + 7x5 + 7x4 + 7x3 + 7x2 + 5x + 2 \( 2^{6}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.29079798784.1 x8 - 2x7 + 8x6 - 2x5 + 14x4 + 10x3 + 28x2 + 10x + 1 \( 2^{10}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.72313663744.1 x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 2x + 1 \( 2^{8}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.100367308864.1 x8 - 3x7 + 4x6 - 16x5 + 46x4 - 70x3 + 82x2 - 48x + 22 \( 2^{6}\cdot 199^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.116319195136.1 x8 - 2x7 - 4x6 - 8x5 + 56x4 - 54x3 + 20x2 - 4x + 1 \( 2^{12}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.116319195136.3 x8 - 2x7 + 10x6 - 6x5 + 2x4 + 8x3 - 16x2 + 16x + 26 \( 2^{12}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.272225149504.1 x8 - x7 - 9x6 - x5 + 41x4 + 21x3 - 67x2 - 35x + 66 \( 2^{6}\cdot 7^{4}\cdot 11^{6} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.272225149504.2 x8 - 3x7 + 9x6 - 21x5 + 33x4 - 69x3 + 7x2 - 7x + 238 \( 2^{6}\cdot 7^{4}\cdot 11^{6} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.387790161984.1 x8 + 4x6 - 14x5 + 6x4 + 16x3 + 32x2 + 18x + 8 \( 2^{6}\cdot 3^{8}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.401469235456.1 x8 - 2x7 + 4x6 - 4x5 - 8x4 + 4x3 + 16x2 - 14x + 6 \( 2^{8}\cdot 199^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.401469235456.2 x8 - 2x7 - 4x6 + 4x5 + 12x4 - 16x3 + 68x + 52 \( 2^{8}\cdot 199^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.525346636864.3 x8 - 2x7 + 2x6 + 20x5 + 20x4 + 56x2 + 52x + 40 \( 2^{6}\cdot 7^{4}\cdot 43^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.525346636864.4 x8 - 2x7 + 2x6 - 12x5 + 64x4 - 184x3 + 296x2 - 280x + 128 \( 2^{6}\cdot 7^{4}\cdot 43^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.525346636864.5 x8 - 2x7 + 14x6 - 38x5 + 100x4 - 198x3 + 338x2 - 322x + 139 \( 2^{6}\cdot 7^{4}\cdot 43^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.591559418641.1 x8 - x7 + 11x6 - 13x5 + 16x4 - 10x3 + 17x2 - 7x + 4 \( 877^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.591559418641.2 x8 - 2x7 - 2x6 + 7x5 + 3x4 - 34x3 + 93x2 - 29x + 39 \( 877^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.777431921841.1 x8 - 9x6 - 4x5 + 24x4 + 21x3 + 22x2 - 3x + 3 \( 3^{4}\cdot 313^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.777431921841.2 x8 - 3x7 + 9x6 - 19x5 + 35x4 - 39x3 + 19x2 - 4x + 4 \( 3^{4}\cdot 313^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.1135929640000.1 x8 - 2x7 + 16x6 - 20x5 + 56x4 - 56x3 + 80x2 - 80x + 64 \( 2^{6}\cdot 5^{4}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$
8.0.1157018619904.1 x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 18x + 23 \( 2^{12}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.1157018619904.2 x8 - 2x7 + 28x4 - 14x3 - 56x2 + 40x + 53 \( 2^{12}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.1464351690816.1 x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 30x + 64 \( 2^{6}\cdot 3^{4}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$
8.0.1605876941824.1 x8 - 2x6 - 12x5 + 40x4 - 76x3 + 74x2 - 24x + 19 \( 2^{10}\cdot 199^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.1624709678881.2 x8 - x7 - 5x6 + 11x5 + 3x4 - 27x3 + 29x2 - 11x + 3 \( 1129^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.1688107729984.5 x8 - x7 + 4x6 - 2x5 + 4x4 - 60x3 + 120x2 - 88x + 24 \( 2^{6}\cdot 13^{4}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.1688107729984.6 x8 - x7 + 4x6 + 16x4 - 20x3 + 24x2 + 20x + 4 \( 2^{6}\cdot 13^{4}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.1861107122176.20 x8 + 4x6 - 12x5 + 16x4 - 40x3 + 72x2 - 52x + 202 \( 2^{16}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.1861107122176.22 x8 - 4x7 + 12x6 - 8x5 - 4x4 - 40x3 + 344x2 - 608x + 612 \( 2^{16}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial
8.0.2101386547456.12 x8 - 2x7 + 2x6 - 16x5 + 34x4 + 4x3 - 94x2 + 16x + 153 \( 2^{8}\cdot 7^{4}\cdot 43^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$
8.0.2420662999104.2 x8 - 3x7 - 7x6 + 35x5 - 21x4 - 77x3 + 189x2 - 171x + 72 \( 2^{6}\cdot 3^{8}\cdot 7^{8} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
8.0.2528484794641.1 x8 - 2x7 + x6 + 19x5 + 31x4 + 17x3 + 9x2 + 13x + 9 \( 13^{4}\cdot 97^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.2528484794641.2 x8 - x7 + 12x6 + 2x5 + 49x4 + 87x3 + 148x2 + 87x + 31 \( 13^{4}\cdot 97^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.2528484794641.3 x8 - x7 - 7x6 + 10x5 - 15x4 + 5x3 + 111x2 - 171x + 134 \( 13^{4}\cdot 97^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$
8.0.2528484794641.4 x8 + 7x6 - 11x5 + 65x4 + 43x3 + 191x2 + 137x + 240 \( 13^{4}\cdot 97^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.3490111457856.2 x8 + 18x6 - 6x5 + 54x4 - 108x3 + 66x2 - 18x + 9 \( 2^{6}\cdot 3^{10}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$
8.0.3490111457856.4 x8 - 2x7 + 4x6 + 4x5 + 10x4 + 142x3 + 196x2 + 58x + 136 \( 2^{6}\cdot 3^{10}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$
8.0.3490111457856.5 x8 - 3x7 + 6x6 + 30x5 - 18x4 - 90x3 + 198x2 - 162x + 54 \( 2^{6}\cdot 3^{10}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.4355602392064.2 x8 - 4x7 + 12x6 - 20x5 + 46x4 - 94x3 + 126x2 - 110x + 49 \( 2^{10}\cdot 7^{4}\cdot 11^{6} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.4355602392064.4 x8 - 2x7 + 2x6 - 8x5 + 60x4 - 60x3 - 52x2 + 166x + 235 \( 2^{10}\cdot 7^{4}\cdot 11^{6} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$
8.0.4543718560000.9 x8 + 4x6 - 2x5 + 52x4 - 124x3 + 352x2 - 58x + 91 \( 2^{8}\cdot 5^{4}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$
8.0.4543718560000.10 x8 - 2x6 - 8x5 - 16x4 - 2x3 + 58x2 + 88x + 171 \( 2^{8}\cdot 5^{4}\cdot 73^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$
8.0.5323914784321.1 x8 + 14x6 + 98x4 + 280x2 - 31x + 252 \( 7^{8}\cdot 31^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
8.0.5482378736704.1 x8 - 3x7 + 11x6 - 37x5 + 73x4 - 79x3 + 51x2 - 23x + 12 \( 2^{6}\cdot 541^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
8.0.5482378736704.2 x8 - x7 + 5x6 + x5 - 23x4 + 9x3 + 27x2 - 9x + 14 \( 2^{6}\cdot 541^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
8.0.5482378736704.3 x8 - x7 - 4x6 + 18x5 - 4x4 - 36x3 + 50x2 - 28x + 6 \( 2^{6}\cdot 541^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
8.0.5857406763264.1 x8 - 4x7 + 14x6 - 14x5 + 14x4 + 28x3 + 14x2 - 18x + 121 \( 2^{8}\cdot 3^{4}\cdot 7^{10} \) $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$
8.0.6029426229121.1 x8 - 3x7 + 17x6 - 25x5 + 50x4 + 118x3 - 75x2 + 113x + 228 \( 1567^{4} \) $C_2^3:(C_7: C_3)$ (as 8T36) Trivial (GRH)
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