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Label Polynomial Discriminant Galois group Class group
8.0.1750329.1 x8 - 3x7 + 4x6 - 3x5 + 3x4 - 3x3 + 4x2 - 3x + 1 \( 3^{6}\cdot 7^{4} \) $D_4$ Trivial
8.0.2313441.1 x8 - x7 + 2x6 + 3x5 - x4 + 3x3 + 2x2 - x + 1 \( 3^{4}\cdot 13^{4} \) $D_4$ Trivial
8.0.2560000.1 x8 - 2x7 + 2x6 + 2x5 - 2x4 + 2x3 + 2x2 - 2x + 1 \( 2^{12}\cdot 5^{4} \) $D_4$ Trivial
8.0.2985984.1 x8 - 2x7 + 2x6 - 2x5 + 7x4 - 10x3 + 8x2 - 4x + 1 \( 2^{12}\cdot 3^{6} \) $D_4$ Trivial
8.0.4194304.1 x8 + 6x4 + 1 \( 2^{22} \) $D_4$ Trivial
8.0.9150625.1 x8 - 3x7 + 9x6 - 13x5 + 18x4 - 11x3 + 11x2 - 4x + 1 \( 5^{4}\cdot 11^{4} \) $D_4$ Trivial
8.0.9834496.2 x8 + 4x6 + x4 - 6x2 + 4 \( 2^{12}\cdot 7^{4} \) $D_4$ Trivial
8.0.16777216.2 x8 - 4x6 + 8x4 - 4x2 + 1 \( 2^{24} \) $D_4$ Trivial
8.0.21381376.2 x8 + 5x6 + 4x4 + 5x2 + 1 \( 2^{8}\cdot 17^{4} \) $D_4$ Trivial
8.0.30118144.2 x8 - 2x7 + 2x6 + 4x5 - x4 + 4x3 + 2x2 - 2x + 1 \( 2^{8}\cdot 7^{6} \) $D_4$ Trivial
8.0.40960000.2 x8 + 3x4 + 1 \( 2^{16}\cdot 5^{4} \) $D_4$ Trivial
8.0.47775744.1 x8 + 3x4 + 9 \( 2^{16}\cdot 3^{6} \) $D_4$ Trivial
8.0.64000000.3 x8 - 4x7 + 8x6 - 10x5 + 11x4 - 10x3 + 2x2 + 2x + 1 \( 2^{12}\cdot 5^{6} \) $D_4$ $[2]$
8.0.81450625.1 x8 - x7 + 8x6 + 7x5 + 19x4 + 7x3 + 8x2 - x + 1 \( 5^{4}\cdot 19^{4} \) $D_4$ $[2]$
8.0.95004009.1 x8 - 3x7 + x6 + 6x5 + 6x4 + 6x3 + x2 - 3x + 1 \( 3^{6}\cdot 19^{4} \) $D_4$ Trivial
8.0.116985856.1 x8 - 4x7 + 8x6 - 6x5 + 7x4 - 10x3 + 2x2 - 6x + 9 \( 2^{12}\cdot 13^{4} \) $D_4$ Trivial
8.0.143496441.1 x8 - x7 + 2x6 - 3x5 - x4 + 6x3 + 8x2 + 8x + 16 \( 3^{4}\cdot 11^{6} \) $D_4$ Trivial
8.0.151807041.1 x8 - 5x6 + 28x4 + 15x2 + 9 \( 3^{4}\cdot 37^{4} \) $D_4$ $[2]$
8.0.157351936.3 x8 + 2x6 + 10x4 + 2x2 + 1 \( 2^{16}\cdot 7^{4} \) $D_4$ $[2]$
8.0.207360000.5 x8 - 2x7 + 2x6 - 6x5 + 14x4 - 30x3 + 50x2 - 50x + 25 \( 2^{12}\cdot 3^{4}\cdot 5^{4} \) $D_4$ $[2]$
8.0.228765625.2 x8 - x6 + 16x4 - x2 + 1 \( 5^{6}\cdot 11^{4} \) $D_4$ $[2]$
8.0.339738624.3 x8 - 4x7 + 4x6 - 4x5 + 12x4 + 4x3 + 4x2 + 4x + 1 \( 2^{22}\cdot 3^{4} \) $D_4$ $[2]$
8.0.339738624.6 x8 - 4x7 + 8x6 - 4x5 - 4x4 - 4x3 + 16x2 - 12x + 9 \( 2^{22}\cdot 3^{4} \) $D_4$ $[2]$
8.0.339738624.8 x8 - 4x7 + 8x5 + 14x4 - 32x3 + 28x2 - 48x + 34 \( 2^{22}\cdot 3^{4} \) $D_4$ $[2]$
8.0.339738624.9 x8 - 4x6 + 10x4 - 24x2 + 36 \( 2^{22}\cdot 3^{4} \) $D_4$ Trivial
8.0.339738624.10 x8 + 4x6 + 10x4 + 24x2 + 36 \( 2^{22}\cdot 3^{4} \) $D_4$ Trivial
8.0.342102016.2 x8 - 2x7 + 3x6 + 20x5 + 3x4 - 2x3 + 9x2 - 8x + 8 \( 2^{12}\cdot 17^{4} \) $D_4$ Trivial
8.0.342102016.4 x8 - 2x7 + x6 - 10x5 + 50x4 - 74x3 + 59x2 - 30x + 9 \( 2^{12}\cdot 17^{4} \) $D_4$ Trivial
8.0.390971529.2 x8 - 9x6 + 32x4 - 9x2 + 1 \( 3^{4}\cdot 13^{6} \) $D_4$ $[2]$
8.8.442050625.1 x8 - 2x7 - 12x6 + 26x5 + 17x4 - 36x3 - 5x2 + 11x - 1 \( 5^{4}\cdot 29^{4} \) $D_4$ Trivial
8.0.448084224.6 x8 - 3x6 + 12x4 + 9x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 7^{4} \) $D_4$ $[2]$
8.0.481890304.3 x8 - 2x7 - 3x6 + 8x5 + x4 - 2x3 + 23x2 - 12x + 2 \( 2^{12}\cdot 7^{6} \) $D_4$ Trivial
8.0.577200625.1 x8 - 5x6 + 32x4 - 45x2 + 81 \( 5^{4}\cdot 31^{4} \) $D_4$ $[3]$
8.0.592240896.5 x8 + x6 + 4x4 - 3x2 + 9 \( 2^{8}\cdot 3^{4}\cdot 13^{4} \) $D_4$ $[2]$
8.0.673246809.1 x8 - 3x7 - 2x6 + 15x5 + 27x4 + 15x3 - 2x2 - 3x + 1 \( 3^{6}\cdot 31^{4} \) $D_4$ $[3]$
8.0.723394816.1 x8 + 13x6 + 40x4 + 52x2 + 16 \( 2^{8}\cdot 41^{4} \) $D_4$ $[2]$
8.0.741200625.3 x8 - 3x7 + 4x6 - 14x5 + 29x4 - 28x3 + 36x2 - 55x + 55 \( 3^{4}\cdot 5^{4}\cdot 11^{4} \) $D_4$ $[2]$
8.0.796594176.7 x8 - 2x7 + 8x6 + 12x5 + 11x4 + 12x3 + 8x2 - 2x + 1 \( 2^{12}\cdot 3^{4}\cdot 7^{4} \) $D_4$ $[2]$
8.0.796594176.12 x8 - 2x7 + 5x6 - 4x5 + x4 - 18x3 + 15x2 + 18 \( 2^{12}\cdot 3^{4}\cdot 7^{4} \) $D_4$ $[2]$
8.0.796594176.14 x8 - 2x7 + 4x6 + 12x5 - 21x4 + 36x3 + 36x2 - 54x + 81 \( 2^{12}\cdot 3^{4}\cdot 7^{4} \) $D_4$ $[2]$
8.0.1024000000.6 x8 + 4x6 + 16x4 - 56x2 + 36 \( 2^{16}\cdot 5^{6} \) $D_4$ $[2]$
8.0.1093955625.1 x8 - 5x6 - 18x4 + 100x2 + 1 \( 3^{6}\cdot 5^{4}\cdot 7^{4} \) $D_4$ $[2]$
8.0.1121513121.2 x8 + 7x6 + 52x4 - 21x2 + 9 \( 3^{4}\cdot 61^{4} \) $D_4$ $[2]$
8.0.1146228736.5 x8 - 6x6 - 4x5 + 43x4 + 104x3 + 86x2 + 24x + 36 \( 2^{12}\cdot 23^{4} \) $D_4$ $[3]$
8.0.1358954496.9 x8 - 12x6 + 72x4 - 108x2 + 81 \( 2^{24}\cdot 3^{4} \) $D_4$ $[2]$
8.0.1445900625.2 x8 - x7 + x6 + 16x5 - 7x4 - 2x3 + 64x2 + 8x + 1 \( 3^{4}\cdot 5^{4}\cdot 13^{4} \) $D_4$ $[4]$
8.0.1698181681.1 x8 - 2x7 + 2x6 + 6x5 + 16x4 - 70x3 + 49x2 - 98x + 196 \( 7^{4}\cdot 29^{4} \) $D_4$ Trivial
8.0.1722499009.1 x8 + x6 - 11x4 + 4x2 + 16 \( 7^{6}\cdot 11^{4} \) $D_4$ Trivial
8.0.1731891456.3 x8 + 3x6 + 11x4 + 45x2 + 4 \( 2^{8}\cdot 3^{4}\cdot 17^{4} \) $D_4$ $[2]$
8.0.1766100625.1 x8 + 15x6 + 48x4 + 15x2 + 1 \( 5^{4}\cdot 41^{4} \) $D_4$ Trivial

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