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Label Polynomial Discriminant Galois group Class group
8.0.67108864.2 x8 + 4x4 - 4x2 + 1 \( 2^{26} \) $C_2^3 : C_4 $ Trivial (GRH)
8.0.268435456.1 x8 - 4x6 + 10x4 + 4x2 + 1 \( 2^{28} \) $C_2^3 : C_4 $ Trivial
8.0.342102016.6 x8 - 2x7 + 12x5 - 2x4 - 16x3 + 24x2 + 48x + 20 \( 2^{12}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.534534400.2 x8 - 2x7 - 3x6 + 14x5 - x4 - 22x3 + 10x2 + 12x + 20 \( 2^{8}\cdot 5^{2}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.534534400.3 x8 - 2x7 + 5x6 - 8x5 + 20x4 - 36x3 + 65x2 - 66x + 41 \( 2^{8}\cdot 5^{2}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.655360000.3 x8 - 4x7 + 12x6 - 20x5 + 22x4 - 16x3 + 8x2 + 2 \( 2^{20}\cdot 5^{4} \) $C_2^3 : C_4 $ Trivial
8.0.655360000.4 x8 - 4x6 - 4x5 + 24x4 - 40x3 + 40x2 - 20x + 5 \( 2^{20}\cdot 5^{4} \) $C_2^3 : C_4 $ Trivial
8.0.829440000.2 x8 - 2x7 + 2x5 + 8x4 + 2x3 - 2x + 1 \( 2^{14}\cdot 3^{4}\cdot 5^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.829440000.3 x8 - 2x7 + 10x6 - 20x5 + 30x4 - 52x3 + 64x2 - 40x + 10 \( 2^{14}\cdot 3^{4}\cdot 5^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.1366263369.1 x8 - 3x7 + 5x6 - 15x5 + 18x4 - 9x3 + 47x2 + 54x + 13 \( 3^{6}\cdot 37^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.1368408064.2 x8 - x7 + 7x6 - 8x5 + 11x4 + 5x3 + 11x2 - 2x + 2 \( 2^{14}\cdot 17^{4} \) $C_2^3 : C_4 $ Trivial
8.0.1368408064.3 x8 + x6 + 2x2 + 4 \( 2^{14}\cdot 17^{4} \) $C_2^3 : C_4 $ Trivial
8.0.1677721600.2 x8 - 8x6 + 12x4 + 20x2 + 25 \( 2^{26}\cdot 5^{2} \) $C_2^3 : C_4 $ Trivial (GRH)
8.0.1677721600.3 x8 - 4x6 + 12x4 + 40x2 + 25 \( 2^{26}\cdot 5^{2} \) $C_2^3 : C_4 $ Trivial (GRH)
8.0.1766100625.2 x8 - 2x7 + 12x6 - 13x5 + 24x4 - 13x3 + 12x2 - 2x + 1 \( 5^{4}\cdot 41^{4} \) $C_2^3 : C_4 $ Trivial
8.0.2304000000.1 x8 - 2x7 - 2x5 + 4x4 + 2x3 + 2x + 1 \( 2^{14}\cdot 3^{2}\cdot 5^{6} \) $C_2^3 : C_4 $ $[4]$
8.0.2304000000.2 x8 - 2x7 + 2x6 - 14x4 + 28x2 + 24x + 6 \( 2^{14}\cdot 3^{2}\cdot 5^{6} \) $C_2^3 : C_4 $ $[4]$
8.0.2385443281.1 x8 - 2x7 + 5x6 - 2x5 - 9x4 + 2x3 + 5x2 + 2x + 1 \( 13^{4}\cdot 17^{4} \) $C_2^3 : C_4 $ Trivial
8.0.2415919104.3 x8 - 8x5 + 36x4 - 64x3 + 64x2 - 32x + 6 \( 2^{28}\cdot 3^{2} \) $C_2^3 : C_4 $ Trivial
8.0.2415919104.4 x8 - 8x6 - 8x5 + 24x4 + 64x3 + 56x2 + 16x + 2 \( 2^{28}\cdot 3^{2} \) $C_2^3 : C_4 $ Trivial
8.0.2621440000.3 x8 - 8x6 + 30x4 - 40x2 + 25 \( 2^{22}\cdot 5^{4} \) $C_2^3 : C_4 $ Trivial
8.0.2621440000.13 x8 - 4x6 + 10x4 + 20x2 + 25 \( 2^{22}\cdot 5^{4} \) $C_2^3 : C_4 $ Trivial
8.0.3186376704.5 x8 - 3x6 + 8x4 - 6x2 + 4 \( 2^{14}\cdot 3^{4}\cdot 7^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.3186376704.6 x8 - 2x6 + 2x4 + 20x2 + 16 \( 2^{14}\cdot 3^{4}\cdot 7^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.3613452544.1 x8 - 2x7 - x6 - 34x3 + 11x2 + 188x + 157 \( 2^{8}\cdot 13^{2}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.3613452544.2 x8 - 5x6 - 11x4 - 48x3 + 36x2 + 240x + 212 \( 2^{8}\cdot 13^{2}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.3991080625.1 x8 - 2x7 + 2x6 - 12x5 + 19x4 - 18x3 + 27x2 - 7x + 7 \( 5^{4}\cdot 7^{2}\cdot 19^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.3991080625.2 x8 - x7 + 5x6 - 3x5 + 20x4 + 5x3 + 45x2 + 15x + 25 \( 5^{4}\cdot 7^{2}\cdot 19^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.4569760000.7 x8 - 2x7 + 3x6 - 8x5 + 28x4 - 42x3 + 11x2 + 20x + 5 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.4569760000.8 x8 - 2x7 + x6 + 12x5 - 7x4 - 20x3 + 20x2 + 40x + 20 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.5435817984.8 x8 - 4x6 + 20x4 - 8x2 + 1 \( 2^{26}\cdot 3^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.5435817984.9 x8 - 4x4 - 12x2 + 25 \( 2^{26}\cdot 3^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.5435817984.10 x8 + 36x4 - 108x2 + 81 \( 2^{26}\cdot 3^{4} \) $C_2^3 : C_4 $ $[2]$ (GRH)
8.0.5473632256.7 x8 - x6 - 2x2 + 4 \( 2^{16}\cdot 17^{4} \) $C_2^3 : C_4 $ Trivial
8.0.5473632256.8 x8 - 8x6 + 34x4 - 72x2 + 64 \( 2^{16}\cdot 17^{4} \) $C_2^3 : C_4 $ Trivial
8.0.5473632256.9 x8 - 8x6 + 51x4 - 136x2 + 289 \( 2^{16}\cdot 17^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.7269949696.1 x8 - 2x7 + x6 + 12x5 - 7x4 - 12x3 + 52x2 + 24x + 4 \( 2^{8}\cdot 73^{4} \) $C_2^3 : C_4 $ Trivial
8.0.7438545009.1 x8 - 6x6 - 12x5 + 23x4 + 78x3 + 3x2 - 411x + 367 \( 3^{4}\cdot 7^{2}\cdot 37^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.7438545009.2 x8 - 3x7 - 5x6 + 27x5 - 23x4 - 6x3 + 84x2 - 360x + 432 \( 3^{4}\cdot 7^{2}\cdot 37^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.8653650625.1 x8 + 9x6 - 18x5 + 14x4 - 20x3 + 30x2 - 20x + 5 \( 5^{4}\cdot 61^{4} \) $C_2^3 : C_4 $ Trivial
8.0.9475854336.13 x8 - 4x7 + 4x6 + 2x5 + 24x4 - 56x3 - 17x2 + 46x + 19 \( 2^{12}\cdot 3^{4}\cdot 13^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.9475854336.14 x8 - 4x7 + 8x6 - 7x4 - 12x3 + 50x2 + 80x + 28 \( 2^{12}\cdot 3^{4}\cdot 13^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.9855525625.1 x8 - 2x7 + 3x6 - 7x5 + 8x4 - 7x3 + 51x2 - 5x + 1 \( 5^{4}\cdot 11^{2}\cdot 19^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.9855525625.2 x8 - x7 + 4x6 - 10x5 + 19x4 - 30x3 + 60x2 - 40x + 80 \( 5^{4}\cdot 11^{2}\cdot 19^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.10093618089.2 x8 - x7 - 6x6 + 20x5 - 32x4 - 51x3 + 228x2 - 240x + 129 \( 3^{6}\cdot 61^{4} \) $C_2^3 : C_4 $ $[2]$
8.0.11051265625.2 x8 - x7 + 8x6 - 5x5 + 21x4 + 5x3 + 12x2 + 3x + 1 \( 5^{6}\cdot 29^{4} \) $C_2^3 : C_4 $ $[4]$
8.0.11051265625.3 x8 - 2x7 - 2x6 - 4x5 + 40x4 - 14x3 - 37x2 - 142x + 236 \( 5^{6}\cdot 29^{4} \) $C_2^3 : C_4 $ $[4]$
8.0.11209515625.1 x8 - 3x7 + 7x6 - 5x5 - 4x4 + 10x3 - 7x2 - 14x + 16 \( 5^{6}\cdot 7^{2}\cdot 11^{4} \) $C_2^3 : C_4 $ $[4]$
8.0.11209515625.2 x8 - 4x7 + 14x5 - x4 - 26x3 - 5x2 + 21x + 26 \( 5^{6}\cdot 7^{2}\cdot 11^{4} \) $C_2^3 : C_4 $ $[4]$
8.0.11341398016.3 x8 - 12x6 + 28x4 + 104x2 + 169 \( 2^{26}\cdot 13^{2} \) $C_2^3 : C_4 $ Trivial (GRH)

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