## Results (displaying matches 1-50 of 19550) Next

Label Polynomial Discriminant Galois group Class group
8.0.1265625.1 x8 - x7 + x5 - x4 + x3 - x + 1 $$3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.4000000.1 x8 - x6 + x4 - x2 + 1 $$2^{8}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.16777216.1 x8 + 1 $$2^{24}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.37515625.1 x8 - x7 - x6 + 3x5 - x4 + 6x3 - 4x2 - 8x + 16 $$5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.64000000.1 x8 - 2x6 + 4x4 - 8x2 + 16 $$2^{12}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.64000000.2 x8 + 2x6 + 4x4 + 8x2 + 16 $$2^{12}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.228765625.1 x8 - x7 - 2x6 + 5x5 + x4 + 15x3 - 18x2 - 27x + 81 $$5^{6}\cdot 11^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.324000000.1 x8 + 9x6 + 26x4 + 24x2 + 1 $$2^{8}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.8.324000000.1 x8 - 7x6 + 14x4 - 8x2 + 1 $$2^{8}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.324000000.2 x8 + 5x6 + 20x4 + 25x2 + 25 $$2^{8}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.324000000.3 x8 + 3x6 + 9x4 + 27x2 + 81 $$2^{8}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.339738624.1 x8 - 4x6 + 14x4 - 8x2 + 4 $$2^{22}\cdot 3^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.339738624.2 x8 + 4x6 + 14x4 + 8x2 + 4 $$2^{22}\cdot 3^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.390971529.1 x8 - x7 - x6 - 10x5 + 5x4 + 14x3 + 10x2 + 12x + 9 $$3^{4}\cdot 13^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.446265625.1 x8 - x7 + 4x6 - 7x5 + 19x4 + 21x3 + 36x2 + 27x + 81 $$5^{6}\cdot 13^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.1024000000.1 x8 + 8x6 + 19x4 + 12x2 + 1 $$2^{16}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.8.1024000000.1 x8 - 8x6 + 19x4 - 12x2 + 1 $$2^{16}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.1024000000.2 x8 + 15x4 + 25 $$2^{16}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.1235663104.1 x8 - 3x6 + 18x4 + 4x2 + 9 $$2^{8}\cdot 13^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.1305015625.1 x8 - x7 + 5x6 - 9x5 + 29x4 + 36x3 + 80x2 + 64x + 256 $$5^{6}\cdot 17^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.8.1358954496.1 x8 - 8x6 + 20x4 - 16x2 + 1 $$2^{24}\cdot 3^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.1358954496.3 x8 + 8x6 + 20x4 + 16x2 + 1 $$2^{24}\cdot 3^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.1358954496.4 x8 + 81 $$2^{24}\cdot 3^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.1955143089.1 x8 - x7 + 7x6 + 4x5 + 36x4 - 4x3 + 7x2 + x + 1 $$3^{4}\cdot 17^{6}$$ $C_4\times C_2$ (as 8T2) $[5]$
8.0.2036265625.1 x8 - x7 - 4x6 + 9x5 + 11x4 + 45x3 - 100x2 - 125x + 625 $$5^{6}\cdot 19^{4}$$ $C_4\times C_2$ (as 8T2) $[4]$
8.0.2621440000.1 x8 + 12x6 + 30x4 + 24x2 + 4 $$2^{22}\cdot 5^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.8.2621440000.1 x8 - 12x6 + 30x4 - 24x2 + 4 $$2^{22}\cdot 5^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.3016755625.1 x8 - x7 + 5x6 + 18x5 + 37x4 + 20x3 + 2x2 - 12x + 9 $$5^{4}\cdot 13^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.3038765625.1 x8 - x7 + 10x6 - 9x5 + 79x4 - 59x3 + 180x2 + 99x + 121 $$3^{4}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.8.3038765625.1 x8 - x7 - 14x6 + 9x5 + 61x4 - 5x3 - 90x2 - 45x - 5 $$3^{4}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.3038765625.2 x8 - 2x7 - 2x5 + 29x4 + 2x3 + 55x2 + 27x + 151 $$3^{4}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.3038765625.3 x8 - x7 + 6x6 - 11x5 + 41x4 + 55x3 + 150x2 + 125x + 625 $$3^{4}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.4372515625.1 x8 - x7 - 5x6 + 11x5 + 19x4 + 66x3 - 180x2 - 216x + 1296 $$5^{6}\cdot 23^{4}$$ $C_4\times C_2$ (as 8T2) $[3]$
8.0.5184000000.1 x8 + 14x6 + 56x4 + 64x2 + 16 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[4]$
8.8.5184000000.1 x8 - 2x7 - 15x6 + 28x5 + 44x4 - 58x3 - 20x2 + 12x + 1 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.5184000000.2 x8 - 2x7 + x6 + 4x5 + 24x4 - 58x3 + 124x2 - 124x + 241 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.8.5184000000.2 x8 - 14x6 + 56x4 - 64x2 + 16 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.5184000000.3 x8 - 10x6 + 80x4 - 200x2 + 400 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2, 2]$
8.0.5184000000.4 x8 + 10x6 + 80x4 + 200x2 + 400 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.5184000000.5 x8 - 6x6 + 36x4 - 216x2 + 1296 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[4]$
8.0.5184000000.6 x8 + 6x6 + 36x4 + 216x2 + 1296 $$2^{12}\cdot 3^{4}\cdot 5^{6}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.6179217664.1 x8 + 13x6 + 40x4 + 13x2 + 1 $$2^{8}\cdot 17^{6}$$ $C_4\times C_2$ (as 8T2) $[4]$
8.0.9604000000.1 x8 + 19x6 + 121x4 + 279x2 + 121 $$2^{8}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.8.9604000000.1 x8 - 12x6 + 34x4 - 23x2 + 1 $$2^{8}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) Trivial
8.0.9604000000.2 x8 - 4x7 + 4x6 + 2x5 + 29x4 - 66x3 + 36x2 - 2x + 281 $$2^{8}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.9604000000.3 x8 + 7x6 + 49x4 + 343x2 + 2401 $$2^{8}\cdot 5^{6}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.10070523904.1 x8 - 4x7 + 22x6 - 52x5 + 113x4 - 144x3 + 120x2 - 56x + 14 $$2^{22}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.10070523904.2 x8 + 12x6 + 66x4 + 96x2 + 64 $$2^{22}\cdot 7^{4}$$ $C_4\times C_2$ (as 8T2) $[4]$
8.0.10485760000.1 x8 - 8x6 + 20x4 - 16x2 + 49 $$2^{24}\cdot 5^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$
8.0.10485760000.2 x8 + 8x6 + 20x4 + 16x2 + 49 $$2^{24}\cdot 5^{4}$$ $C_4\times C_2$ (as 8T2) $[2]$

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