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Label Polynomial Discriminant Galois group Class group
8.0.6036849.1 x8 - 2x7 + 5x6 - 2x5 + 7x4 + 2x3 + 5x2 + 2x + 1 \( 3^{6}\cdot 7^{2}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.6036849.2 x8 - x7 + 5x6 - x5 + 4x4 + x3 + 5x2 + x + 1 \( 3^{6}\cdot 7^{2}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.9144576.1 x8 + x6 - 2x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 7^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.9144576.2 x8 - x6 + 2x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 7^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.12895281.1 x8 + 2x6 - 6x5 - 3x4 + 5x2 + 3x + 1 \( 3^{6}\cdot 7^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.12895281.2 x8 - 2x6 + 9x4 - 12x3 + 7x2 - 3x + 1 \( 3^{6}\cdot 7^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.17305600.1 x8 - 2x6 + 7x4 - 2x2 + 1 \( 2^{12}\cdot 5^{2}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.17305600.2 x8 - 2x6 + x4 + 4 \( 2^{12}\cdot 5^{2}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.18740241.1 x8 - 2x7 + 5x6 - 4x5 + x4 + 12x3 - 9x2 + 9 \( 3^{4}\cdot 13^{2}\cdot 37^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.18740241.2 x8 - x7 - x6 + 7x5 - 2x4 + 3x3 + 9x2 - 9x + 9 \( 3^{4}\cdot 13^{2}\cdot 37^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.19360000.1 x8 + 3x6 + 3x4 + 3x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 11^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.19360000.1 x8 - 3x6 + 3x4 - 3x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 11^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.21381376.1 x8 + x6 - 2x4 + x2 + 1 \( 2^{8}\cdot 17^{4} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.26214400.1 x8 - 2x6 + 2x2 + 1 \( 2^{20}\cdot 5^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial (GRH)
8.0.26214400.2 x8 - 2x6 + 4x4 - 2x2 + 1 \( 2^{20}\cdot 5^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial (GRH)
8.0.27300625.1 x8 - x7 + 3x6 - x5 + 8x4 + x3 + 3x2 + x + 1 \( 5^{4}\cdot 11^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.27300625.1 x8 - 2x7 - 3x6 + 2x5 + 3x4 + 2x3 - 3x2 - 2x + 1 \( 5^{4}\cdot 11^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.29593600.1 x8 - 2x7 + 8x5 + 3x4 + 4x3 + 4x2 - 2x + 1 \( 2^{12}\cdot 5^{2}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.29593600.2 x8 - 2x7 - 4x6 + 11x4 + 12x3 + 8x2 + 2x + 1 \( 2^{12}\cdot 5^{2}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.30118144.1 x8 - 3x6 + 6x4 - 3x2 + 1 \( 2^{8}\cdot 7^{6} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.31539456.1 x8 + 3x6 + 12x4 + 18x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.31539456.2 x8 - 3x6 + 12x4 - 18x2 + 9 \( 2^{8}\cdot 3^{6}\cdot 13^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.34327881.1 x8 + x6 - 9x5 + 6x4 + 3x3 + x2 + 3x + 1 \( 3^{6}\cdot 7^{2}\cdot 31^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.34327881.2 x8 - 3x7 + 2x6 - 3x5 + 3x4 + 9x3 + 8x2 + 3x + 1 \( 3^{6}\cdot 7^{2}\cdot 31^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.44475561.1 x8 - 2x7 - 4x6 + x5 + 19x4 + 2x3 - 16x2 - 16x + 16 \( 3^{6}\cdot 13^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.44475561.2 x8 - x7 - 4x6 - 4x5 + 25x4 - 8x3 - 16x2 - 8x + 16 \( 3^{6}\cdot 13^{2}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.48902049.1 x8 - 2x7 + 9x6 - 5x5 + 16x4 + 9x3 + 15x2 + 9x + 9 \( 3^{6}\cdot 7^{2}\cdot 37^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.48902049.2 x8 - x7 + 6x6 - 7x5 + 13x4 + 3x3 + 24x2 + 9x + 9 \( 3^{6}\cdot 7^{2}\cdot 37^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.50936769.1 x8 - x7 - 7x6 + x5 + 22x4 + 15x3 - 9x2 + 9 \( 3^{4}\cdot 13^{2}\cdot 61^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.50936769.2 x8 - x7 - 4x6 + 7x5 + 19x4 + 3x3 - 18x2 - 9x + 9 \( 3^{4}\cdot 13^{2}\cdot 61^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.51380224.1 x8 + 2x6 + x4 + 2x2 + 1 \( 2^{20}\cdot 7^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.51380224.1 x8 - 2x6 + x4 - 2x2 + 1 \( 2^{20}\cdot 7^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.57760000.1 x8 + 5x6 + 7x4 + 5x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.57760000.1 x8 - 5x6 + 7x4 - 5x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.58003456.1 x8 - 2x7 + 3x6 - 2x5 + 5x4 - 4x3 + 2x2 + 4 \( 2^{12}\cdot 7^{2}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.58003456.2 x8 - 2x7 + 5x6 - 10x5 + 13x4 - 16x3 + 14x2 - 8x + 4 \( 2^{12}\cdot 7^{2}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.63600625.1 x8 - 2x7 - x6 + 3x5 - 2x4 - 9x3 - 9x2 - x + 1 \( 5^{4}\cdot 11^{2}\cdot 29^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.63600625.2 x8 - x7 - 4x6 + 11x5 - 7x4 - 7x3 + 4x2 + 3x + 1 \( 5^{4}\cdot 11^{2}\cdot 29^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.65804544.1 x8 + x6 - x4 + x2 + 1 \( 2^{8}\cdot 3^{2}\cdot 13^{4} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.65804544.1 x8 - x6 - x4 - x2 + 1 \( 2^{8}\cdot 3^{2}\cdot 13^{4} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.66048129.1 x8 - 3x7 + 2x6 + 3x4 - 6x3 + 20x2 - 24x + 16 \( 3^{6}\cdot 7^{2}\cdot 43^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.66048129.2 x8 - 3x7 + 4x6 - 12x5 + 27x4 - 24x3 + 16x2 - 24x + 16 \( 3^{6}\cdot 7^{2}\cdot 43^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.67371264.1 x8 + x6 + 6x4 - 5x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.67371264.2 x8 - x6 + 6x4 + 5x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 19^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.72675625.1 x8 - 3x7 + 8x6 - 5x5 + 11x4 + 5x3 + 8x2 + 3x + 1 \( 5^{4}\cdot 11^{2}\cdot 31^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.4.72675625.1 x8 - 2x7 - 2x6 + 11x4 - 17x2 - 3x + 1 \( 5^{4}\cdot 11^{2}\cdot 31^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.72948681.1 x8 - x7 + 2x6 - 12x5 + 17x4 + 6x3 - 28x2 + 8x + 16 \( 3^{4}\cdot 13^{2}\cdot 73^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.72948681.2 x8 - x7 - x6 + 9x5 + 11x4 + 6x3 - 16x2 - 16x + 16 \( 3^{4}\cdot 13^{2}\cdot 73^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.74287161.1 x8 + 5x6 + 5x4 + 5x2 + 1 \( 3^{2}\cdot 13^{4}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial
8.0.74287161.2 x8 - 4x7 + 12x6 - 22x5 + 33x4 - 34x3 + 29x2 - 15x + 3 \( 3^{2}\cdot 13^{4}\cdot 17^{2} \) $V_4 \wr C_2 $ (as 8T18) Trivial

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