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Label Polynomial Discriminant Galois group Class group
8.4.31878125.1 x8 - 3x7 + x6 + 2x5 - x4 + 2x3 + x2 - 3x + 1 \( 5^{5}\cdot 101^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.37879808.1 x8 - 2x6 + 3x4 + 2 \( 2^{17}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.55278125.1 x8 + x6 - 3x5 - x4 - 4x3 + 6x2 + 5 \( 5^{5}\cdot 7^{2}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.55278125.1 x8 - 2x7 - 2x6 + 5x5 + x4 - 5x3 - 2x2 + 2x + 1 \( 5^{5}\cdot 7^{2}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.84050000.1 x8 - x7 - x6 + x5 + 4x4 - x3 - x2 + x + 1 \( 2^{4}\cdot 5^{5}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.84050000.2 x8 - 2x7 + 3x6 - 4x4 + 3x2 + 2x + 1 \( 2^{4}\cdot 5^{5}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.90870848.1 x8 - 3x7 + 5x6 - 5x5 + 6x4 - 5x3 + 5x2 - 3x + 1 \( 2^{6}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.97903125.1 x8 - x7 + 3x6 + 2x5 - x4 + 2x3 + 3x2 - x + 1 \( 3^{2}\cdot 5^{5}\cdot 59^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.97903125.1 x8 - x7 - x6 - 4x5 - x4 + 4x3 - x2 + x + 1 \( 3^{2}\cdot 5^{5}\cdot 59^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.102378125.1 x8 - x7 - 3x6 + x4 - 3x2 - x + 1 \( 5^{5}\cdot 181^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.104653125.1 x8 - 2x7 + 2x6 + x5 - x4 - x3 + 2x2 + 2x + 1 \( 3^{2}\cdot 5^{5}\cdot 61^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.104653125.2 x8 - 3x7 + 3x6 + x4 + 3x2 + 3x + 1 \( 3^{2}\cdot 5^{5}\cdot 61^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.125960192.1 x8 - 2x7 + 7x6 - 12x5 + 20x4 - 20x3 + 18x2 - 8x + 4 \( 2^{17}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.131328125.1 x8 - 2x7 - 2x6 + x5 + 5x4 + x3 - 2x2 - 2x + 1 \( 5^{7}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.151519232.1 x8 + 2x6 + 3x4 + 2 \( 2^{19}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.239955833.1 x8 - x7 - 5x5 + 2x4 + 8x2 + x + 2 \( 13^{2}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.288800000.1 x8 + 4x6 + 4x4 + 5x2 + 5 \( 2^{8}\cdot 5^{5}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.288800000.1 x8 - 3x6 + 6x4 - 10x2 + 5 \( 2^{8}\cdot 5^{5}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.288800000.2 x8 + 3x6 + 6x4 + 10x2 + 5 \( 2^{8}\cdot 5^{5}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.288800000.2 x8 - 4x6 + 4x4 - 5x2 + 5 \( 2^{8}\cdot 5^{5}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.289538048.1 x8 - 2x7 + x6 - 2x5 + 8x4 - 6x3 - x2 + 2x + 1 \( 2^{17}\cdot 47^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.290703125.1 x8 - 3x7 - 2x6 + 4x5 + 5x4 + 4x3 - 2x2 - 3x + 1 \( 5^{7}\cdot 61^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.312050000.1 x8 - 2x5 - 4x4 + 11x2 - 6x + 4 \( 2^{4}\cdot 5^{5}\cdot 79^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.312050000.1 x8 - 3x7 + x6 + 7x5 - 16x4 + 7x3 + x2 - 3x + 1 \( 2^{4}\cdot 5^{5}\cdot 79^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.336200000.1 x8 - 3x7 + 3x6 + 5x5 - 4x4 - 5x3 + 3x2 + 3x + 1 \( 2^{6}\cdot 5^{5}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.336200000.2 x8 - 2x7 + 4x6 - 6x5 + 9x4 - 2x3 - 4x2 + 5 \( 2^{6}\cdot 5^{5}\cdot 41^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.363378125.1 x8 - 2x7 - 4x6 + 3x5 + 9x4 + 3x3 - 4x2 - 2x + 1 \( 5^{5}\cdot 11^{2}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.363378125.2 x8 + 3x6 - 14x4 + 5 \( 5^{5}\cdot 11^{2}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.363483392.1 x8 + 2x6 - x5 - 13x4 - 18x3 - 18x2 - 10x - 2 \( 2^{8}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial (GRH)
8.4.407253125.1 x8 - 2x7 - 4x6 + 9x5 + 6x4 - 5x3 - 6x2 - 5x + 5 \( 5^{5}\cdot 19^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.407253125.1 x8 - 3x7 + 12x6 - 21x5 + 39x4 - 34x3 + 32x2 - 2x + 1 \( 5^{5}\cdot 19^{4} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.0.451250000.1 x8 + 5x6 + 5x2 + 5 \( 2^{4}\cdot 5^{7}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.4.451250000.1 x8 - x7 - 3x6 - 3x5 + 3x3 - 3x2 + x + 1 \( 2^{4}\cdot 5^{7}\cdot 19^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.463203125.1 x8 - 2x7 + 3x6 - 9x5 + 5x4 + 6x3 + 8x2 + 3x + 1 \( 5^{7}\cdot 7^{2}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.4.463203125.1 x8 - x7 + 2x6 - 8x5 - 5x4 + 8x3 + 2x2 + x + 1 \( 5^{7}\cdot 7^{2}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.502503125.1 x8 - x7 - 6x6 + 6x5 + 9x4 - 11x3 - 11x2 - 4x + 1 \( 5^{5}\cdot 401^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.503840768.1 x8 - 4x6 - 3x4 - 4x3 + 6x2 + 4x - 2 \( 2^{19}\cdot 31^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.533028125.1 x8 - 4x7 + 5x6 - x5 + x4 - 5x3 - 4x2 + 7x - 1 \( 5^{5}\cdot 7^{2}\cdot 59^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.533028125.1 x8 - 3x7 + 8x6 - 15x5 + 21x4 - 20x3 + 18x2 - 2x + 1 \( 5^{5}\cdot 7^{2}\cdot 59^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.536870912.1 x8 + 4x6 + 8x4 + 8x2 + 2 \( 2^{29} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.536870912.1 x8 - 4x6 + 8x4 - 8x2 + 2 \( 2^{29} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.567942800.1 x8 - x7 + 2x6 - 7x5 + 21x4 - 34x3 + 34x2 - 20x + 8 \( 2^{4}\cdot 5^{2}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.567942800.2 x8 - 3x7 + 9x6 - 14x5 + 26x4 - 28x3 + 36x2 - 24x + 16 \( 2^{4}\cdot 5^{2}\cdot 17^{5} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.591328125.1 x8 - x7 + 2x6 + 2x5 + 5x4 - 2x3 + 2x2 + x + 1 \( 3^{2}\cdot 5^{7}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.0.591328125.2 x8 - 3x7 + 3x6 + 4x5 - 16x3 + 23x2 + 7x + 1 \( 3^{2}\cdot 5^{7}\cdot 29^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.0.596778125.1 x8 - 2x7 + 7x6 - 5x5 + 14x4 - 8x3 + 27x2 - 12x + 19 \( 5^{5}\cdot 19^{2}\cdot 23^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.596778125.1 x8 - 9x6 - 2x5 + 29x4 + 19x3 - 29x2 - 35x - 5 \( 5^{5}\cdot 19^{2}\cdot 23^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.4.605000000.1 x8 - x7 - 3x6 + 7x5 - 7x3 - 3x2 + x + 1 \( 2^{6}\cdot 5^{7}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
8.0.605000000.1 x8 - x7 + 2x6 - 3x5 - 7x3 + 2x2 + 11x + 11 \( 2^{6}\cdot 5^{7}\cdot 11^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$
8.0.606076928.2 x8 - 2x6 + 5x4 - 4x2 + 2 \( 2^{21}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) Trivial
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