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Label Polynomial Discriminant Galois group Class group
8.0.26265625.2 x8 - 2x7 + 10x6 - 12x5 + 29x4 - 18x3 + 25x2 - 3x + 1 \( 5^{6}\cdot 41^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.58140625.1 x8 - 2x7 + x6 + 4x5 + 4x4 - 28x3 + 59x2 - 54x + 31 \( 5^{6}\cdot 61^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.159390625.2 x8 - x7 - 7x6 + 10x5 + 21x4 - 30x3 - 28x2 + 48x + 41 \( 5^{6}\cdot 101^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.4.268435456.1 x8 - 4x6 - 2x4 + 12x2 + 1 \( 2^{28} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.324000000.1 x8 - 3x6 - x4 + 3x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 5^{6} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.324000000.4 x8 - x6 - 4x4 + 4x2 + 1 \( 2^{8}\cdot 3^{4}\cdot 5^{6} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.484000000.7 x8 - 12x6 + 64x4 - 143x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.484000000.8 x8 - 11x6 + 51x4 - 121x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.484000000.10 x8 + 11x6 + 51x4 + 121x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.484000000.11 x8 + 12x6 + 64x4 + 143x2 + 121 \( 2^{8}\cdot 5^{6}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.511890625.2 x8 - x7 - 7x6 + 10x5 + 21x4 - 50x3 - 38x2 + 138x + 131 \( 5^{6}\cdot 181^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.907515625.2 x8 - 2x7 - 14x6 + 34x5 + 49x4 - 148x3 - x2 + 21x + 181 \( 5^{6}\cdot 241^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1024000000.4 x8 - 2x6 - 6x4 + 2x2 + 1 \( 2^{16}\cdot 5^{6} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1024000000.5 x8 - 4x6 + x4 + 6x2 + 1 \( 2^{16}\cdot 5^{6} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1064390625.1 x8 - 3x7 + x6 - 4x5 - x4 - 2x3 - 6x2 + 4x + 1 \( 3^{4}\cdot 5^{6}\cdot 29^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1064390625.2 x8 - x7 + x6 + 4x5 - 9x4 - 10x3 - 20x2 - 20x - 5 \( 3^{4}\cdot 5^{6}\cdot 29^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1212153856.4 x8 - 8x6 + 12x4 - 24x3 - 28x2 + 24x + 31 \( 2^{22}\cdot 17^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.1212153856.11 x8 - 4x7 + 6x6 - 3x4 + 6x2 + 4x + 7 \( 2^{22}\cdot 17^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1216265625.2 x8 - 3x7 + x6 + 11x5 - 31x4 + 28x3 + 24x2 - 56x + 16 \( 3^{4}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1216265625.3 x8 - x7 - 2x6 + 10x5 - 9x4 - 10x3 + 22x2 - 17x + 1 \( 3^{4}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.1233765625.2 x8 - 2x7 - 14x6 + 29x5 + 64x4 - 158x3 - 136x2 + 371x + 341 \( 5^{6}\cdot 281^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1444000000.4 x8 - 2x7 + x6 + 4x5 - 11x4 + 12x3 - 16x2 + 16x - 4 \( 2^{8}\cdot 5^{6}\cdot 19^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.1444000000.7 x8 - 3x6 - 10x5 - x4 + 20x3 + 23x2 + 10x + 1 \( 2^{8}\cdot 5^{6}\cdot 19^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.1816890625.6 x8 - x7 - 17x6 + 10x5 + 121x4 - 40x3 - 388x2 + 58x + 461 \( 5^{6}\cdot 11^{2}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.1816890625.7 x8 - 3x7 - 14x6 + 41x5 + 89x4 - 247x3 - 196x2 + 419x + 331 \( 5^{6}\cdot 11^{2}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.1816890625.8 x8 - x7 - 14x6 + 14x5 + 81x4 - 90x3 - 270x2 + 225x + 505 \( 5^{6}\cdot 11^{2}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.1816890625.9 x8 - 3x7 - 15x6 + 42x5 + 79x4 - 162x3 - 220x2 + 48x + 571 \( 5^{6}\cdot 11^{2}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.2127515625.4 x8 - 3x7 - 16x6 + 43x5 + 111x4 - 245x3 - 300x2 + 355x + 505 \( 3^{4}\cdot 5^{6}\cdot 41^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.2512515625.2 x8 - x7 - 17x6 + 15x5 + 116x4 - 85x3 - 413x2 + 188x + 701 \( 5^{6}\cdot 401^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.2769390625.2 x8 - 3x7 + 25x6 - 63x5 + 224x4 - 417x3 + 805x2 - 877x + 961 \( 5^{6}\cdot 421^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.3178140625.1 x8 - 3x7 - 6x6 + 33x5 + 51x4 - 125x3 - 80x2 + 505x + 655 \( 5^{6}\cdot 11^{2}\cdot 41^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.3178140625.3 x8 - 2x7 + 12x6 - 20x5 + 111x4 - 10x3 + 543x2 + 139x + 881 \( 5^{6}\cdot 11^{2}\cdot 41^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.3320640625.1 x8 - x7 + 21x6 - 16x5 + 171x4 - 80x3 + 600x2 - 130x + 755 \( 5^{6}\cdot 461^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.0.3844000000.1 x8 - 22x6 + 194x4 - 713x2 + 961 \( 2^{8}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.3844000000.2 x8 - 19x6 + 151x4 - 589x2 + 961 \( 2^{8}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.3844000000.6 x8 + 19x6 + 151x4 + 589x2 + 961 \( 2^{8}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.3844000000.7 x8 + 22x6 + 194x4 + 713x2 + 961 \( 2^{8}\cdot 5^{6}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.4030726144.1 x8 - 4x7 + 2x6 - 4x5 + 7x4 + 8x3 - 16x2 + 8 \( 2^{22}\cdot 31^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.4059346369.1 x8 - x7 + 5x6 - 8x5 + 37x4 - 58x3 + 80x2 - 38x + 9 \( 13^{6}\cdot 29^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.4079249161.1 x8 - 2x7 - 3x6 + 2x5 - 9x4 + 2x3 - 3x2 - 2x + 1 \( 13^{2}\cdot 17^{6} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.4241265625.2 x8 - x7 + 23x6 - 15x5 + 196x4 - 65x3 + 727x2 - 82x + 991 \( 5^{6}\cdot 521^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.4.4405640625.1 x8 - 2x7 - 5x6 + 8x5 - 6x4 + 22x3 - 5x2 - 28x + 31 \( 3^{4}\cdot 5^{6}\cdot 59^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.4405640625.2 x8 - 3x7 - x6 + 18x5 - 29x4 + 60x2 - 90x + 45 \( 3^{4}\cdot 5^{6}\cdot 59^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.4.4539390625.1 x8 - 3x7 - 3x6 + 20x5 - 19x4 - 20x3 + 58x2 - 44x + 11 \( 5^{6}\cdot 7^{4}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.4539390625.3 x8 - 2x7 + 8x5 - 21x4 + 2x3 + 15x2 + 7x + 1 \( 5^{6}\cdot 7^{4}\cdot 11^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.4573140625.2 x8 - x7 + 11x6 + 4x5 + 81x4 + 40x3 + 430x2 + 480x + 1055 \( 5^{6}\cdot 541^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.4.4709390625.1 x8 - x7 - 5x6 - 9x5 + 4x4 + 31x3 - 15x2 - 21x + 31 \( 3^{4}\cdot 5^{6}\cdot 61^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.4.4709390625.2 x8 - 3x7 + 2x6 - 14x4 + 15x3 - 12x2 + 36x - 9 \( 3^{4}\cdot 5^{6}\cdot 61^{2} \) $C_2^3: C_4$ (as 8T20) Trivial
8.0.4709390625.4 x8 - 3x7 - 16x6 + 58x5 + 111x4 - 410x3 - 300x2 + 1000x + 880 \( 3^{4}\cdot 5^{6}\cdot 61^{2} \) $C_2^3: C_4$ (as 8T20) $[2]$
8.4.4848615424.5 x8 + 4x6 - 8x5 + 6x4 + 8x3 - 36x2 - 24x + 2 \( 2^{24}\cdot 17^{2} \) $C_2^3: C_4$ (as 8T20) Trivial

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