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Label Polynomial Discriminant Galois group Class group
8.4.56953125.1 x8 - x7 + 2x6 + 2x5 - 5x4 + 13x3 - 13x2 + x + 1 \( 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.4.2147483648.1 x8 - 8x6 - 12x4 + 2 \( 2^{31} \) $C_8:C_2$ (as 8T7) Trivial
8.0.5120000000.1 x8 + 10x6 + 25x4 + 20x2 + 5 \( 2^{16}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.5120000000.1 x8 - 15x4 - 10x2 + 5 \( 2^{16}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.8.5120000000.1 x8 - 10x6 + 25x4 - 20x2 + 5 \( 2^{16}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.4.5120000000.2 x8 - 15x4 + 10x2 + 5 \( 2^{16}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.4.6565418768.1 x8 - 3x7 + 5x6 + 9x5 - 26x4 + 35x3 - 31x2 + 10x - 1 \( 2^{4}\cdot 17^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.0.6891328125.1 x8 - 3x7 + 13x6 - 21x5 + 45x4 - 36x3 + 73x2 + 12x + 61 \( 3^{6}\cdot 5^{7}\cdot 11^{2} \) $C_8:C_2$ (as 8T7) $[2, 2]$
8.8.6891328125.1 x8 - x7 - 13x6 + 17x5 + 40x4 - 62x3 - 13x2 + 31x + 1 \( 3^{6}\cdot 5^{7}\cdot 11^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.9191328125.1 x8 - x7 - 13x6 - 13x5 + 25x4 + 38x3 - 33x2 - 34x + 11 \( 5^{7}\cdot 7^{6} \) $C_8:C_2$ (as 8T7) Trivial
8.0.14580000000.1 x8 + 15x6 + 60x4 + 90x2 + 45 \( 2^{8}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2, 2]$
8.4.14580000000.1 x8 - 30x4 + 45x2 + 45 \( 2^{8}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.8.14580000000.1 x8 - 15x6 + 60x4 - 90x2 + 45 \( 2^{8}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.0.20560078125.1 x8 - 2x7 + 13x6 + x5 + 55x4 + 46x3 + 133x2 + 73x + 211 \( 3^{6}\cdot 5^{7}\cdot 19^{2} \) $C_8:C_2$ (as 8T7) $[2, 2]$
8.8.20560078125.1 x8 - 2x7 - 17x6 + 16x5 + 100x4 + x3 - 197x2 - 152x - 29 \( 3^{6}\cdot 5^{7}\cdot 19^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.0.26261675072.1 x8 - 2x7 + 6x6 - 3x5 + 19x4 - 14x3 + 6x2 + 36x + 52 \( 2^{6}\cdot 17^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.26261675072.1 x8 - 3x7 + 5x6 - 25x5 + 42x4 - 33x3 + 3x2 + 10x - 1 \( 2^{6}\cdot 17^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.47897578125.1 x8 - x7 + 2x6 + 17x5 - 80x4 + 193x3 - 358x2 + 226x + 61 \( 3^{6}\cdot 5^{7}\cdot 29^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.47897578125.2 x8 - 3x7 - 2x6 + 9x5 - 45x4 + 39x3 - 107x2 - 258x + 211 \( 3^{6}\cdot 5^{7}\cdot 29^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.0.54731953125.1 x8 - x7 + 17x6 - 28x5 + 130x4 - 182x3 + 422x2 - 359x + 331 \( 3^{6}\cdot 5^{7}\cdot 31^{2} \) $C_8:C_2$ (as 8T7) $[2, 2, 2]$
8.8.54731953125.1 x8 - 3x7 - 17x6 + 39x5 + 105x4 - 126x3 - 242x2 + 27x + 61 \( 3^{6}\cdot 5^{7}\cdot 31^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.0.69347235737.1 x8 - x7 + 10x6 - 11x5 + 15x4 + 7x3 + 24x2 + 21x + 103 \( 13^{2}\cdot 17^{7} \) $C_8:C_2$ (as 8T7) $[2, 2]$
8.4.95738203125.1 x8 - 3x7 - 2x6 + 9x5 - 90x4 + 84x3 + 208x2 + 327x + 211 \( 3^{6}\cdot 5^{7}\cdot 41^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.95738203125.2 x8 - x7 + 2x6 - 28x5 - 35x4 + 193x3 - 133x2 + x + 331 \( 3^{6}\cdot 5^{7}\cdot 41^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.8.105226698752.1 x8 - 24x6 + 180x4 - 448x2 + 98 \( 2^{31}\cdot 7^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.105226698752.3 x8 - 8x6 - 92x4 - 112x2 + 98 \( 2^{31}\cdot 7^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.105226698752.6 x8 + 8x6 - 92x4 + 112x2 + 98 \( 2^{31}\cdot 7^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.0.105226698752.7 x8 + 24x6 + 180x4 + 448x2 + 98 \( 2^{31}\cdot 7^{2} \) $C_8:C_2$ (as 8T7) $[10]$
8.4.136744453125.1 x8 - 2x7 - 2x6 + 31x5 - 65x4 - 239x3 + 58x2 + 868x + 961 \( 3^{6}\cdot 5^{7}\cdot 7^{4} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.148132260953.1 x8 - x7 - 7x6 + 6x5 - 19x4 + 24x3 + 58x2 + 106x - 67 \( 17^{7}\cdot 19^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.173946175488.1 x8 - 24x6 - 108x4 + 162 \( 2^{31}\cdot 3^{4} \) $C_8:C_2$ (as 8T7) Trivial
8.0.198253828125.1 x8 - 3x7 + 28x6 - 51x5 + 255x4 - 201x3 + 853x2 + 222x + 991 \( 3^{6}\cdot 5^{7}\cdot 59^{2} \) $C_8:C_2$ (as 8T7) $[2, 2, 4]$
8.8.198253828125.1 x8 - x7 - 28x6 + 47x5 + 190x4 - 347x3 - 358x2 + 496x + 331 \( 3^{6}\cdot 5^{7}\cdot 59^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.211922578125.1 x8 - 3x7 + 13x6 - 21x5 - 135x4 + 84x3 + 13x2 + 672x + 271 \( 3^{6}\cdot 5^{7}\cdot 61^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.211922578125.2 x8 - x7 - 13x6 - 13x5 - 20x4 + 358x3 + 227x2 - 539x + 991 \( 3^{6}\cdot 5^{7}\cdot 61^{2} \) $C_8:C_2$ (as 8T7) $[2]$
8.8.233280000000.1 x8 - 30x6 + 240x4 - 720x2 + 720 \( 2^{12}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.0.233280000000.3 x8 + 30x6 + 240x4 + 720x2 + 720 \( 2^{12}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2, 10]$
8.4.233280000000.3 x8 - 120x4 - 360x2 + 720 \( 2^{12}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.4.233280000000.5 x8 - 120x4 + 360x2 + 720 \( 2^{12}\cdot 3^{6}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.0.287100703125.1 x8 - 2x7 + 28x6 + x5 + 235x4 + 151x3 + 898x2 + 478x + 1711 \( 3^{6}\cdot 5^{7}\cdot 71^{2} \) $C_8:C_2$ (as 8T7) $[2, 10]$
8.8.287100703125.1 x8 - 2x7 - 32x6 + 31x5 + 355x4 + 31x3 - 1382x2 - 1352x - 89 \( 3^{6}\cdot 5^{7}\cdot 71^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.327680000000.1 x8 - 60x4 - 160x2 + 20 \( 2^{22}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.8.327680000000.1 x8 - 20x6 + 130x4 - 280x2 + 20 \( 2^{22}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.0.327680000000.2 x8 + 20x6 + 130x4 + 280x2 + 20 \( 2^{22}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[10]$
8.4.327680000000.3 x8 - 60x4 + 160x2 + 20 \( 2^{22}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) Trivial
8.0.355444453125.1 x8 - 2x7 + 28x6 - 14x5 + 265x4 + 181x3 + 1093x2 + 1258x + 2581 \( 3^{6}\cdot 5^{7}\cdot 79^{2} \) $C_8:C_2$ (as 8T7) $[2, 10]$
8.8.355444453125.1 x8 - 2x7 - 32x6 + 16x5 + 325x4 + 121x3 - 1097x2 - 962x + 271 \( 3^{6}\cdot 5^{7}\cdot 79^{2} \) $C_8:C_2$ (as 8T7) Trivial
8.4.414720000000.1 x8 - 135x4 - 270x2 + 405 \( 2^{16}\cdot 3^{4}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.8.414720000000.1 x8 - 30x6 + 225x4 - 540x2 + 405 \( 2^{16}\cdot 3^{4}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2]$
8.0.414720000000.3 x8 + 30x6 + 225x4 + 540x2 + 405 \( 2^{16}\cdot 3^{4}\cdot 5^{7} \) $C_8:C_2$ (as 8T7) $[2, 10]$

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