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Label Polynomial Discriminant Galois group Class group Regulator
8.0.1817487424.1 $x^{8} - x^{7} + 6 x^{6} - 2 x^{5} + 12 x^{4} + 4 x^{3} + 14 x^{2} + 2$ $2^{6}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $102.03813641$
8.0.9597924961.1 $x^{8} - x^{7} + x^{6} + 3 x^{5} + 5 x^{4} - 5 x^{3} + 7 x + 9$ $313^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $59.1447316068$
8.0.9597924961.2 $x^{8} - x^{7} - x^{6} - 4 x^{5} + x^{4} + 11 x^{3} + 16 x^{2} + 5 x + 1$ $313^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $29.1413635159$
8.0.18078415936.1 $x^{8} - x^{7} + 7 x^{6} + 7 x^{5} + 7 x^{4} + 7 x^{3} + 7 x^{2} + 5 x + 2$ $2^{6}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $415.852538984$
8.0.29079798784.1 $x^{8} - 2 x^{7} + 8 x^{6} - 2 x^{5} + 14 x^{4} + 10 x^{3} + 28 x^{2} + 10 x + 1$ $2^{10}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $116.321485113$
8.0.72313663744.1 $x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 2 x + 1$ $2^{8}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $124.833646442$
8.0.100367308864.1 $x^{8} - 3 x^{7} + 4 x^{6} - 16 x^{5} + 46 x^{4} - 70 x^{3} + 82 x^{2} - 48 x + 22$ $2^{6}\cdot 199^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $650.808510845$
8.0.116319195136.1 $x^{8} - 2 x^{7} - 4 x^{6} - 8 x^{5} + 56 x^{4} - 54 x^{3} + 20 x^{2} - 4 x + 1$ $2^{12}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $163.136738927$
8.0.116319195136.3 $x^{8} - 2 x^{7} + 10 x^{6} - 6 x^{5} + 2 x^{4} + 8 x^{3} - 16 x^{2} + 16 x + 26$ $2^{12}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $229.398855642$
8.0.272225149504.1 $x^{8} - x^{7} - 9 x^{6} - x^{5} + 41 x^{4} + 21 x^{3} - 67 x^{2} - 35 x + 66$ $2^{6}\cdot 7^{4}\cdot 11^{6}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $851.951772132$
8.0.272225149504.2 $x^{8} - 3 x^{7} + 9 x^{6} - 21 x^{5} + 33 x^{4} - 69 x^{3} + 7 x^{2} - 7 x + 238$ $2^{6}\cdot 7^{4}\cdot 11^{6}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $675.641426127$
8.0.387790161984.1 $x^{8} + 4 x^{6} - 14 x^{5} + 6 x^{4} + 16 x^{3} + 32 x^{2} + 18 x + 8$ $2^{6}\cdot 3^{8}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1287.38900997$
8.0.401469235456.1 $x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} - 8 x^{4} + 4 x^{3} + 16 x^{2} - 14 x + 6$ $2^{8}\cdot 199^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1372.0493131$
8.0.401469235456.2 $x^{8} - 2 x^{7} - 4 x^{6} + 4 x^{5} + 12 x^{4} - 16 x^{3} + 68 x + 52$ $2^{8}\cdot 199^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $902.529001489$
8.0.525346636864.3 $x^{8} - 2 x^{7} + 2 x^{6} + 20 x^{5} + 20 x^{4} + 56 x^{2} + 52 x + 40$ $2^{6}\cdot 7^{4}\cdot 43^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $3007.85075383$
8.0.525346636864.4 $x^{8} - 2 x^{7} + 2 x^{6} - 12 x^{5} + 64 x^{4} - 184 x^{3} + 296 x^{2} - 280 x + 128$ $2^{6}\cdot 7^{4}\cdot 43^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1572.57786938$
8.0.525346636864.5 $x^{8} - 2 x^{7} + 14 x^{6} - 38 x^{5} + 100 x^{4} - 198 x^{3} + 338 x^{2} - 322 x + 139$ $2^{6}\cdot 7^{4}\cdot 43^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1575.4928373$
8.0.591559418641.1 $x^{8} - x^{7} + 11 x^{6} - 13 x^{5} + 16 x^{4} - 10 x^{3} + 17 x^{2} - 7 x + 4$ $877^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1078.82360069$
8.0.591559418641.2 $x^{8} - 2 x^{7} - 2 x^{6} + 7 x^{5} + 3 x^{4} - 34 x^{3} + 93 x^{2} - 29 x + 39$ $877^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $426.628363544$
8.0.777431921841.1 $x^{8} - 9 x^{6} - 4 x^{5} + 24 x^{4} + 21 x^{3} + 22 x^{2} - 3 x + 3$ $3^{4}\cdot 313^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $407.692725067$
8.0.777431921841.2 $x^{8} - 3 x^{7} + 9 x^{6} - 19 x^{5} + 35 x^{4} - 39 x^{3} + 19 x^{2} - 4 x + 4$ $3^{4}\cdot 313^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1184.59775683$
8.0.1135929640000.1 $x^{8} - 2 x^{7} + 16 x^{6} - 20 x^{5} + 56 x^{4} - 56 x^{3} + 80 x^{2} - 80 x + 64$ $2^{6}\cdot 5^{4}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$ $689.315412453$
8.0.1157018619904.1 $x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 18 x + 23$ $2^{12}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1128.81219385$
8.0.1157018619904.2 $x^{8} - 2 x^{7} + 28 x^{4} - 14 x^{3} - 56 x^{2} + 40 x + 53$ $2^{12}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1476.21477276$
8.0.1464351690816.1 $x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 30 x + 64$ $2^{6}\cdot 3^{4}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$ $910.730819764$
8.0.1605876941824.1 $x^{8} - 2 x^{6} - 12 x^{5} + 40 x^{4} - 76 x^{3} + 74 x^{2} - 24 x + 19$ $2^{10}\cdot 199^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $546.35131695$
8.0.1624709678881.2 $x^{8} - x^{7} - 5 x^{6} + 11 x^{5} + 3 x^{4} - 27 x^{3} + 29 x^{2} - 11 x + 3$ $1129^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $1182.63201875$
8.0.1688107729984.5 $x^{8} - x^{7} + 4 x^{6} - 2 x^{5} + 4 x^{4} - 60 x^{3} + 120 x^{2} - 88 x + 24$ $2^{6}\cdot 13^{4}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1220.44122503$
8.0.1688107729984.6 $x^{8} - x^{7} + 4 x^{6} + 16 x^{4} - 20 x^{3} + 24 x^{2} + 20 x + 4$ $2^{6}\cdot 13^{4}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1551.27496399$
8.0.1861107122176.20 $x^{8} + 4 x^{6} - 12 x^{5} + 16 x^{4} - 40 x^{3} + 72 x^{2} - 52 x + 202$ $2^{16}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $2341.1398307$
8.0.1861107122176.22 $x^{8} - 4 x^{7} + 12 x^{6} - 8 x^{5} - 4 x^{4} - 40 x^{3} + 344 x^{2} - 608 x + 612$ $2^{16}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $2410.50749801$
8.0.2101386547456.12 $x^{8} - 2 x^{7} + 2 x^{6} - 16 x^{5} + 34 x^{4} + 4 x^{3} - 94 x^{2} + 16 x + 153$ $2^{8}\cdot 7^{4}\cdot 43^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$ $574.051605692$
8.0.2420662999104.2 $x^{8} - 3 x^{7} - 7 x^{6} + 35 x^{5} - 21 x^{4} - 77 x^{3} + 189 x^{2} - 171 x + 72$ $2^{6}\cdot 3^{8}\cdot 7^{8}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $13681.3207265$
8.0.2528484794641.1 $x^{8} - 2 x^{7} + x^{6} + 19 x^{5} + 31 x^{4} + 17 x^{3} + 9 x^{2} + 13 x + 9$ $13^{4}\cdot 97^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1031.97284673$
8.0.2528484794641.2 $x^{8} - x^{7} + 12 x^{6} + 2 x^{5} + 49 x^{4} + 87 x^{3} + 148 x^{2} + 87 x + 31$ $13^{4}\cdot 97^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1616.08902495$
8.0.2528484794641.3 $x^{8} - x^{7} - 7 x^{6} + 10 x^{5} - 15 x^{4} + 5 x^{3} + 111 x^{2} - 171 x + 134$ $13^{4}\cdot 97^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$ $342.699629465$
8.0.2528484794641.4 $x^{8} + 7 x^{6} - 11 x^{5} + 65 x^{4} + 43 x^{3} + 191 x^{2} + 137 x + 240$ $13^{4}\cdot 97^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $1419.45248175$
8.0.3490111457856.2 $x^{8} + 18 x^{6} - 6 x^{5} + 54 x^{4} - 108 x^{3} + 66 x^{2} - 18 x + 9$ $2^{6}\cdot 3^{10}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$ $1297.68066456$
8.0.3490111457856.4 $x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{5} + 10 x^{4} + 142 x^{3} + 196 x^{2} + 58 x + 136$ $2^{6}\cdot 3^{10}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$ $2073.07291275$
8.0.3490111457856.5 $x^{8} - 3 x^{7} + 6 x^{6} + 30 x^{5} - 18 x^{4} - 90 x^{3} + 198 x^{2} - 162 x + 54$ $2^{6}\cdot 3^{10}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $2961.55985368$
8.0.4355602392064.2 $x^{8} - 4 x^{7} + 12 x^{6} - 20 x^{5} + 46 x^{4} - 94 x^{3} + 126 x^{2} - 110 x + 49$ $2^{10}\cdot 7^{4}\cdot 11^{6}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $2900.6474635$
8.0.4355602392064.4 $x^{8} - 2 x^{7} + 2 x^{6} - 8 x^{5} + 60 x^{4} - 60 x^{3} - 52 x^{2} + 166 x + 235$ $2^{10}\cdot 7^{4}\cdot 11^{6}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2]$ $2770.51838232$
8.0.4543718560000.9 $x^{8} + 4 x^{6} - 2 x^{5} + 52 x^{4} - 124 x^{3} + 352 x^{2} - 58 x + 91$ $2^{8}\cdot 5^{4}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$ $845.863359859$
8.0.4543718560000.10 $x^{8} - 2 x^{6} - 8 x^{5} - 16 x^{4} - 2 x^{3} + 58 x^{2} + 88 x + 171$ $2^{8}\cdot 5^{4}\cdot 73^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[4]$ $751.513061741$
8.0.5323914784321.1 $x^{8} + 14 x^{6} + 98 x^{4} + 280 x^{2} - 31 x + 252$ $7^{8}\cdot 31^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $8569.14979186$
8.0.5482378736704.1 $x^{8} - 3 x^{7} + 11 x^{6} - 37 x^{5} + 73 x^{4} - 79 x^{3} + 51 x^{2} - 23 x + 12$ $2^{6}\cdot 541^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $9436.04255562$
8.0.5482378736704.2 $x^{8} - x^{7} + 5 x^{6} + x^{5} - 23 x^{4} + 9 x^{3} + 27 x^{2} - 9 x + 14$ $2^{6}\cdot 541^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $7746.14226788$
8.0.5482378736704.3 $x^{8} - x^{7} - 4 x^{6} + 18 x^{5} - 4 x^{4} - 36 x^{3} + 50 x^{2} - 28 x + 6$ $2^{6}\cdot 541^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $8256.46485434$
8.0.5857406763264.1 $x^{8} - 4 x^{7} + 14 x^{6} - 14 x^{5} + 14 x^{4} + 28 x^{3} + 14 x^{2} - 18 x + 121$ $2^{8}\cdot 3^{4}\cdot 7^{10}$ $C_2^3:(C_7: C_3)$ (as 8T36) $[2, 2]$ $1208.01278238$
8.0.6029426229121.1 $x^{8} - 3 x^{7} + 17 x^{6} - 25 x^{5} + 50 x^{4} + 118 x^{3} - 75 x^{2} + 113 x + 228$ $1567^{4}$ $C_2^3:(C_7: C_3)$ (as 8T36) trivial $11464.0244055$
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