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Label Polynomial Discriminant Galois group Class group Regulator
8.0.1142440000.2 $x^{8} + x^{6} + 3 x^{2} + 4$ $2^{6}\cdot 5^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $19.8160023787$
8.0.1142440000.3 $x^{8} - 6 x^{6} + 15 x^{4} - 13 x^{2} + 4$ $2^{6}\cdot 5^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $27.331290014$
8.0.1662029824.1 $x^{8} - 2 x^{7} + 2 x^{5} + 4 x^{4} - 6 x^{3} + 14 x + 7$ $2^{12}\cdot 7^{4}\cdot 13^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $39.7231535292$
8.0.1662029824.2 $x^{8} - 2 x^{7} + 4 x^{6} - x^{4} + 6 x^{3} - 2 x^{2} - 4 x + 2$ $2^{12}\cdot 7^{4}\cdot 13^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $50.8070750037$
8.0.2924646400.1 $x^{8} - 2 x^{7} + 6 x^{6} - 4 x^{5} + 13 x^{4} + 4 x^{3} + 6 x^{2} + 2 x + 1$ $2^{12}\cdot 5^{2}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $62.5529047916$
8.0.2924646400.2 $x^{8} - 2 x^{7} + 8 x^{6} - 16 x^{5} + 11 x^{4} + 2 x^{3} + 6 x^{2} - 8 x + 2$ $2^{12}\cdot 5^{2}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $86.2763109029$
8.0.4388797504.1 $x^{8} + 5 x^{6} + 12 x^{4} + 3 x^{2} + 4$ $2^{6}\cdot 7^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $36.4854490288$
8.0.4388797504.2 $x^{8} + 3 x^{6} + 8 x^{4} + 7 x^{2} + 4$ $2^{6}\cdot 7^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $46.6659562662$
8.0.4569760000.5 $x^{8} - x^{6} - 3 x^{2} + 4$ $2^{8}\cdot 5^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $24.6964592526$
8.0.4569760000.6 $x^{8} + 6 x^{6} + 15 x^{4} + 13 x^{2} + 4$ $2^{8}\cdot 5^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $63.975098573$
8.0.6648119296.1 $x^{8} - 2 x^{7} - 2 x^{6} + 10 x^{5} + 8 x^{4} + 14 x^{3} + 22 x^{2} - 10 x + 1$ $2^{14}\cdot 7^{4}\cdot 13^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $81.7629238546$
8.0.6648119296.2 $x^{8} - 2 x^{7} + 2 x^{6} - 10 x^{5} + 4 x^{4} + 2 x^{3} + 26 x^{2} + 14 x + 25$ $2^{14}\cdot 7^{4}\cdot 13^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $71.1351951065$
8.0.7766544384.1 $x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 13 x^{4} - 34 x^{3} + 54 x^{2} - 36 x + 18$ $2^{12}\cdot 3^{8}\cdot 17^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $388.347620982$
8.0.7766544384.2 $x^{8} - 2 x^{7} - 4 x^{6} + 14 x^{5} - 4 x^{4} - 38 x^{3} + 80 x^{2} - 70 x + 31$ $2^{12}\cdot 3^{8}\cdot 17^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $212.535721167$
8.0.8270811136.1 $x^{8} - 2 x^{7} + 10 x^{6} - 24 x^{5} + 41 x^{4} - 52 x^{3} + 42 x^{2} - 6 x + 1$ $2^{12}\cdot 7^{4}\cdot 29^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $38.2433047156$
8.0.8270811136.2 $x^{8} - 2 x^{7} + 4 x^{6} + 10 x^{5} + 10 x^{3} + 80 x^{2} - 2 x + 27$ $2^{12}\cdot 7^{4}\cdot 29^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $216.951931431$
8.0.9701462016.1 $x^{8} - 2 x^{7} + 8 x^{6} - 10 x^{5} + 20 x^{4} - 14 x^{3} + 20 x^{2} - 22 x + 7$ $2^{12}\cdot 3^{8}\cdot 19^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $189.292051368$
8.0.9701462016.2 $x^{8} - 2 x^{7} - 2 x^{6} - 16 x^{5} + 14 x^{4} + 32 x^{3} + 108 x^{2} + 72 x + 36$ $2^{12}\cdot 3^{8}\cdot 19^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $215.25070957$
8.0.11698585600.1 $x^{8} - 2 x^{7} + 10 x^{6} - 6 x^{5} + 24 x^{4} + 6 x^{3} + 10 x^{2} + 2 x + 1$ $2^{14}\cdot 5^{2}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $38.979488264$
8.0.11698585600.2 $x^{8} - 8 x^{6} + 18 x^{4} + 25$ $2^{14}\cdot 5^{2}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $100.974661125$
8.0.15130968064.2 $x^{8} + 2 x^{6} + 18 x^{4} - 6 x^{2} + 1$ $2^{14}\cdot 31^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[8]$ $25.9595081912$
8.0.15130968064.3 $x^{8} - 2 x^{6} + 18 x^{4} + 6 x^{2} + 1$ $2^{14}\cdot 31^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[8]$ $49.2806273428$
8.0.15130968064.5 $x^{8} + 5 x^{4} - 8 x^{2} + 16$ $2^{14}\cdot 31^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $77.1465029331$
8.0.15130968064.6 $x^{8} + 5 x^{4} + 8 x^{2} + 16$ $2^{14}\cdot 31^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $104.602759193$
8.0.16531787776.1 $x^{8} - 2 x^{7} + 10 x^{6} - 24 x^{5} + 49 x^{4} - 64 x^{3} + 58 x^{2} - 26 x + 5$ $2^{12}\cdot 7^{4}\cdot 41^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $126.608038666$
8.0.16531787776.2 $x^{8} - 2 x^{7} + 4 x^{6} + 6 x^{5} - 16 x^{4} + 18 x^{3} + 36 x^{2} + 2 x + 11$ $2^{12}\cdot 7^{4}\cdot 41^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $174.139399328$
8.0.17555190016.2 $x^{8} - 3 x^{6} + 8 x^{4} - 7 x^{2} + 4$ $2^{8}\cdot 7^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $150.19738997$
8.0.17555190016.3 $x^{8} - 5 x^{6} + 12 x^{4} - 3 x^{2} + 4$ $2^{8}\cdot 7^{4}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $130.67439539$
8.0.18183983104.1 $x^{8} - 4 x^{7} + 14 x^{5} + 9 x^{4} - 46 x^{3} + 16 x^{2} + 10 x + 3$ $2^{12}\cdot 7^{4}\cdot 43^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $166.5440114$
8.0.18183983104.2 $x^{8} - 2 x^{7} - 2 x^{6} + 12 x^{5} - 22 x^{4} + 8 x^{3} + 56 x^{2} - 96 x + 56$ $2^{12}\cdot 7^{4}\cdot 43^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $292.866423318$
8.0.20025646144.1 $x^{8} - 3 x^{6} + 9 x^{4} - 4 x^{2} + 1$ $2^{6}\cdot 7^{4}\cdot 19^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $25.7973960594$
8.0.20025646144.2 $x^{8} + 3 x^{4} + 7 x^{2} + 4$ $2^{6}\cdot 7^{4}\cdot 19^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $62.4040738617$
8.0.26155945984.1 $x^{8} - 4 x^{7} + 12 x^{6} - 8 x^{5} - 2 x^{4} + 20 x^{3} + 12 x^{2} - 32 x + 13$ $2^{12}\cdot 7^{2}\cdot 19^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $223.92274722$
8.0.26155945984.2 $x^{8} - 2 x^{7} + 12 x^{6} - 18 x^{5} + 52 x^{4} - 54 x^{3} + 92 x^{2} - 54 x + 47$ $2^{12}\cdot 7^{2}\cdot 19^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $92.568055886$
8.0.28561000000.1 $x^{8} - x^{7} + 9 x^{6} - 2 x^{5} + 9 x^{4} - 9 x^{3} - 24 x^{2} + 7 x + 11$ $2^{6}\cdot 5^{6}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $34.9018095052$
8.0.28561000000.2 $x^{8} - x^{7} + 9 x^{6} - 17 x^{5} + 34 x^{4} - 64 x^{3} + 81 x^{2} - 53 x + 16$ $2^{6}\cdot 5^{6}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $124.005031871$
8.0.28561000000.3 $x^{8} + 5 x^{6} + 5 x^{4} + 25$ $2^{6}\cdot 5^{6}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $56.0281597804$
8.0.28561000000.4 $x^{8} + 5 x^{4} + 25 x^{2} + 25$ $2^{6}\cdot 5^{6}\cdot 13^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[4]$ $91.7479849048$
8.0.31066177536.1 $x^{8} - 2 x^{7} + 6 x^{6} - 14 x^{5} + 4 x^{4} - 18 x^{3} + 66 x^{2} - 42 x + 9$ $2^{14}\cdot 3^{8}\cdot 17^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $302.622081325$
8.0.31066177536.2 $x^{8} - 2 x^{7} + 10 x^{6} - 26 x^{5} + 52 x^{4} - 86 x^{3} + 134 x^{2} - 94 x + 29$ $2^{14}\cdot 3^{8}\cdot 17^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $90.7852134273$
8.0.33083244544.1 $x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} - 16 x^{2} - 28 x + 34$ $2^{14}\cdot 7^{4}\cdot 29^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $120.620109502$
8.0.33083244544.2 $x^{8} - 2 x^{7} + 14 x^{6} - 26 x^{5} + 60 x^{4} - 90 x^{3} + 98 x^{2} - 98 x + 49$ $2^{14}\cdot 7^{4}\cdot 29^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $179.398341368$
8.0.35070801984.1 $x^{8} - 3 x^{6} + 9 x^{4} - 8 x^{2} + 9$ $2^{6}\cdot 3^{8}\cdot 17^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $265.624122767$
8.0.35070801984.2 $x^{8} + 8 x^{6} + 27 x^{4} + 27 x^{2} + 9$ $2^{6}\cdot 3^{8}\cdot 17^{4}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $485.351335699$
8.0.36790308864.1 $x^{8} - 2 x^{7} - 4 x^{6} + 22 x^{5} - 17 x^{4} - 10 x^{3} + 116 x^{2} - 136 x + 55$ $2^{12}\cdot 3^{8}\cdot 37^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $179.464154724$
8.0.36790308864.2 $x^{8} - 2 x^{7} + 2 x^{6} - 8 x^{5} - 2 x^{4} + 8 x^{3} + 8 x^{2} + 80 x + 112$ $2^{12}\cdot 3^{8}\cdot 37^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) trivial $392.124454474$
8.0.38805848064.1 $x^{8} - 2 x^{7} - 8 x^{5} + 28 x^{4} - 24 x^{3} + 12 x^{2} - 24 x + 18$ $2^{14}\cdot 3^{8}\cdot 19^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $273.250649805$
8.0.38805848064.2 $x^{8} - 2 x^{7} + 4 x^{6} - 20 x^{5} + 28 x^{4} + 4 x^{3} + 128 x^{2} + 32 x + 86$ $2^{14}\cdot 3^{8}\cdot 19^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $62.8749792809$
8.0.39432030625.1 $x^{8} - 2 x^{7} - 2 x^{6} + 5 x^{5} + 13 x^{4} - 2 x^{3} - 5 x^{2} + 4 x + 9$ $5^{4}\cdot 13^{4}\cdot 47^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $143.883184151$
8.0.39432030625.2 $x^{8} - x^{7} + 5 x^{5} + 3 x^{4} + 15 x^{3} + 20 x^{2} - 43 x + 16$ $5^{4}\cdot 13^{4}\cdot 47^{2}$ $((C_2 \times D_4): C_2):C_3$ (as 8T32) $[2]$ $179.738313918$
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