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Label Polynomial Discriminant Galois group Class group Regulator
8.2.5754585088.3 $x^{8} - 4 x^{6} + 4 x^{4} + 4 x^{2} - 7$ $-\,2^{24}\cdot 7^{3}$ $QD_{16}$ (as 8T8) trivial $72.2696726962$
8.0.12230590464.1 $x^{8} + 12 x^{6} + 36 x^{4} + 36 x^{2} + 9$ $2^{24}\cdot 3^{6}$ $Q_8$ (as 8T5) $[2]$ $21.2871886415$
8.6.31255953408.4 $x^{8} - 12 x^{6} + 20 x^{4} + 60 x^{2} - 23$ $-\,2^{24}\cdot 3^{4}\cdot 23$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $421.902443004$
8.4.33973862400.4 $x^{8} - 4 x^{6} - 28 x^{4} + 100 x^{2} + 25$ $2^{24}\cdot 3^{4}\cdot 5^{2}$ $Q_8:C_2$ (as 8T11) trivial $288.087800891$
8.4.60012101632.1 $x^{8} - 12 x^{6} + 52 x^{4} - 100 x^{2} + 73$ $2^{24}\cdot 7^{2}\cdot 73$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $562.8166936404576$
8.4.79876325376.1 $x^{8} + 4 x^{6} + 4 x^{4} - 36 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 23^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $647.558278288$
8.0.94371840000.6 $x^{8} + 4 x^{6} + 20 x^{4} + 12 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 5^{4}$ $Q_8:C_2$ (as 8T11) $[2]$ $190.847543261$
8.0.99472113664.6 $x^{8} - 12 x^{6} + 4 x^{4} + 220 x^{2} + 121$ $2^{24}\cdot 7^{2}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $157.267966778$
8.8.164433494016.1 $x^{8} - 20 x^{6} + 116 x^{4} - 220 x^{2} + 121$ $2^{24}\cdot 3^{4}\cdot 11^{2}$ $Q_8:C_2$ (as 8T11) trivial $1350.61030515$
8.2.204128387072.1 $x^{8} - 4 x^{6} - 28 x^{4} - 44 x^{2} - 23$ $-\,2^{24}\cdot 23^{3}$ $QD_{16}$ (as 8T8) trivial $405.809364686$
8.6.226945400832.3 $x^{8} - 4 x^{6} - 76 x^{4} + 340 x^{2} - 167$ $-\,2^{24}\cdot 3^{4}\cdot 167$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $877.188348622$
8.4.229663309824.1 $x^{8} + 4 x^{6} - 76 x^{4} - 52 x^{2} + 169$ $2^{24}\cdot 3^{4}\cdot 13^{2}$ $Q_8:C_2$ (as 8T11) trivial $501.375916115$
8.2.466121392128.7 $x^{8} - 12 x^{6} + 36 x^{4} + 108 x^{2} - 567$ $-\,2^{24}\cdot 3^{4}\cdot 7^{3}$ $QD_{16}$ (as 8T8) $[2]$ $593.938628291$
8.8.490582573056.1 $x^{8} - 28 x^{6} + 260 x^{4} - 836 x^{2} + 361$ $2^{24}\cdot 3^{4}\cdot 19^{2}$ $Q_8:C_2$ (as 8T11) trivial $2058.93464172$
8.6.574837751808.2 $x^{8} - 12 x^{6} - 12 x^{4} + 396 x^{2} - 423$ $-\,2^{24}\cdot 3^{6}\cdot 47$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$ $818.138049662$
8.4.599298932736.5 $x^{8} - 12 x^{6} - 60 x^{4} + 252 x^{2} + 441$ $2^{24}\cdot 3^{6}\cdot 7^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $662.596881185$
8.6.625840488448.2 $x^{8} - 4 x^{6} - 12 x^{4} + 20 x^{2} - 7$ $-\,2^{24}\cdot 7\cdot 73^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $2986.96452803$
8.4.718886928384.10 $x^{8} - 4 x^{6} + 4 x^{4} - 12 x^{2} + 9$ $2^{24}\cdot 3^{4}\cdot 23^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $1982.2316471$
8.4.718886928384.18 $x^{8} - 12 x^{6} + 52 x^{4} - 132 x^{2} + 169$ $2^{24}\cdot 3^{4}\cdot 23^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $1731.33956143$
8.0.761165512704.2 $x^{8} + 12 x^{6} + 52 x^{4} + 84 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 71^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $515.056733402$
8.4.804652056576.6 $x^{8} - 4 x^{6} - 28 x^{4} + 84 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 73^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $1568.952048$
8.6.814013743104.2 $x^{8} - 8 x^{6} - 84 x^{4} + 976 x^{2} - 2396$ $-\,2^{24}\cdot 3^{4}\cdot 599$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $2270.15416464$
8.0.849346560000.13 $x^{8} - 4 x^{6} + 20 x^{4} - 92 x^{2} + 169$ $2^{24}\cdot 3^{4}\cdot 5^{4}$ $Q_8:C_2$ (as 8T11) $[2, 2]$ $285.166452578$
8.6.879243558912.4 $x^{8} + 4 x^{6} - 156 x^{4} + 652 x^{2} - 647$ $-\,2^{24}\cdot 3^{4}\cdot 647$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $2545.49866714$
8.4.1142880731136.1 $x^{8} - 8 x^{6} - 8 x^{5} + 12 x^{4} + 56 x^{3} + 32 x^{2} - 32 x - 23$ $2^{24}\cdot 3^{4}\cdot 29^{2}$ $(A_4\wr C_2):C_2$ (as 8T45) $[2]$ $1607.40057579$
8.4.1142880731136.4 $x^{8} - 4 x^{6} - 220 x^{4} - 812 x^{2} + 841$ $2^{24}\cdot 3^{4}\cdot 29^{2}$ $Q_8:C_2$ (as 8T11) trivial $1036.31294093$
8.4.1186367275008.2 $x^{8} + 12 x^{6} - 204 x^{4} + 180 x^{2} + 873$ $2^{24}\cdot 3^{6}\cdot 97$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$ $901.495188326795$
8.0.1268776960000.19 $x^{8} + 8 x^{6} + 140 x^{4} + 176 x^{2} + 484$ $2^{24}\cdot 5^{4}\cdot 11^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $415.120981956$
8.2.1663075090432.13 $x^{8} + 12 x^{6} - 60 x^{4} - 748 x^{2} - 2023$ $-\,2^{24}\cdot 7^{3}\cdot 17^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $773.250693963$
8.2.1663075090432.17 $x^{8} + 28 x^{6} + 260 x^{4} + 68 x^{2} - 2023$ $-\,2^{24}\cdot 7^{3}\cdot 17^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $773.250693963$
8.4.1664719257600.13 $x^{8} - 12 x^{6} - 124 x^{4} + 1260 x^{2} + 1225$ $2^{24}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ $Q_8:C_2^2$ (as 8T22) trivial $1837.72504651$
8.2.1719446536192.3 $x^{8} + 12 x^{6} + 20 x^{4} - 140 x^{2} - 343$ $-\,2^{24}\cdot 7\cdot 11^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $2493.20528677$
8.4.1860408705024.2 $x^{8} + 4 x^{6} - 220 x^{4} - 148 x^{2} + 1369$ $2^{24}\cdot 3^{4}\cdot 37^{2}$ $Q_8:C_2$ (as 8T11) trivial $1983.3522476$
8.8.2210716975104.1 $x^{8} - 20 x^{6} + 116 x^{4} - 204 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 11^{4}$ $Q_8:C_2$ (as 8T11) trivial $8002.69825014$
8.8.2512706863104.1 $x^{8} - 44 x^{6} + 644 x^{4} - 3268 x^{2} + 1849$ $2^{24}\cdot 3^{4}\cdot 43^{2}$ $Q_8:C_2$ (as 8T11) trivial $5120.11239704$
8.2.3044175511552.12 $x^{8} + 4 x^{6} - 156 x^{4} - 1380 x^{2} - 3703$ $-\,2^{24}\cdot 7^{3}\cdot 23^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $997.103441621$
8.2.3044175511552.18 $x^{8} - 28 x^{6} + 228 x^{4} + 828 x^{2} - 3703$ $-\,2^{24}\cdot 7^{3}\cdot 23^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $997.103441621$
8.8.3534640644096.1 $x^{8} - 36 x^{6} + 420 x^{4} - 1836 x^{2} + 2601$ $2^{24}\cdot 3^{6}\cdot 17^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $3593.46671762$
8.2.3596615680000.5 $x^{8} + 20 x^{6} + 100 x^{4} - 500 x^{2} - 4375$ $-\,2^{24}\cdot 5^{4}\cdot 7^{3}$ $QD_{16}$ (as 8T8) $[2]$ $858.849033107$
8.0.3785359360000.8 $x^{8} + 24 x^{6} + 300 x^{4} + 912 x^{2} + 1444$ $2^{24}\cdot 5^{4}\cdot 19^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $977.603792562$
8.4.4211097993216.1 $x^{8} - 4 x^{6} + 20 x^{4} - 60 x^{2} + 9$ $2^{24}\cdot 3^{2}\cdot 167^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $3156.411787380642$
8.0.4312566595584.2 $x^{8} + 4 x^{6} + 20 x^{4} - 228 x^{2} + 441$ $2^{24}\cdot 3^{2}\cdot 13^{4}$ $Q_8:C_2$ (as 8T11) $[6]$ $332.143053419$
8.2.4586471424000.1 $x^{8} + 12 x^{6} + 36 x^{4} - 60 x^{2} - 375$ $-\,2^{24}\cdot 3^{7}\cdot 5^{3}$ $QD_{16}$ (as 8T8) $[4]$ $2181.85803445$
8.2.4586471424000.5 $x^{8} + 12 x^{6} + 36 x^{4} - 108 x^{2} - 135$ $-\,2^{24}\cdot 3^{7}\cdot 5^{3}$ $QD_{16}$ (as 8T8) $[4]$ $588.144092084$
8.0.4624220160000.10 $x^{8} - 4 x^{6} + 52 x^{4} + 84 x^{2} + 441$ $2^{24}\cdot 3^{2}\cdot 5^{4}\cdot 7^{2}$ $Q_8:C_2^2$ (as 8T22) $[2, 2]$ $608.712533523$
8.4.4874133569536.2 $x^{8} - 52 x^{6} + 676 x^{4} - 3388 x^{2} + 5929$ $2^{24}\cdot 7^{4}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $1874.52037935$
8.2.5530156269568.6 $x^{8} + 12 x^{6} - 60 x^{4} - 1612 x^{2} - 6727$ $-\,2^{24}\cdot 7^{3}\cdot 31^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $2048.99589568$
8.2.5530156269568.10 $x^{8} - 20 x^{6} + 68 x^{4} + 1364 x^{2} - 6727$ $-\,2^{24}\cdot 7^{3}\cdot 31^{2}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $2048.99589568$
8.2.6004750155776.7 $x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} - 284$ $-\,2^{24}\cdot 71^{3}$ $QD_{16}$ (as 8T8) $[3]$ $779.761839165$
8.4.6140880486400.4 $x^{8} + 4 x^{6} - 28 x^{4} - 20 x^{2} + 25$ $2^{24}\cdot 5^{2}\cdot 11^{4}$ $Q_8:C_2$ (as 8T11) trivial $3712.95223494$
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