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Label Polynomial Discriminant Galois group Class group Regulator
8.0.19365101568.7 $x^{8} - 4 x^{6} - 14 x^{4} + 72 x^{2} + 228$ $2^{22}\cdot 3^{5}\cdot 19$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$ $126.430690817$
8.0.57415827456.5 $x^{8} - 28 x^{6} + 346 x^{4} - 2184 x^{2} + 6084$ $2^{22}\cdot 3^{4}\cdot 13^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $129.992116604$
8.0.93117743104.8 $x^{8} - 8 x^{6} - 8 x^{5} + 44 x^{4} + 56 x^{3} - 124 x^{2} - 112 x + 187$ $2^{22}\cdot 149^{2}$ $V_4^2:(S_3\times C_2)$ (as 8T41) $[2]$ $150.372523969$
8.0.107479040000.10 $x^{8} + 12 x^{6} + 50 x^{4} + 104 x^{2} + 164$ $2^{22}\cdot 5^{4}\cdot 41$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $221.273076185$
8.0.122645643264.22 $x^{8} - 8 x^{6} + 60 x^{4} - 48 x^{2} + 36$ $2^{22}\cdot 3^{4}\cdot 19^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $167.319715019$
8.0.149824733184.14 $x^{8} + 36 x^{6} + 570 x^{4} + 4536 x^{2} + 15876$ $2^{22}\cdot 3^{6}\cdot 7^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $550.224443166$
8.0.176265625600.28 $x^{8} - 8 x^{6} + 28 x^{4} + 80 x^{2} + 100$ $2^{22}\cdot 5^{2}\cdot 41^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $465.370331178$
8.0.185459539968.14 $x^{8} - 4 x^{6} + 82 x^{4} - 408 x^{2} + 612$ $2^{22}\cdot 3^{2}\cdot 17^{3}$ $C_4\wr C_2$ (as 8T17) $[2]$ $144.713647136$
8.0.185459539968.15 $x^{8} - 20 x^{6} + 146 x^{4} - 408 x^{2} + 612$ $2^{22}\cdot 3^{2}\cdot 17^{3}$ $C_4\wr C_2$ (as 8T17) $[2]$ $128.245447564$
8.0.204854001664.5 $x^{8} - 8 x^{6} - 4 x^{4} + 208 x^{2} + 676$ $2^{22}\cdot 13^{2}\cdot 17^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $985.666176151$
8.0.317194240000.22 $x^{8} - 20 x^{6} + 146 x^{4} - 440 x^{2} + 484$ $2^{22}\cdot 5^{4}\cdot 11^{2}$ $Q_8:C_2$ (as 8T11) trivial $370.802905551$
8.0.355177857024.12 $x^{8} + 12 x^{6} + 50 x^{4} + 72 x^{2} + 36$ $2^{22}\cdot 3^{2}\cdot 97^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $1281.84142695$
8.0.416179814400.10 $x^{8} - 36 x^{6} + 466 x^{4} - 2520 x^{2} + 4900$ $2^{22}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ $Q_8:C_2^2$ (as 8T22) $[2]$ $965.115792443$
8.0.465102176256.27 $x^{8} + 40 x^{6} + 748 x^{4} + 8880 x^{2} + 49284$ $2^{22}\cdot 3^{4}\cdot 37^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $1692.04373642$
8.0.552679243776.40 $x^{8} - 4 x^{6} + 66 x^{4} - 88 x^{2} + 484$ $2^{22}\cdot 3^{2}\cdot 11^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $531.225843817$
8.0.589824000000.11 $x^{8} + 20 x^{6} + 170 x^{4} + 600 x^{2} + 900$ $2^{22}\cdot 3^{2}\cdot 5^{6}$ $Q_8:C_2$ (as 8T11) $[2]$ $277.920180284$
8.0.628176715776.27 $x^{8} - 4 x^{6} + 18 x^{4} - 24 x^{2} + 36$ $2^{22}\cdot 3^{4}\cdot 43^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $859.234294289$
8.0.946339840000.7 $x^{8} - 20 x^{6} + 194 x^{4} - 760 x^{2} + 1444$ $2^{22}\cdot 5^{4}\cdot 19^{2}$ $Q_8:C_2$ (as 8T11) trivial $706.103888086$
8.0.1078141648896.7 $x^{8} + 4 x^{6} - 6 x^{4} - 72 x^{2} + 324$ $2^{22}\cdot 3^{2}\cdot 13^{4}$ $Q_8:C_2$ (as 8T11) $[3]$ $270.995731769$
8.4.1103810789376.12 $x^{8} + 4 x^{6} - 6 x^{4} - 8 x^{2} + 4$ $2^{22}\cdot 3^{6}\cdot 19^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $1512.34303417$
8.0.1103810789376.42 $x^{8} + 4 x^{6} - 6 x^{4} - 104 x^{2} + 196$ $2^{22}\cdot 3^{6}\cdot 19^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[4]$ $605.805561856$
8.2.1146617856000.2 $x^{8} + 12 x^{6} + 18 x^{4} - 216 x^{2} - 540$ $-\,2^{22}\cdot 3^{7}\cdot 5^{3}$ $QD_{16}$ (as 8T8) $[2]$ $1353.2435417$
8.2.1146617856000.8 $x^{8} - 12 x^{6} - 54 x^{4} - 72 x^{2} - 60$ $-\,2^{22}\cdot 3^{7}\cdot 5^{3}$ $QD_{16}$ (as 8T8) $[2]$ $418.775294169$
8.0.1264167419904.19 $x^{8} + 52 x^{6} + 1258 x^{4} + 19032 x^{2} + 133956$ $2^{22}\cdot 3^{4}\cdot 61^{2}$ $Q_8:C_2$ (as 8T11) $[10]$ $757.368137081$
8.0.1535220121600.13 $x^{8} + 40 x^{6} + 572 x^{4} + 3440 x^{2} + 8100$ $2^{22}\cdot 5^{2}\cdot 11^{4}$ $Q_8:C_2$ (as 8T11) $[2]$ $1151.28399682$
8.0.2026490560512.2 $x^{8} - 24 x^{6} + 188 x^{4} - 528 x^{2} + 1188$ $2^{22}\cdot 3\cdot 11^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$ $2238.42100811$
8.0.2854748160000.25 $x^{8} + 4 x^{6} - 38 x^{4} - 264 x^{2} + 4356$ $2^{22}\cdot 3^{2}\cdot 5^{4}\cdot 11^{2}$ $Q_8:C_2^2$ (as 8T22) $[2]$ $637.13326042$
8.0.2938399358976.22 $x^{8} - 60 x^{6} + 1722 x^{4} - 33480 x^{2} + 311364$ $2^{22}\cdot 3^{6}\cdot 31^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $2053.00725846$
8.0.3196600713216.5 $x^{8} - 24 x^{6} + 188 x^{4} - 528 x^{2} + 676$ $2^{22}\cdot 3^{4}\cdot 97^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[8]$ $543.195574631$
8.4.3196600713216.39 $x^{8} - 4 x^{6} - 30 x^{4} + 104 x^{2} + 100$ $2^{22}\cdot 3^{4}\cdot 97^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $3569.05846035$
8.0.3211264000000.19 $x^{8} - 20 x^{6} + 290 x^{4} - 1400 x^{2} + 4900$ $2^{22}\cdot 5^{6}\cdot 7^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $467.461409236$
8.0.3873527824384.1 $x^{8} + 20 x^{6} + 42 x^{4} + 24 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) $[6]$ $153.831959383$
8.8.3873527824384.1 $x^{8} - 12 x^{6} + 42 x^{4} - 40 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) trivial $5750.25732435$
8.0.3987210240000.22 $x^{8} - 12 x^{6} + 250 x^{4} - 2184 x^{2} + 6084$ $2^{22}\cdot 3^{2}\cdot 5^{4}\cdot 13^{2}$ $Q_8:C_2^2$ (as 8T22) $[2]$ $704.289387316$
8.4.4406640640000.30 $x^{8} - 12 x^{6} + 10 x^{4} + 56 x^{2} + 4$ $2^{22}\cdot 5^{4}\cdot 41^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $2594.61298517$
8.0.4406640640000.75 $x^{8} + 4 x^{6} + 10 x^{4} - 8 x^{2} + 4$ $2^{22}\cdot 5^{4}\cdot 41^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$ $864.144660319$
8.0.4974113193984.52 $x^{8} + 20 x^{6} + 154 x^{4} + 792 x^{2} + 4356$ $2^{22}\cdot 3^{4}\cdot 11^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2, 2]$ $314.097464901$
8.4.5308416000000.47 $x^{8} - 20 x^{6} + 50 x^{4} + 200 x^{2} + 100$ $2^{22}\cdot 3^{4}\cdot 5^{6}$ $Q_8:C_2$ (as 8T11) $[2]$ $1968.0229537$
8.0.5308416000000.65 $x^{8} + 20 x^{6} + 410 x^{4} + 4600 x^{2} + 16900$ $2^{22}\cdot 3^{4}\cdot 5^{6}$ $Q_8:C_2$ (as 8T11) $[4]$ $1784.01075813$
8.4.5653590441984.11 $x^{8} + 8 x^{6} - 84 x^{4} - 16 x^{2} + 4$ $2^{22}\cdot 3^{6}\cdot 43^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $5594.22952159$
8.0.5653590441984.11 $x^{8} + 8 x^{6} + 60 x^{4} + 176 x^{2} + 676$ $2^{22}\cdot 3^{6}\cdot 43^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[8]$ $1371.35090747$
8.0.6990801666048.4 $x^{8} - 92 x^{6} + 2698 x^{4} - 25992 x^{2} + 82308$ $2^{22}\cdot 3^{5}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2, 2]$ $2706.92042417$
8.4.7341411926016.35 $x^{8} + 12 x^{6} - 78 x^{4} + 72 x^{2} + 36$ $2^{22}\cdot 3^{6}\cdot 7^{4}$ $Q_8:C_2$ (as 8T11) trivial $5862.36596181$
8.0.7341411926016.86 $x^{8} - 12 x^{6} + 42 x^{4} + 216 x^{2} + 324$ $2^{22}\cdot 3^{6}\cdot 7^{4}$ $Q_8:C_2$ (as 8T11) $[2, 2]$ $752.119462633$
8.0.7929856000000.14 $x^{8} + 20 x^{6} + 410 x^{4} + 2200 x^{2} + 12100$ $2^{22}\cdot 5^{6}\cdot 11^{2}$ $Q_8:C_2$ (as 8T11) $[2]$ $724.223030047$
8.4.9703274840064.4 $x^{8} - 4 x^{6} - 62 x^{4} - 24 x^{2} + 36$ $2^{22}\cdot 3^{4}\cdot 13^{4}$ $Q_8:C_2$ (as 8T11) trivial $2897.05586447$
8.8.10404495360000.2 $x^{8} - 40 x^{6} + 488 x^{4} - 2240 x^{2} + 3136$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2}$ $Q_8:C_2$ (as 8T11) trivial $15932.9443503$
8.0.10404495360000.180 $x^{8} + 20 x^{6} + 122 x^{4} + 280 x^{2} + 196$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2}$ $Q_8:C_2$ (as 8T11) $[2, 10]$ $54.5213185364$
8.0.10404495360000.183 $x^{8} + 36 x^{6} + 362 x^{4} + 504 x^{2} + 196$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 7^{2}$ $Q_8:C_2^2$ (as 8T22) $[4]$ $2600.91821024$
8.0.12135803387904.14 $x^{8} + 24 x^{6} - 80 x^{5} + 204 x^{4} - 960 x^{3} + 2512 x^{2} - 3552 x + 2628$ $2^{22}\cdot 3^{10}\cdot 7^{2}$ $V_4^2:(S_3\times C_2)$ (as 8T41) $[4]$ $2367.06312661$
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