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Label Polynomial Discriminant Galois group Class group Regulator
8.2.21434375.1 $x^{8} - x^{7} + 2 x^{6} - 5 x^{5} + x^{4} - 5 x^{3} + 2 x^{2} - x + 1$ $-\,5^{5}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $2.43892189738$
8.2.107171875.2 $x^{8} - x^{7} + 6 x^{5} - 11 x^{4} + 6 x^{3} - x + 1$ $-\,5^{6}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $8.10768565961$
8.0.215378125.1 $x^{8} - 3 x^{7} + 2 x^{6} + 4 x^{5} - x^{4} - 4 x^{3} + 2 x^{2} + 3 x + 1$ $5^{5}\cdot 41^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $11.7418369446$
8.2.363483392.1 $x^{8} - 4 x^{7} + 9 x^{6} - 12 x^{5} + 7 x^{4} + 10 x^{3} - 22 x^{2} + 16 x - 4$ $-\,2^{8}\cdot 17^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $14.8185388509$
8.2.363483392.2 $x^{8} - 2 x^{6} - 4 x^{5} + 4 x^{4} + 4 x^{3} + x^{2} - 6 x - 2$ $-\,2^{8}\cdot 17^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $36.5334876323$
8.2.536870912.1 $x^{8} + 4 x^{6} + 4 x^{4} - 2$ $-\,2^{29}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $29.1140922281$
8.2.536870912.2 $x^{8} - 4 x^{6} + 4 x^{4} - 2$ $-\,2^{29}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $20.7809276166$
8.2.641809375.1 $x^{8} - 2 x^{7} + 3 x^{6} + 4 x^{5} - 4 x^{4} + 10 x^{3} + 10 x^{2} + 18 x + 9$ $-\,5^{5}\cdot 59^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $19.8188437057$
8.0.643956736.1 $x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 7 x^{4} - 6 x^{3} + 5 x^{2} + 4 x + 2$ $2^{17}\cdot 17^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $53.5371848088$
8.0.709315625.1 $x^{8} - x^{7} + 4 x^{6} - 9 x^{5} - x^{4} + 9 x^{3} + 4 x^{2} + x + 1$ $5^{5}\cdot 61^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $13.3852432186$
8.2.1050284375.1 $x^{8} - 3 x^{6} - 2 x^{5} - 22 x^{3} + 50 x^{2} - 24 x - 1$ $-\,5^{5}\cdot 7^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$ $13.9802232105$
8.2.1050284375.2 $x^{8} - x^{7} - 5 x^{6} + 12 x^{5} + 5 x^{4} - 38 x^{3} + 18 x^{2} + 40 x - 31$ $-\,5^{5}\cdot 7^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$ $13.6597572536$
8.2.1050284375.3 $x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 16 x^{4} + 33 x^{3} - 59 x^{2} + 63 x - 29$ $-\,5^{5}\cdot 7^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $20.6356871873$
8.2.1050284375.4 $x^{8} - 2 x^{7} - x^{6} + 2 x^{5} - 6 x^{4} - 18 x^{3} + 2 x^{2} - 19$ $-\,5^{5}\cdot 7^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $19.0309715219$
8.2.1073741824.2 $x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} - 1$ $-\,2^{30}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $46.6347157788$
8.2.1073741824.3 $x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} - 1$ $-\,2^{30}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $33.2867205828$
8.4.1076890625.1 $x^{8} - 4 x^{6} - 9 x^{4} - 20 x^{3} - 9 x^{2} - 5 x + 1$ $5^{6}\cdot 41^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $37.7111446048$
8.2.1331000000.1 $x^{8} - 2 x^{7} - x^{6} + 7 x^{5} - 4 x^{4} - 5 x^{3} - 5 x^{2} + 15 x - 5$ $-\,2^{6}\cdot 5^{6}\cdot 11^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $31.8668473127$
8.2.1331000000.2 $x^{8} - 2 x^{7} + 6 x^{6} - 16 x^{5} + 24 x^{4} - 38 x^{3} + 49 x^{2} - 44 x + 16$ $-\,2^{6}\cdot 5^{6}\cdot 11^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $37.1574597468$
8.2.1453933568.1 $x^{8} + x^{6} - 6 x^{5} - 12 x^{4} - 20 x^{3} - 29 x^{2} - 10 x - 1$ $-\,2^{10}\cdot 17^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $33.0078359942$
8.2.1453933568.2 $x^{8} - 4 x^{7} + 6 x^{6} + 6 x^{5} - 30 x^{4} + 32 x^{3} - 3 x^{2} - 4 x - 8$ $-\,2^{10}\cdot 17^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $80.9895283793$
8.2.1540746875.1 $x^{8} - 2 x^{7} + 2 x^{6} - 11 x^{5} + 19 x^{4} - 15 x^{3} + 35 x^{2} - 50 x + 20$ $-\,5^{5}\cdot 79^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $48.1480202978$
8.2.1736184375.1 $x^{8} - x^{7} - 9 x^{6} + 15 x^{5} + 24 x^{4} - 67 x^{3} + 5 x^{2} + 98 x - 71$ $-\,3^{4}\cdot 5^{5}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $35.9431080142$
8.2.1872286839.1 $x^{8} + 5 x^{6} - 10 x^{5} + 2 x^{4} + 12 x^{3} - 18 x^{2} + 12 x - 3$ $-\,3^{3}\cdot 37^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $67.4707639807$
8.0.2575826944.1 $x^{8} - 2 x^{6} - 5 x^{4} + 34$ $2^{19}\cdot 17^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$ $42.9422856282$
8.2.2593559375.1 $x^{8} - x^{7} + 6 x^{6} - 16 x^{4} - 7 x^{3} - 40 x^{2} + 8 x - 31$ $-\,5^{5}\cdot 11^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $45.0583444053$
8.2.2593559375.2 $x^{8} - 2 x^{7} - 5 x^{6} + 5 x^{5} + 10 x^{4} + 13 x^{3} + 29 x^{2} - 85 x - 25$ $-\,5^{5}\cdot 11^{2}\cdot 19^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) $[2]$ $23.1806941734$
8.2.3209046875.1 $x^{8} - x^{7} - 4 x^{5} - 21 x^{4} + x^{3} + 15 x^{2} - 16 x - 19$ $-\,5^{6}\cdot 59^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $58.9189370164$
8.4.3219690625.1 $x^{8} - 2 x^{7} + 5 x^{6} - 20 x^{5} + 4 x^{4} + 4 x^{3} + 32 x^{2} - 12 x - 1$ $5^{5}\cdot 101^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $60.495178236$
8.4.3219690625.2 $x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{5} + 4 x^{4} + 2 x^{3} - 13 x^{2} + 1$ $5^{5}\cdot 101^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $55.0377286145$
8.4.3219690625.3 $x^{8} - x^{7} - 5 x^{6} + 12 x^{5} - x^{4} - 20 x^{3} + 30 x^{2} - 20 x + 5$ $5^{5}\cdot 101^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $52.896016206$
8.2.3258096075.1 $x^{8} - 3 x^{7} + 4 x^{6} - 10 x^{5} + 15 x^{4} - 4 x^{3} + 10 x^{2} - 3 x - 23$ $-\,3^{3}\cdot 5^{2}\cdot 13^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $78.1734594151$
8.2.3258096075.2 $x^{8} - x^{7} - 4 x^{6} + 2 x^{5} + 4 x^{4} - 3 x^{3} - 9 x^{2} + 18 x - 12$ $-\,3^{3}\cdot 5^{2}\cdot 13^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $77.3347452369$
8.2.3276800000.1 $x^{8} + 2 x^{6} + x^{4} - 10 x^{2} - 5$ $-\,2^{20}\cdot 5^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $64.9545602537$
8.2.3276800000.2 $x^{8} - 4 x^{6} + 4 x^{4} - 5$ $-\,2^{20}\cdot 5^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $40.8524812179$
8.2.3276800000.3 $x^{8} + 4 x^{6} + 4 x^{4} - 5$ $-\,2^{20}\cdot 5^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $48.3939206573$
8.2.3276800000.4 $x^{8} - 2 x^{6} + x^{4} + 10 x^{2} - 5$ $-\,2^{20}\cdot 5^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $61.564140028$
8.2.3514671875.1 $x^{8} - 8 x^{6} - 5 x^{5} - x^{4} - 25 x^{3} - 27 x^{2} - 20 x - 4$ $-\,5^{6}\cdot 11^{3}\cdot 13^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $45.6133508795$
8.2.3514671875.2 $x^{8} - 2 x^{7} - 3 x^{6} + 5 x^{5} + x^{4} + 10 x^{3} - 7 x^{2} - 6 x - 4$ $-\,5^{6}\cdot 11^{3}\cdot 13^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $71.9991231294$
8.4.3546578125.1 $x^{8} - 2 x^{7} - 7 x^{5} - 6 x^{4} + 17 x^{3} - 8 x + 1$ $5^{6}\cdot 61^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $67.9700593496$
8.2.3641573376.1 $x^{8} - 2 x^{7} + x^{6} + 6 x^{5} - 17 x^{4} + 20 x^{3} - 18 x^{2} + 12 x - 2$ $-\,2^{17}\cdot 3^{4}\cdot 7^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $74.8682850741$
8.2.3641573376.2 $x^{8} + 6 x^{6} + 11 x^{4} - 14$ $-\,2^{17}\cdot 3^{4}\cdot 7^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $229.556419619$
8.2.3904765952.1 $x^{8} - 2 x^{7} - x^{6} - 8 x^{5} - 13 x^{4} - 14 x^{3} - 17 x^{2} - 12 x - 2$ $-\,2^{17}\cdot 31^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $208.362011766$
8.2.3904765952.2 $x^{8} - 2 x^{7} + 5 x^{6} + 2 x^{5} - 17 x^{4} - 4 x^{3} - 2 x^{2} - 12 x - 2$ $-\,2^{17}\cdot 31^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $78.0692517928$
8.2.3904765952.3 $x^{8} - 2 x^{7} - 7 x^{6} + 6 x^{5} + 26 x^{4} + 10 x^{3} - 29 x^{2} - 38 x - 17$ $-\,2^{17}\cdot 31^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $71.2898661541$
8.2.4096000000.4 $x^{8} - 2 x^{6} - 6 x^{4} - 8 x^{2} - 4$ $-\,2^{18}\cdot 5^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $53.2542185263$
8.2.4096000000.5 $x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} - 4$ $-\,2^{18}\cdot 5^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $71.4780761519$
8.2.4096000000.7 $x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} - 4$ $-\,2^{18}\cdot 5^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $67.7471492681$
8.2.4096000000.8 $x^{8} + 2 x^{6} - 6 x^{4} + 8 x^{2} - 4$ $-\,2^{18}\cdot 5^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $44.9553772989$
8.2.4517521931.1 $x^{8} - 4 x^{7} + x^{6} + 11 x^{5} - 14 x^{4} + 5 x^{3} + x^{2} - x - 1$ $-\,13^{5}\cdot 23^{3}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) trivial $62.3098628193$
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