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Label Polynomial Discriminant Galois group Class group Regulator
8.4.36507222016.2 $x^{8} + 8 x^{6} - 28 x^{4} - 32 x^{2} + 34$ $2^{31}\cdot 17$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $238.264297488$
8.4.36507222016.5 $x^{8} - 8 x^{6} - 28 x^{4} + 32 x^{2} + 34$ $2^{31}\cdot 17$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $283.533814772$
8.6.100931731456.2 $x^{8} - 8 x^{6} - 12 x^{4} + 96 x^{2} - 94$ $-\,2^{31}\cdot 47$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $753.287100582$
8.2.100931731456.4 $x^{8} + 8 x^{6} - 12 x^{4} - 96 x^{2} - 94$ $-\,2^{31}\cdot 47$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $256.789549393$
8.8.105226698752.1 $x^{8} - 24 x^{6} + 180 x^{4} - 448 x^{2} + 98$ $2^{31}\cdot 7^{2}$ $C_8:C_2$ (as 8T7) trivial $1043.69189352$
8.0.105226698752.7 $x^{8} + 24 x^{6} + 180 x^{4} + 448 x^{2} + 98$ $2^{31}\cdot 7^{2}$ $C_8:C_2$ (as 8T7) $[10]$ $19.534360053$
8.6.169651208192.2 $x^{8} - 8 x^{6} - 12 x^{4} + 128 x^{2} - 158$ $-\,2^{31}\cdot 79$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $832.072244545$
8.2.169651208192.3 $x^{8} + 8 x^{6} - 12 x^{4} - 128 x^{2} - 158$ $-\,2^{31}\cdot 79$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $143.929050844$
8.4.173946175488.1 $x^{8} - 24 x^{6} - 108 x^{4} + 162$ $2^{31}\cdot 3^{4}$ $C_8:C_2$ (as 8T7) trivial $429.250289797$
8.8.242665652224.1 $x^{8} - 24 x^{6} + 148 x^{4} - 320 x^{2} + 226$ $2^{31}\cdot 113$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1794.50134954$
8.0.242665652224.17 $x^{8} + 24 x^{6} + 148 x^{4} + 320 x^{2} + 226$ $2^{31}\cdot 113$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[18]$ $19.534360053$
8.6.513248591872.2 $x^{8} - 24 x^{6} + 132 x^{4} + 32 x^{2} - 478$ $-\,2^{31}\cdot 239$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1547.88643455$
8.2.513248591872.4 $x^{8} + 24 x^{6} + 132 x^{4} - 32 x^{2} - 478$ $-\,2^{31}\cdot 239$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $332.308106473$
8.4.517543559168.2 $x^{8} + 8 x^{6} - 60 x^{4} - 192 x^{2} + 482$ $2^{31}\cdot 241$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1092.17897608$
8.4.517543559168.5 $x^{8} - 8 x^{6} - 60 x^{4} + 192 x^{2} + 482$ $2^{31}\cdot 241$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1208.1483563$
8.6.581968068608.3 $x^{8} - 8 x^{6} - 28 x^{4} + 320 x^{2} - 542$ $-\,2^{31}\cdot 271$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1589.73154823$
8.2.581968068608.3 $x^{8} + 8 x^{6} - 28 x^{4} - 320 x^{2} - 542$ $-\,2^{31}\cdot 271$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $684.369232251$
8.0.620622774272.10 $x^{8} - 8 x^{6} + 20 x^{4} + 162$ $2^{31}\cdot 17^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[4]$ $204.684844296$
8.0.620622774272.11 $x^{8} + 8 x^{6} + 20 x^{4} + 162$ $2^{31}\cdot 17^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[4]$ $172.004495026$
8.4.723701989376.4 $x^{8} + 24 x^{6} + 4 x^{4} - 576 x^{2} + 674$ $2^{31}\cdot 337$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $597.88694282$
8.4.723701989376.10 $x^{8} - 24 x^{6} + 4 x^{4} + 576 x^{2} + 674$ $2^{31}\cdot 337$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $510.939178474$
8.2.788126498816.1 $x^{8} + 8 x^{6} - 92 x^{4} - 832 x^{2} - 734$ $-\,2^{31}\cdot 367$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $909.471880651$
8.6.788126498816.4 $x^{8} - 8 x^{6} - 92 x^{4} + 832 x^{2} - 734$ $-\,2^{31}\cdot 367$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2106.58363505$
8.4.861140942848.3 $x^{8} - 8 x^{6} - 140 x^{4} - 128 x^{2} + 802$ $2^{31}\cdot 401$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1569.01778539$
8.4.861140942848.4 $x^{8} + 8 x^{6} - 140 x^{4} + 128 x^{2} + 802$ $2^{31}\cdot 401$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1324.41319801$
8.2.925565452288.1 $x^{8} + 24 x^{6} + 84 x^{4} - 704 x^{2} - 862$ $-\,2^{31}\cdot 431$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $445.372866287$
8.6.925565452288.4 $x^{8} - 24 x^{6} + 84 x^{4} + 704 x^{2} - 862$ $-\,2^{31}\cdot 431$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1638.25776657$
8.4.929860419584.3 $x^{8} + 8 x^{6} - 92 x^{4} - 32 x^{2} + 866$ $2^{31}\cdot 433$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1563.12851299$
8.4.929860419584.4 $x^{8} - 8 x^{6} - 92 x^{4} + 32 x^{2} + 866$ $2^{31}\cdot 433$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1061.10899562$
8.6.994284929024.2 $x^{8} - 24 x^{6} + 20 x^{4} + 480 x^{2} - 926$ $-\,2^{31}\cdot 463$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2435.44397194$
8.2.994284929024.4 $x^{8} + 24 x^{6} + 20 x^{4} - 480 x^{2} - 926$ $-\,2^{31}\cdot 463$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $382.65329284$
8.8.1136018849792.1 $x^{8} - 40 x^{6} + 516 x^{4} - 2208 x^{2} + 1058$ $2^{31}\cdot 23^{2}$ $C_8:C_2$ (as 8T7) trivial $3586.15596796$
8.0.1136018849792.13 $x^{8} + 40 x^{6} + 516 x^{4} + 2208 x^{2} + 1058$ $2^{31}\cdot 23^{2}$ $C_8:C_2$ (as 8T7) $[26]$ $19.534360053$
8.4.1273457803264.1 $x^{8} + 8 x^{6} - 156 x^{4} - 1120 x^{2} + 1186$ $2^{31}\cdot 593$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1584.48364931$
8.4.1273457803264.10 $x^{8} - 8 x^{6} - 156 x^{4} + 1120 x^{2} + 1186$ $2^{31}\cdot 593$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1764.52363383$
8.4.1342177280000.2 $x^{8} - 40 x^{6} - 300 x^{4} + 1250$ $2^{31}\cdot 5^{4}$ $C_8:C_2$ (as 8T7) $[2]$ $649.132196281$
8.6.1544040742912.3 $x^{8} - 8 x^{6} - 60 x^{4} + 672 x^{2} - 1438$ $-\,2^{31}\cdot 719$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2977.19343054$
8.2.1544040742912.3 $x^{8} + 8 x^{6} - 60 x^{4} - 672 x^{2} - 1438$ $-\,2^{31}\cdot 719$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $675.828515079$
8.6.1612760219648.1 $x^{8} - 24 x^{6} + 164 x^{4} - 96 x^{2} - 1502$ $-\,2^{31}\cdot 751$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $3221.44779447$
8.2.1612760219648.6 $x^{8} + 24 x^{6} + 164 x^{4} + 96 x^{2} - 1502$ $-\,2^{31}\cdot 751$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2]$ $588.703125035$
8.4.1891933093888.7 $x^{8} - 8 x^{6} - 188 x^{4} - 288 x^{2} + 1762$ $2^{31}\cdot 881$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1874.06754713$
8.4.1891933093888.8 $x^{8} + 8 x^{6} - 188 x^{4} + 288 x^{2} + 1762$ $2^{31}\cdot 881$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1437.01073778$
8.6.1956357603328.1 $x^{8} - 24 x^{6} + 132 x^{4} + 256 x^{2} - 1822$ $-\,2^{31}\cdot 911$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $3641.80304364$
8.2.1956357603328.6 $x^{8} + 24 x^{6} + 132 x^{4} - 256 x^{2} - 1822$ $-\,2^{31}\cdot 911$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1305.00640006$
8.4.2098091524096.2 $x^{8} + 8 x^{6} - 108 x^{4} - 512 x^{2} + 1954$ $2^{31}\cdot 977$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2457.77735781$
8.4.2098091524096.5 $x^{8} - 8 x^{6} - 108 x^{4} + 512 x^{2} + 1954$ $2^{31}\cdot 977$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2745.17918617$
8.4.2166811000832.2 $x^{8} + 8 x^{6} - 108 x^{4} - 480 x^{2} + 2018$ $2^{31}\cdot 1009$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1488.31786054$
8.4.2166811000832.5 $x^{8} - 8 x^{6} - 108 x^{4} + 480 x^{2} + 2018$ $2^{31}\cdot 1009$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1828.42713668$
8.6.2231235510272.2 $x^{8} - 24 x^{6} - 92 x^{4} + 1184 x^{2} - 2078$ $-\,2^{31}\cdot 1039$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $3546.20045228$
8.2.2231235510272.4 $x^{8} + 24 x^{6} - 92 x^{4} - 1184 x^{2} - 2078$ $-\,2^{31}\cdot 1039$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1153.86207478$
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