Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
20.4.424...625.1 |
$x^{20} + 3 x^{18} - 98 x^{16} - 2142 x^{14} - 12663 x^{12} - 43302 x^{10} + 43057 x^{8} - 80742 x^{6} + 847702 x^{4} - 395577 x^{2} + 53361$ |
$20$ |
[4,8] |
$3^{14}\cdot 5^{14}\cdot 7^{14}\cdot 11^{8}$ |
$4$ |
$67.8249657948$ |
$108.78983470289555$ |
|
|
|
$C_5^2:Q_8$ (as 20T47) |
$[5]$ |
$2$ |
$11$ |
$44976855810.1$ |
20.4.424...625.2 |
$x^{20} + 12 x^{18} - 99 x^{17} - 236 x^{16} - 1221 x^{15} + 1054 x^{14} + 9342 x^{13} + 40177 x^{12} + 54018 x^{11} - 90176 x^{10} - 379482 x^{9} - 366539 x^{8} + 711180 x^{7} + 1068910 x^{6} - 370575 x^{5} - 745940 x^{4} - 236625 x^{3} + 219900 x^{2} + 314550 x + 103525$ |
$20$ |
[4,8] |
$3^{14}\cdot 5^{14}\cdot 7^{14}\cdot 11^{8}$ |
$4$ |
$67.8249657948$ |
$108.78983470289555$ |
|
|
|
$C_5^2:Q_8$ (as 20T47) |
$[5]$ |
$2$ |
$11$ |
$46597258073.0$ |
20.20.134...625.1 |
$x^{20} - 10 x^{19} - 45 x^{18} + 690 x^{17} + 255 x^{16} - 18970 x^{15} + 17675 x^{14} + 269325 x^{13} - 405450 x^{12} - 2157325 x^{11} + 3803273 x^{10} + 10037010 x^{9} - 18164180 x^{8} - 27345215 x^{7} + 44354270 x^{6} + 45162920 x^{5} - 49287350 x^{4} - 48627275 x^{3} + 16874650 x^{2} + 25430025 x + 6117451$ |
$20$ |
[20,0] |
$3^{14}\cdot 5^{18}\cdot 43^{14}$ |
$3$ |
$127.78674301$ |
$243.6451595219869$ |
|
|
|
$C_5^2:Q_8$ (as 20T47) |
trivial |
$2$ |
$19$ |
$2777762864880000$ |
20.20.257...000.1 |
$x^{20} - 120 x^{18} - 108 x^{17} + 5641 x^{16} + 8736 x^{15} - 134648 x^{14} - 281880 x^{13} + 1734073 x^{12} + 4608864 x^{11} - 11471684 x^{10} - 40112652 x^{9} + 29464915 x^{8} + 179834256 x^{7} + 31646308 x^{6} - 379196064 x^{5} - 261172829 x^{4} + 293301600 x^{3} + 299329500 x^{2} - 50884740 x - 82487645$ |
$20$ |
[20,0] |
$2^{50}\cdot 3^{14}\cdot 5^{14}\cdot 23^{8}$ |
$4$ |
$131.986649661$ |
$629.9168144486933$ |
|
|
|
$C_5^2:Q_8$ (as 20T47) |
trivial |
$2$ |
$19$ |
$7402171873190000$ |