| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 20.0.126...000.1 |
$x^{20} - 10 x^{19} + 40 x^{18} - 35 x^{17} - 165 x^{16} + 372 x^{15} + 1190 x^{14} - 2340 x^{13} - 1135 x^{12} + 9840 x^{11} + 39944 x^{10} + 41385 x^{9} + 3915 x^{8} + 294830 x^{7} + 1808560 x^{6} + 4266328 x^{5} + 7080685 x^{4} + 7638660 x^{3} + 5928390 x^{2} + 2987145 x + 729891$ |
$20$ |
[0,10] |
$2^{32}\cdot 5^{20}\cdot 5560781^{2}$ |
$3$ |
$71.6360410349$ |
|
|
|
? |
$C_5^4.C_4:\OD_{16}.C_2^3$ (as 20T902) |
trivial |
trivial |
$10$ |
$9$ |
$110575417768$ |
| 20.4.481...000.1 |
$x^{20} - 10 x^{18} - 40 x^{17} + 80 x^{16} + 724 x^{15} - 2500 x^{14} - 2690 x^{13} + 18530 x^{12} - 9290 x^{11} - 65224 x^{10} + 66300 x^{9} + 88995 x^{8} - 141150 x^{7} - 46310 x^{6} + 90124 x^{5} + 17005 x^{4} - 46950 x^{3} - 27270 x^{2} - 4860 x - 324$ |
$20$ |
[4,8] |
$2^{20}\cdot 5^{20}\cdot 421^{3}\cdot 254021^{2}$ |
$4$ |
$85.9269262268$ |
|
|
|
? |
$F_5\wr C_4$ (as 20T944) |
trivial |
$[2]$ |
$2$ |
$11$ |
$404290125078$ |
| 20.0.857...000.1 |
$x^{20} - 5 x^{19} - 65 x^{18} + 395 x^{17} + 1690 x^{16} - 14101 x^{15} - 15115 x^{14} + 308995 x^{13} - 203380 x^{12} - 4322105 x^{11} + 7644351 x^{10} + 37252835 x^{9} - 103297030 x^{8} - 167837925 x^{7} + 773861465 x^{6} + 87215539 x^{5} - 3097968570 x^{4} + 2693267725 x^{3} + 4634401475 x^{2} - 8910663885 x + 4107009251$ |
$20$ |
[0,10] |
$2^{32}\cdot 5^{20}\cdot 61^{2}\cdot 750121^{2}$ |
$4$ |
$88.4431319229$ |
|
|
|
? |
$C_5^4.C_4:\OD_{16}.C_2^3$ (as 20T902) |
trivial |
trivial |
$10$ |
$9$ |
$1020241460600$ |
| 20.0.181...125.1 |
$x^{20} - 5 x + 5$ |
$20$ |
[0,10] |
$5^{20}\cdot 1967018160689\cdot 9655782912389$ |
$3$ |
$91.8120738776$ |
|
|
|
✓ |
$S_{20}$ (as 20T1117) |
$[4]$ |
$[4]$ |
$2$ |
$9$ |
$66609463984.3$ |
