| 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 |
| 15.3.612...272.2 |
$x^{15} - 15 x^{13} - 4 x^{12} + 90 x^{11} + 48 x^{10} - 270 x^{9} - 216 x^{8} + 405 x^{7} + 456 x^{6} - 243 x^{5} - 468 x^{4} + 216 x^{2} - 32$ |
$15$ |
[3,6] |
$2^{10}\cdot 3^{15}\cdot 1609^{3}$ |
$3$ |
$20.85062739$ |
$794.7710856468104$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
trivial |
$2$ |
$8$ |
$7486.61022211$ |
| 15.9.106...744.1 |
$x^{15} - 15 x^{13} - 4 x^{12} + 90 x^{11} + 48 x^{10} - 290 x^{9} - 216 x^{8} + 585 x^{7} + 536 x^{6} - 783 x^{5} - 948 x^{4} + 428 x^{3} + 936 x^{2} + 336 x + 32$ |
$15$ |
[9,3] |
$-\,2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 23$ |
$4$ |
$39.9672182762$ |
$647.0563489165986$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
trivial |
$2$ |
$11$ |
$3518070.951$ |
| 18.18.195...744.1 |
$x^{18} - 102 x^{16} - 172 x^{15} + 3627 x^{14} + 11268 x^{13} - 48748 x^{12} - 244656 x^{11} + 89250 x^{10} + 2092016 x^{9} + 2933640 x^{8} - 4599624 x^{7} - 16888252 x^{6} - 15303168 x^{5} + 2472792 x^{4} + 13082176 x^{3} + 7580592 x^{2} + 737856 x - 366976$ |
$18$ |
[18,0] |
$2^{28}\cdot 3^{16}\cdot 61^{2}\cdot 877^{6}$ |
$4$ |
$117.963190507$ |
$29376.363290553763$ |
|
|
|
$C_3\wr A_6:C_2$ (as 18T900) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$226589227104000$ |
| 20.4.878...248.1 |
$x^{20} - 4 x^{19} - 55 x^{18} + 246 x^{17} + 993 x^{16} - 5492 x^{15} - 6022 x^{14} + 59770 x^{13} - 18271 x^{12} - 339764 x^{11} + 402509 x^{10} + 970604 x^{9} - 1970202 x^{8} - 1018122 x^{7} + 4196623 x^{6} - 856632 x^{5} - 3375201 x^{4} + 2301472 x^{3} - 474883 x^{2} - 672470 x + 955037$ |
$20$ |
[4,8] |
$2^{20}\cdot 3^{15}\cdot 53^{2}\cdot 1609^{4}\cdot 55681^{2}$ |
$5$ |
$88.5483422752$ |
|
|
|
? |
$C_2^{10}.(S_3^5.S_5)$ (as 20T1101) |
$[2]$ |
$[2]$ |
$2$ |
$11$ |
$208571434024$ |
