| 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 |
| 21.9.111...281.1 |
$x^{21} - 2 x^{20} - 10 x^{19} + 31 x^{18} - 24 x^{17} - 152 x^{16} + 288 x^{15} + 7 x^{14} - 127 x^{13} + 465 x^{12} - 466 x^{11} + 1998 x^{10} + 1430 x^{9} + 2635 x^{8} + 613 x^{7} - 570 x^{6} - 1087 x^{5} - 669 x^{4} + 195 x^{3} + 193 x^{2} + 93 x - 53$ |
$21$ |
[9,6] |
$13^{16}\cdot 109^{6}$ |
$2$ |
$26.9674946452$ |
$88.51143378673154$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$14$ |
$12045126.3727$ |
| 21.9.111...281.2 |
$x^{21} - x^{20} - 12 x^{19} + 8 x^{18} + 49 x^{17} - 14 x^{16} - 94 x^{15} + 123 x^{14} - 7 x^{13} - 1078 x^{12} + 1150 x^{11} + 1019 x^{10} - 4414 x^{9} + 6562 x^{8} + 4203 x^{7} - 14456 x^{6} + 3035 x^{5} + 9936 x^{4} - 5649 x^{3} - 1996 x^{2} + 1631 x - 79$ |
$21$ |
[9,6] |
$13^{16}\cdot 109^{6}$ |
$2$ |
$26.9674946452$ |
$88.51143378673154$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$14$ |
$12045126.3727$ |
| 21.21.204...216.1 |
$x^{21} - 2 x^{20} - 38 x^{19} + 69 x^{18} + 568 x^{17} - 933 x^{16} - 4319 x^{15} + 6417 x^{14} + 18052 x^{13} - 24428 x^{12} - 41833 x^{11} + 52044 x^{10} + 51770 x^{9} - 58979 x^{8} - 31596 x^{7} + 30977 x^{6} + 9259 x^{5} - 5733 x^{4} - 1455 x^{3} + 114 x^{2} + 17 x - 1$ |
$21$ |
[21,0] |
$2^{30}\cdot 7^{14}\cdot 809^{6}$ |
$3$ |
$66.7242927341$ |
$467.30950158582186$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$20$ |
$2811089509780$ |
| 21.21.204...216.2 |
$x^{21} - 40 x^{19} - 8 x^{18} + 579 x^{17} + 128 x^{16} - 4024 x^{15} - 828 x^{14} + 14642 x^{13} + 3152 x^{12} - 29068 x^{11} - 6976 x^{10} + 31979 x^{9} + 8240 x^{8} - 19278 x^{7} - 4888 x^{6} + 6120 x^{5} + 1376 x^{4} - 924 x^{3} - 168 x^{2} + 48 x + 8$ |
$21$ |
[21,0] |
$2^{30}\cdot 7^{14}\cdot 809^{6}$ |
$3$ |
$66.7242927341$ |
$467.30950158582186$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$20$ |
$2811089509780$ |
