| 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 |
| 21.5.162...041.1 |
$x^{21} - x^{20} - 6 x^{19} + 8 x^{18} + 15 x^{17} - 28 x^{16} - 39 x^{15} + 74 x^{14} + 112 x^{13} - 127 x^{12} - 227 x^{11} + 89 x^{10} + 306 x^{9} + x^{8} - 244 x^{7} - 55 x^{6} + 122 x^{5} + 40 x^{4} - 41 x^{3} - 6 x^{2} + 8 x - 1$ |
$21$ |
[5,8] |
$13^{8}\cdot 109^{8}$ |
$2$ |
$15.8679874279$ |
$37.64306044943742$ |
|
|
? |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$17240.5464964$ |
| 21.5.267...304.1 |
$x^{21} - 5 x^{20} + 11 x^{19} - 16 x^{18} + 25 x^{17} - 38 x^{16} + 36 x^{15} - 25 x^{14} + 18 x^{13} - 4 x^{12} - 3 x^{11} - 17 x^{10} - 23 x^{9} - 12 x^{8} + 55 x^{7} + 18 x^{6} - 46 x^{5} - 17 x^{4} + 19 x^{3} + 9 x^{2} - 2 x - 1$ |
$21$ |
[5,8] |
$2^{18}\cdot 317^{8}$ |
$2$ |
$16.2483846421$ |
$32.251902756545775$ |
|
|
? |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$25357.2549184$ |
| 21.21.504...024.1 |
$x^{21} - 3 x^{20} - 35 x^{19} + 103 x^{18} + 465 x^{17} - 1353 x^{16} - 2985 x^{15} + 8673 x^{14} + 9901 x^{13} - 29145 x^{12} - 17071 x^{11} + 52175 x^{10} + 14997 x^{9} - 49437 x^{8} - 6223 x^{7} + 23447 x^{6} + 1118 x^{5} - 4872 x^{4} - 114 x^{3} + 334 x^{2} - 6 x - 2$ |
$21$ |
[21,0] |
$2^{38}\cdot 809^{8}$ |
$2$ |
$44.9273556543$ |
$127.70441679847741$ |
|
|
|
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$20$ |
$232658701418$ |
| 21.21.354...944.1 |
$x^{21} - 2 x^{20} - 43 x^{19} + 68 x^{18} + 733 x^{17} - 988 x^{16} - 6395 x^{15} + 8040 x^{14} + 30708 x^{13} - 39018 x^{12} - 79894 x^{11} + 110250 x^{10} + 98768 x^{9} - 165588 x^{8} - 29458 x^{7} + 106634 x^{6} - 26074 x^{5} - 14068 x^{4} + 6574 x^{3} - 756 x^{2} - 8 x + 4$ |
$21$ |
[21,0] |
$2^{22}\cdot 4129^{8}$ |
$2$ |
$49.29801977$ |
$144.25275061524383$ |
|
|
|
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$20$ |
$646551468945$ |
