| 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 |
| 21.3.378...943.1 |
$x^{21} - x^{14} - 2 x^{7} + 1$ |
$21$ |
[3,9] |
$-\,7^{35}$ |
$1$ |
$25.6151399702$ |
$31.448918161367093$ |
|
|
✓ |
$C_7:F_7$ (as 21T16) |
trivial |
$2$ |
$11$ |
$2535367.84349$ |
| 21.3.378...943.2 |
$x^{21} - 4 x^{14} + 3 x^{7} + 1$ |
$21$ |
[3,9] |
$-\,7^{35}$ |
$1$ |
$25.6151399702$ |
$31.448918161367093$ |
|
|
✓ |
$C_7:F_7$ (as 21T16) |
trivial |
$2$ |
$11$ |
$3187973.81132$ |
| 21.21.196...248.1 |
$x^{21} - 7 x^{20} - 84 x^{19} + 553 x^{18} + 2989 x^{17} - 17227 x^{16} - 59164 x^{15} + 268223 x^{14} + 701288 x^{13} - 2160550 x^{12} - 4812654 x^{11} + 8210370 x^{10} + 16233798 x^{9} - 11164454 x^{8} - 15807117 x^{7} + 9478959 x^{6} + 3446688 x^{5} - 2593367 x^{4} + 284319 x^{3} + 17031 x^{2} - 2184 x - 43$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{29}\cdot 13^{12}$ |
$3$ |
$115.240443113$ |
$300.25753390948324$ |
|
|
|
$C_7:F_7$ (as 21T16) |
trivial |
$2$ |
$20$ |
$1720832574690000$ |
| 21.21.298...728.1 |
$x^{21} - 7 x^{20} - 112 x^{19} + 917 x^{18} + 4501 x^{17} - 49049 x^{16} - 58303 x^{15} + 1363504 x^{14} - 1028629 x^{13} - 20451844 x^{12} + 43800414 x^{11} + 146916245 x^{10} - 561540210 x^{9} - 174494054 x^{8} + 2966333481 x^{7} - 3053607823 x^{6} - 4087297767 x^{5} + 9329430684 x^{4} - 3704545313 x^{3} - 2362982118 x^{2} + 1114112720 x + 364464491$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{29}\cdot 29^{12}$ |
$3$ |
$182.27279781$ |
$597.26810557336$ |
|
|
|
$C_7:F_7$ (as 21T16) |
trivial |
$2$ |
$20$ |
$238931036050000000$ |
