| 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 |
| 21.5.115...601.1 |
$x^{21} - 6 x^{20} + 61 x^{18} - 66 x^{17} - 276 x^{16} + 428 x^{15} + 753 x^{14} - 1425 x^{13} - 1350 x^{12} + 3009 x^{11} + 1563 x^{10} - 4228 x^{9} - 1029 x^{8} + 3927 x^{7} + 143 x^{6} - 2298 x^{5} + 384 x^{4} + 686 x^{3} - 288 x^{2} - 21 x + 31$ |
$21$ |
[5,8] |
$3^{32}\cdot 53^{8}$ |
$2$ |
$24.2052130678$ |
|
|
|
? |
$A_7$ (as 21T33) |
trivial |
$2$ |
$12$ |
$3200562.51046$ |
| 21.5.159...441.1 |
$x^{21} - 2 x^{20} - 2 x^{19} + 26 x^{18} - 25 x^{17} - 37 x^{16} + 153 x^{15} - 69 x^{14} - 124 x^{13} + 277 x^{12} - 70 x^{11} - 106 x^{10} + 228 x^{9} - 76 x^{8} - 41 x^{7} + 116 x^{6} - 32 x^{5} - 16 x^{4} + 25 x^{3} - 2 x^{2} - 2 x + 1$ |
$21$ |
[5,8] |
$11^{14}\cdot 29^{10}$ |
$2$ |
$24.583391024$ |
$69.62404259846498$ |
|
|
? |
$A_7$ (as 21T33) |
trivial |
$2$ |
$12$ |
$2549812.08882$ |
| 21.21.444...209.1 |
$x^{21} - 6 x^{20} - 45 x^{19} + 304 x^{18} + 681 x^{17} - 5892 x^{16} - 2835 x^{15} + 55011 x^{14} - 24204 x^{13} - 253860 x^{12} + 274332 x^{11} + 500406 x^{10} - 903062 x^{9} - 112956 x^{8} + 1002705 x^{7} - 558462 x^{6} - 98895 x^{5} + 163020 x^{4} - 32917 x^{3} - 5658 x^{2} + 2316 x - 173$ |
$21$ |
[21,0] |
$3^{32}\cdot 547^{10}$ |
$2$ |
$107.360716369$ |
|
|
|
? |
$A_7$ (as 21T33) |
$[2]$ |
$2$ |
$20$ |
$406277532862000$ |
| 21.21.584...921.1 |
$x^{21} - 3 x^{20} - 65 x^{19} + 151 x^{18} + 1727 x^{17} - 3019 x^{16} - 24355 x^{15} + 31328 x^{14} + 199461 x^{13} - 184556 x^{12} - 979409 x^{11} + 630480 x^{10} + 2868715 x^{9} - 1213360 x^{8} - 4787032 x^{7} + 1195047 x^{6} + 4026302 x^{5} - 482093 x^{4} - 1211172 x^{3} + 65247 x^{2} + 18885 x - 477$ |
$21$ |
[21,0] |
$3^{28}\cdot 29^{8}\cdot 59^{10}$ |
$3$ |
$108.774860462$ |
|
|
|
|
$A_7$ (as 21T33) |
trivial |
$2$ |
$20$ |
$3149865113890000$ |
