| 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 |
| 21.3.214...807.1 |
$x^{21} - x^{20} - x^{19} + x^{18} - x^{17} + 6 x^{16} - 7 x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 9 x^{11} - 17 x^{10} + 11 x^{9} - 4 x^{8} - 3 x^{7} + 9 x^{6} - 6 x^{5} - x^{4} + 3 x^{3} - x^{2} - x + 1$ |
$21$ |
[3,9] |
$-\,184607^{5}$ |
$1$ |
$17.9419073895$ |
$429.65916724771506$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$11$ |
$59489.8190642$ |
| 21.3.270...407.1 |
$x^{21} - 4 x^{18} - x^{17} + x^{16} + 7 x^{15} + x^{14} - 6 x^{13} - 11 x^{12} + 2 x^{11} + 10 x^{10} + 14 x^{9} - 2 x^{8} - 5 x^{7} - 6 x^{6} + 2 x^{5} - 2 x^{4} - 3 x^{3} + 2 x^{2} - 1$ |
$21$ |
[3,9] |
$-\,193327^{5}$ |
$1$ |
$18.1401583673$ |
$439.68966328536766$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$11$ |
$75073.7253$ |
| 21.5.123...001.1 |
$x^{21} - 2 x^{19} - x^{18} - 8 x^{17} + 16 x^{15} + 16 x^{14} + 21 x^{13} - 27 x^{12} - 29 x^{11} - 63 x^{10} - 3 x^{9} + 86 x^{8} + 60 x^{7} + 11 x^{6} - 69 x^{5} - 49 x^{4} + 30 x^{3} + 16 x^{2} - 6 x - 1$ |
$21$ |
[5,8] |
$7^{9}\cdot 12503^{5}$ |
$2$ |
$21.7602786875$ |
$295.8394835041462$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$564369.598704$ |
| 21.5.348...177.1 |
$x^{21} - 2 x^{20} - 5 x^{18} + 12 x^{17} - 5 x^{16} + 4 x^{15} - 27 x^{14} + 16 x^{13} - 8 x^{12} + 8 x^{11} - 22 x^{10} - 8 x^{9} - 2 x^{8} + 9 x^{7} + 15 x^{6} + 12 x^{5} + 13 x^{4} + 2 x^{3} - x^{2} - 2 x - 1$ |
$21$ |
[5,8] |
$3^{8}\cdot 37^{5}\cdot 2381^{5}$ |
$3$ |
$22.8629450794$ |
$514.0924041454026$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$1358971.01083$ |
| 21.11.391...159.1 |
$x^{21} - 2 x^{20} - 9 x^{19} + 12 x^{18} + 25 x^{17} + 8 x^{16} - 79 x^{15} + 7 x^{14} + 170 x^{13} - 132 x^{12} - 294 x^{11} - 136 x^{10} + 534 x^{9} + 158 x^{8} - 345 x^{7} + 242 x^{6} + 243 x^{5} - 58 x^{4} - 53 x^{3} - 6 x^{2} + 2 x + 1$ |
$21$ |
[11,5] |
$-\,7^{5}\cdot 17^{8}\cdot 2017^{5}$ |
$3$ |
$28.6279996321$ |
$489.9214222709597$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$15$ |
$47695486.7102$ |
| 21.11.344...967.1 |
$x^{21} - 6 x^{20} - x^{19} + 71 x^{18} - 93 x^{17} - 305 x^{16} + 665 x^{15} + 567 x^{14} - 2100 x^{13} - 214 x^{12} + 3718 x^{11} - 982 x^{10} - 3941 x^{9} + 1934 x^{8} + 2506 x^{7} - 1669 x^{6} - 928 x^{5} + 820 x^{4} + 128 x^{3} - 214 x^{2} + 45 x - 1$ |
$21$ |
[11,5] |
$-\,3^{9}\cdot 280909^{5}$ |
$2$ |
$31.751048717$ |
$918.0016339854739$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$15$ |
$130916585.101$ |
| 21.21.539...056.1 |
$x^{21} - 3 x^{20} - 30 x^{19} + 86 x^{18} + 349 x^{17} - 953 x^{16} - 2026 x^{15} + 5248 x^{14} + 6380 x^{13} - 15522 x^{12} - 11326 x^{11} + 25300 x^{10} + 11568 x^{9} - 22602 x^{8} - 6770 x^{7} + 10604 x^{6} + 2191 x^{5} - 2351 x^{4} - 352 x^{3} + 194 x^{2} + 23 x - 1$ |
$21$ |
[21,0] |
$2^{18}\cdot 728809^{5}$ |
$2$ |
$45.069850945$ |
$1546.4382179402714$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$20$ |
$47133176363.7$ |
| 21.21.330...193.1 |
$x^{21} - 6 x^{20} - 13 x^{19} + 122 x^{18} - 9 x^{17} - 857 x^{16} + 633 x^{15} + 2723 x^{14} - 2843 x^{13} - 4388 x^{12} + 5538 x^{11} + 3675 x^{10} - 5631 x^{9} - 1441 x^{8} + 3112 x^{7} + 105 x^{6} - 903 x^{5} + 87 x^{4} + 121 x^{3} - 21 x^{2} - 5 x + 1$ |
$21$ |
[21,0] |
$71^{5}\cdot 283583^{5}$ |
$2$ |
$54.8318609847$ |
$4487.136391954227$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$20$ |
$324140206962$ |
