| 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 |
| 21.7.133...103.1 |
$x^{21} - x^{20} - 9 x^{19} + 10 x^{18} + 28 x^{17} - 211 x^{16} + 324 x^{15} + 384 x^{14} - 1692 x^{13} + 1991 x^{12} + 2315 x^{11} - 1214 x^{10} - 9164 x^{9} - 5328 x^{8} + 34796 x^{7} - 21283 x^{6} - 16215 x^{5} + 19798 x^{4} - 2184 x^{3} - 3057 x^{2} + 711 x - 41$ |
$21$ |
[7,7] |
$-\,3^{7}\cdot 29^{19}$ |
$2$ |
$30.3502600324$ |
$39.49131773649383$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$35353252.3989$ |
| 21.7.999...896.1 |
$x^{21} - 3 x^{19} - 10 x^{18} - 79 x^{17} + 237 x^{16} + 265 x^{15} - 691 x^{14} - 190 x^{13} - 2867 x^{12} + 8917 x^{11} - 86 x^{10} - 12167 x^{9} - 1656 x^{8} + 3245 x^{7} + 25876 x^{6} - 21636 x^{5} - 3866 x^{4} + 177 x^{3} + 4752 x^{2} + 2525 x - 2917$ |
$21$ |
[7,7] |
$-\,2^{14}\cdot 29^{19}$ |
$2$ |
$33.40478353734483$ |
$45.60064585163551$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$109720182.39051026$ |
| 21.7.716...967.1 |
$x^{21} - x^{20} - 12 x^{19} + 23 x^{18} + 209 x^{17} - 147 x^{16} - 1451 x^{15} + 840 x^{14} + 5070 x^{13} - 2978 x^{12} - 15769 x^{11} + 12105 x^{10} + 20201 x^{9} - 20848 x^{8} - 11002 x^{7} + 12758 x^{6} + 6317 x^{5} + 686 x^{4} - 267 x^{3} - 53 x^{2} + 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 29^{18}$ |
$2$ |
$50.9792306286$ |
$85.9701958689459$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$13$ |
$9787612489.51$ |
| 21.21.211...097.1 |
$x^{21} - 6 x^{20} - 55 x^{19} + 395 x^{18} + 737 x^{17} - 8463 x^{16} + 1551 x^{15} + 74059 x^{14} - 69748 x^{13} - 277632 x^{12} + 287628 x^{11} + 551344 x^{10} - 344830 x^{9} - 626935 x^{8} - 12040 x^{7} + 210641 x^{6} + 62865 x^{5} - 3790 x^{4} - 2084 x^{3} + 82 x^{2} + 18 x - 1$ |
$21$ |
[21,0] |
$11^{7}\cdot 43^{19}$ |
$2$ |
$66.8391512313$ |
$109.0155574530909$ |
|
|
? |
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$20$ |
$2240296145980$ |
| 21.21.312...112.1 |
$x^{21} - 3 x^{20} - 85 x^{19} + 342 x^{18} + 2160 x^{17} - 10377 x^{16} - 23312 x^{15} + 137697 x^{14} + 119845 x^{13} - 949109 x^{12} - 298102 x^{11} + 3636823 x^{10} + 323164 x^{9} - 7736312 x^{8} - 41098 x^{7} + 8529803 x^{6} - 336531 x^{5} - 4148808 x^{4} + 355302 x^{3} + 499880 x^{2} - 70834 x + 2329$ |
$21$ |
[21,0] |
$2^{21}\cdot 71^{19}$ |
$2$ |
$94.6189284629$ |
$148.1053009690192$ |
|
|
|
$S_3\times C_7$ (as 21T6) |
trivial |
$2$ |
$20$ |
$609186511830000$ |
