| 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 |
| 21.21.343...304.1 |
$x^{21} - 63 x^{19} + 1428 x^{17} - 15085 x^{15} - 1559 x^{14} + 83594 x^{13} + 20916 x^{12} - 253428 x^{11} - 102144 x^{10} + 419440 x^{9} + 233058 x^{8} - 356122 x^{7} - 257152 x^{6} + 124460 x^{5} + 123088 x^{4} - 2968 x^{3} - 16464 x^{2} - 644 x + 716$ |
$21$ |
[21,0] |
$2^{12}\cdot 7^{28}\cdot 67^{10}$ |
$3$ |
$147.358080905$ |
$326.1720425799972$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 21T25) |
trivial |
$2$ |
$20$ |
$41650278420500000$ |
| 21.1.133...689.1 |
$x^{21} - 651 x^{18} - 987 x^{17} - 3843 x^{16} + 66507 x^{15} + 100746 x^{14} + 358092 x^{13} - 2906470 x^{12} - 3682455 x^{11} - 10943856 x^{10} + 57108359 x^{9} + 50250816 x^{8} + 108210663 x^{7} - 400053346 x^{6} + 150599988 x^{5} - 78402555 x^{4} - 2282180516 x^{3} - 831989466 x^{2} - 2678600232 x - 3761024003$ |
$21$ |
[1,10] |
$3^{28}\cdot 7^{30}\cdot 11^{10}$ |
$3$ |
$218.446889908$ |
$353.2708881002367$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 21T25) |
$[3]$ |
$2$ |
$10$ |
$34567368833000000$ |
| 21.1.181...096.1 |
$x^{21} - 35 x^{19} + 938 x^{17} - 12775 x^{15} - 1362 x^{14} + 130732 x^{13} + 67760 x^{12} - 706384 x^{11} - 340816 x^{10} + 2496256 x^{9} - 806008 x^{8} - 4299024 x^{7} + 5752992 x^{6} + 903168 x^{5} - 7451136 x^{4} + 3649408 x^{3} + 1128960 x^{2} + 1013824 x - 1588864$ |
$21$ |
[1,10] |
$2^{12}\cdot 7^{30}\cdot 107^{10}$ |
$3$ |
$221.652830784$ |
$461.2829834966581$ |
|
|
? |
$C_7^2:(C_3\times S_3)$ (as 21T25) |
trivial |
$2$ |
$10$ |
$30683343662500000$ |
