| 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 |
| 21.1.190...129.1 |
$x^{21} - x^{14} + 1$ |
$21$ |
[1,10] |
$7^{21}\cdot 23^{7}$ |
$2$ |
$19.907068859$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$10$ |
$141151.982984$ |
| 21.1.153...777.1 |
$x^{21} + x^{7} - 1$ |
$21$ |
[1,10] |
$7^{21}\cdot 31^{7}$ |
$2$ |
$21.9896645667$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$10$ |
$472261.200133$ |
| 21.7.231...543.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5143 x^{7} - 882 x^{6} + 2044 x^{5} + 588 x^{4} - 315 x^{3} - 147 x^{2} - 14 x + 1$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 23^{10}$ |
$2$ |
$31.1558688265$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$13$ |
$62978395.9714$ |
| 21.7.457...607.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5141 x^{7} - 882 x^{6} + 2030 x^{5} + 588 x^{4} - 287 x^{3} - 147 x^{2} - 28 x - 3$ |
$21$ |
[7,7] |
$-\,7^{21}\cdot 31^{10}$ |
$2$ |
$35.9145372621$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$13$ |
$312384901.42$ |
| 21.3.868...504.1 |
$x^{21} - x^{14} - 3 x^{7} + 1$ |
$21$ |
[3,9] |
$-\,2^{14}\cdot 7^{21}\cdot 37^{7}$ |
$3$ |
$37.0270073089$ |
|
|
|
✓ |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$11$ |
$324236876.686$ |
| 21.3.868...504.2 |
$x^{21} - x^{14} - 5 x^{7} + 1$ |
$21$ |
[3,9] |
$-\,2^{14}\cdot 7^{21}\cdot 37^{7}$ |
$3$ |
$37.0270073089$ |
|
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$11$ |
$329871712.172$ |
| 21.21.135...000.1 |
$x^{21} - 105 x^{19} + 4725 x^{17} - 119000 x^{15} - 690 x^{14} + 1837500 x^{13} + 48300 x^{12} - 17915625 x^{11} - 1328250 x^{10} + 109484375 x^{9} + 18112500 x^{8} - 401820025 x^{7} - 126787500 x^{6} + 799247750 x^{5} + 422625000 x^{4} - 623336875 x^{3} - 528281250 x^{2} - 116462500 x - 5255000$ |
$21$ |
[21,0] |
$2^{26}\cdot 5^{18}\cdot 7^{21}\cdot 37^{7}$ |
$4$ |
$218.60137975$ |
|
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$20$ |
$2081293733350000000$ |
| 21.21.440...000.1 |
$x^{21} - 91 x^{19} + 3101 x^{17} - 52164 x^{15} - 2804 x^{14} + 489510 x^{13} + 66850 x^{12} - 2696225 x^{11} - 624890 x^{10} + 8752625 x^{9} + 2952110 x^{8} - 16034065 x^{7} - 7497000 x^{6} + 14563150 x^{5} + 9775500 x^{4} - 3939775 x^{3} - 4961250 x^{2} - 1429400 x - 125900$ |
$21$ |
[21,0] |
$2^{26}\cdot 5^{12}\cdot 7^{21}\cdot 37^{10}$ |
$4$ |
$231.193702942$ |
|
|
|
? |
$C_7^2:(C_6\times S_3)$ (as 21T29) |
trivial |
$2$ |
$20$ |
$3364406008070000000$ |
