| 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 |
| 21.3.445...007.3 |
$x^{21} - 7 x^{14} - 84 x^{7} + 7$ |
$21$ |
[3,9] |
$-\,7^{41}$ |
$1$ |
$44.6635579203$ |
|
|
|
? |
$C_7^3:C_6$ (as 21T31) |
trivial |
$2$ |
$11$ |
$972809411.943$ |
| 21.3.445...007.4 |
$x^{21} - 21 x^{14} - 28 x^{7} + 7$ |
$21$ |
[3,9] |
$-\,7^{41}$ |
$1$ |
$44.6635579203$ |
|
|
|
? |
$C_7^3:C_6$ (as 21T31) |
trivial |
$2$ |
$11$ |
$985192501.465$ |
| 21.3.445...007.5 |
$x^{21} - 7 x^{14} - 28 x^{7} - 7$ |
$21$ |
[3,9] |
$-\,7^{41}$ |
$1$ |
$44.66355792025241$ |
|
|
|
? |
$C_7^3:C_6$ (as 21T31) |
trivial |
$2$ |
$11$ |
$1259058271.5715961$ |
| 21.21.479...728.1 |
$x^{21} - 56 x^{19} + 1295 x^{17} - 16198 x^{15} - 362 x^{14} + 120442 x^{13} + 10052 x^{12} - 550564 x^{11} - 106400 x^{10} + 1541932 x^{9} + 542556 x^{8} - 2522507 x^{7} - 1388660 x^{6} + 2084446 x^{5} + 1656200 x^{4} - 498043 x^{3} - 679042 x^{2} - 108836 x + 17576$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{35}\cdot 13^{6}$ |
$3$ |
$96.5588251902$ |
|
|
|
|
$C_7^3:C_6$ (as 21T31) |
trivial |
$2$ |
$20$ |
$268570252786000$ |
| 21.21.590...232.1 |
$x^{21} - 70 x^{19} + 2051 x^{17} - 32900 x^{15} - 226 x^{14} + 317128 x^{13} + 9338 x^{12} - 1896692 x^{11} - 147546 x^{10} + 7005922 x^{9} + 1133986 x^{8} - 15314839 x^{7} - 4453414 x^{6} + 17693074 x^{5} + 8406636 x^{4} - 7470603 x^{3} - 5851678 x^{2} - 1271592 x - 87464$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{35}\cdot 29^{6}$ |
$3$ |
$121.436836011$ |
|
|
|
|
$C_7^3:C_6$ (as 21T31) |
trivial |
$2$ |
$20$ |
$2949939511390000$ |
