| 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...527.1 |
$x^{21} - 42 x^{18} + 63 x^{17} + 252 x^{16} - 1008 x^{15} + 1224 x^{14} + 3528 x^{13} + 10192 x^{12} + 11151 x^{11} - 33516 x^{10} + 80388 x^{9} - 14994 x^{8} - 396243 x^{7} + 7644 x^{6} + 31752 x^{5} + 563472 x^{4} + 562625 x^{3} - 283374 x^{2} + 72576 x - 443448$ |
$21$ |
[3,9] |
$-\,3^{48}\cdot 7^{21}$ |
$2$ |
$86.2305007185$ |
|
|
|
? |
$C_7^3:C_{18}$ (as 21T42) |
trivial |
$2$ |
$11$ |
$1357254430200$ |
| 21.3.445...527.2 |
$x^{21} - 63 x^{17} - 252 x^{16} - 189 x^{15} - 1089 x^{14} - 11858 x^{12} - 30807 x^{11} - 87570 x^{10} - 58527 x^{9} + 97020 x^{8} + 658251 x^{7} + 943152 x^{6} + 982989 x^{5} - 874503 x^{4} - 1587250 x^{3} - 1282302 x^{2} + 1545075 x + 2732211$ |
$21$ |
[3,9] |
$-\,3^{48}\cdot 7^{21}$ |
$2$ |
$86.2305007185$ |
|
|
|
? |
$C_7^3:C_{18}$ (as 21T42) |
trivial |
$2$ |
$11$ |
$1324635290840$ |
| 21.3.445...527.3 |
$x^{21} - 42 x^{18} - 63 x^{17} - 252 x^{15} + 2565 x^{14} + 9114 x^{12} - 14742 x^{11} - 23058 x^{10} - 70875 x^{9} - 160650 x^{8} - 121014 x^{7} - 59535 x^{6} - 47628 x^{5} + 221130 x^{4} - 322875 x^{3} - 1051218 x^{2} - 615762 x - 568377$ |
$21$ |
[3,9] |
$-\,3^{48}\cdot 7^{21}$ |
$2$ |
$86.2305007184587$ |
|
|
|
? |
$C_7^3:C_{18}$ (as 21T42) |
trivial |
$2$ |
$11$ |
$1412501764928.5906$ |
