| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 21.15.627...751.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5145 x^{7} - 882 x^{6} + 2058 x^{5} + 588 x^{4} - 343 x^{3} - 147 x^{2} + 3$ |
$21$ |
(15, 3) |
$-\,3^{28}\cdot 7^{21}\cdot 17^{3}$ |
$3$ |
$45.3981473698$ |
|
|
|
✓ |
$D_7^3:C_3^2$ (as 21T70) |
trivial |
trivial |
$2$ |
$17$ |
$20836082403.4$ |
| 21.21.808...472.1 |
$x^{21} - 63 x^{19} + 1638 x^{17} - 22925 x^{15} - 528 x^{14} + 189189 x^{13} + 17598 x^{12} - 950355 x^{11} - 214326 x^{10} + 2897321 x^{9} + 1205064 x^{8} - 5090418 x^{7} - 3298680 x^{6} + 4361112 x^{5} + 4078368 x^{4} - 908327 x^{3} - 1614354 x^{2} - 218484 x + 85544$ |
$21$ |
(21, 0) |
$2^{18}\cdot 3^{28}\cdot 7^{21}\cdot 17^{6}$ |
$4$ |
$123.265703378$ |
|
|
|
|
$C_7^3:(C_3\times C_6)$ (as 21T43) |
trivial |
$[2]$ |
$2$ |
$20$ |
$5102009942530000$ |
| 21.9.137...000.1 |
$x^{21} - 98 x^{15} - 84 x^{14} + 2548 x^{9} + 4368 x^{8} + 1872 x^{7} - 13720 x^{3} - 35280 x^{2} - 30240 x - 8640$ |
$21$ |
(9, 6) |
$2^{32}\cdot 3^{18}\cdot 5^{6}\cdot 7^{21}\cdot 37^{7}$ |
$5$ |
$272.402515268$ |
|
|
|
? |
$A_7^3.D_6$ (as 21T157) |
trivial |
trivial |
$2$ |
$14$ |
$3240486773710000000$ |
