| 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 |
| 21.3.931...983.1 |
$x^{21} - 12 x^{14} + 9 x^{7} + 3$ |
$21$ |
[3,9] |
$-\,3^{34}\cdot 7^{21}$ |
$2$ |
$41.4553008695$ |
|
|
|
? |
$C_5^4:D_4$ (as 21T43) |
trivial |
$2$ |
$11$ |
$472264247.801$ |
| 21.3.931...983.2 |
$x^{21} - 3 x^{14} - 18 x^{7} + 3$ |
$21$ |
[3,9] |
$-\,3^{34}\cdot 7^{21}$ |
$2$ |
$41.4553008695$ |
|
|
|
? |
$C_5^4:D_4$ (as 21T43) |
trivial |
$2$ |
$11$ |
$512291829.442$ |
| 21.3.931...983.3 |
$x^{21} - 9 x^{7} - 9$ |
$21$ |
[3,9] |
$-\,3^{34}\cdot 7^{21}$ |
$2$ |
$41.455300869529914$ |
|
|
|
? |
$C_5^4:D_4$ (as 21T43) |
trivial |
$2$ |
$11$ |
$580590849.5866321$ |
| 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] |
$2^{18}\cdot 3^{28}\cdot 7^{21}\cdot 17^{6}$ |
$4$ |
$123.265703378$ |
|
|
|
|
$C_5^4:D_4$ (as 21T43) |
trivial |
$2$ |
$20$ |
$5102009942530000$ |
| 21.21.859...392.1 |
$x^{21} - 84 x^{19} + 2835 x^{17} - 50722 x^{15} - 870 x^{14} + 533022 x^{13} + 29820 x^{12} - 3420396 x^{11} - 411600 x^{10} + 13380332 x^{9} + 2910348 x^{8} - 30526707 x^{7} - 11030292 x^{6} + 35970438 x^{5} + 20929272 x^{4} - 14384083 x^{3} - 14891982 x^{2} - 4254852 x - 405224$ |
$21$ |
[21,0] |
$2^{18}\cdot 3^{28}\cdot 7^{21}\cdot 37^{6}$ |
$4$ |
$153.93701433$ |
|
|
|
|
$C_5^4:D_4$ (as 21T43) |
trivial |
$2$ |
$20$ |
$56207658188100000$ |
