| 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 |
| 21.21.213...184.1 |
$x^{21} - 42 x^{19} + 756 x^{17} - 7616 x^{15} - 18 x^{14} + 47040 x^{13} + 504 x^{12} - 183456 x^{11} - 5544 x^{10} + 448448 x^{9} + 30240 x^{8} - 659008 x^{7} - 84672 x^{6} + 533120 x^{5} + 112896 x^{4} - 200704 x^{3} - 56448 x^{2} + 25088 x + 7808$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{25}\cdot 67^{7}$ |
$3$ |
$74.6081732713$ |
$326.1720425799972$ |
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
$[2, 2]$ |
$2$ |
$20$ |
$29136142114500$ |
| 21.21.213...184.2 |
$x^{21} - 42 x^{19} + 756 x^{17} - 7616 x^{15} - 22 x^{14} + 47040 x^{13} + 616 x^{12} - 183456 x^{11} - 6776 x^{10} + 448448 x^{9} + 36960 x^{8} - 658680 x^{7} - 103488 x^{6} + 528528 x^{5} + 137984 x^{4} - 182336 x^{3} - 68992 x^{2} + 6720 x + 3424$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{25}\cdot 67^{7}$ |
$3$ |
$74.6081732713$ |
$326.1720425799972$ |
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
trivial |
$2$ |
$20$ |
$37988095885700$ |
| 21.7.806...192.1 |
$x^{21} - 6 x^{19} - 24 x^{18} + 262 x^{17} - 1188 x^{16} - 1310 x^{15} + 16498 x^{14} - 8820 x^{13} - 84272 x^{12} + 91788 x^{11} + 198880 x^{10} - 311512 x^{9} - 182624 x^{8} + 380216 x^{7} + 267120 x^{6} + 75760 x^{5} - 599792 x^{4} - 519200 x^{3} + 413824 x^{2} + 381312 x + 45152$ |
$21$ |
[7,7] |
$-\,2^{18}\cdot 7^{24}\cdot 107^{7}$ |
$3$ |
$79.4901472056$ |
$461.2829834966581$ |
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
trivial |
$2$ |
$13$ |
$3153077248290$ |
| 21.7.231...048.1 |
$x^{21} - 21 x^{17} - 280 x^{15} - 138 x^{14} + 98 x^{13} + 1792 x^{12} + 2352 x^{11} + 1008 x^{10} + 13279 x^{9} - 44576 x^{8} + 4321 x^{7} + 142296 x^{6} - 106484 x^{5} + 32928 x^{4} + 355376 x^{3} - 154252 x^{2} - 254912 x + 83900$ |
$21$ |
[7,7] |
$-\,2^{6}\cdot 7^{30}\cdot 107^{7}$ |
$3$ |
$93.272312364$ |
|
|
|
? |
$C_7^3:(C_3\times S_3)$ (as 21T40) |
trivial |
$[2]$ |
$2$ |
$13$ |
$13512231302100$ |
