| 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 |
| 21.3.682...552.1 |
$x^{21} - 2 x^{20} - x^{19} - 3 x^{18} + 10 x^{17} + 13 x^{16} + x^{15} - 27 x^{14} - 16 x^{13} - 20 x^{12} + 55 x^{11} - 4 x^{10} + 8 x^{9} - 32 x^{8} - x^{7} + 70 x^{6} - 52 x^{5} - 4 x^{4} + 6 x^{3} + 2 x^{2} - 6 x + 1$ |
$21$ |
[3,9] |
$-\,2^{21}\cdot 71^{10}$ |
$2$ |
$15.2258515194$ |
$23.83275057562597$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$11$ |
$7666.61577427$ |
| 21.1.156...857.1 |
$x^{21} - x^{20} - x^{19} + 2 x^{18} + 5 x^{17} + 2 x^{16} - 10 x^{15} - 2 x^{14} + 23 x^{13} + 19 x^{12} - 11 x^{11} - 28 x^{10} + 8 x^{9} + 47 x^{8} + 23 x^{7} - 13 x^{6} - 24 x^{5} - 7 x^{4} + 11 x^{3} + 6 x^{2} - 1$ |
$21$ |
[1,10] |
$23^{7}\cdot 71^{9}$ |
$2$ |
$17.672814291$ |
$40.4103947023535$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$10$ |
$32527.0761402$ |
| 21.1.126...441.1 |
$x^{21} + 3 x^{19} - x^{18} + x^{17} + 8 x^{16} - 7 x^{15} + 24 x^{14} - 15 x^{13} + 7 x^{12} + 25 x^{11} - 42 x^{10} + 46 x^{9} - 39 x^{8} - 12 x^{7} + 15 x^{6} - 14 x^{5} + x^{4} + 10 x^{3} - x^{2} + 2 x + 1$ |
$21$ |
[1,10] |
$31^{7}\cdot 71^{9}$ |
$2$ |
$19.5216714707$ |
$46.9148164229596$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$10$ |
$80948.9311635$ |
| 21.3.822...375.1 |
$x^{21} - 9 x^{20} + 39 x^{19} - 110 x^{18} + 212 x^{17} - 254 x^{16} + 72 x^{15} + 444 x^{14} - 1230 x^{13} + 2243 x^{12} - 3572 x^{11} + 5129 x^{10} - 6067 x^{9} + 5990 x^{8} - 5448 x^{7} + 5112 x^{6} - 4212 x^{5} + 3001 x^{4} - 1825 x^{3} + 903 x^{2} - 185 x + 211$ |
$21$ |
[3,9] |
$-\,5^{9}\cdot 11^{7}\cdot 43^{10}$ |
$3$ |
$26.5785687175$ |
$48.63126566315131$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$11$ |
$7898710.55939$ |
| 21.7.241...839.1 |
$x^{21} - 2 x^{20} - 7 x^{19} + 30 x^{18} + 67 x^{17} - 166 x^{16} - 306 x^{15} + 883 x^{14} + 1278 x^{13} - 2134 x^{12} - 3557 x^{11} + 2894 x^{10} + 3853 x^{9} - 3155 x^{8} - 310 x^{7} + 967 x^{6} + 11 x^{5} - 146 x^{4} + 8 x^{3} + 21 x^{2} - 1$ |
$21$ |
[7,7] |
$-\,23^{7}\cdot 577^{9}$ |
$2$ |
$43.3780816068$ |
$115.19982638875807$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$13$ |
$2208285999.6$ |
| 21.7.195...007.1 |
$x^{21} + 18 x^{19} - 20 x^{18} + 115 x^{17} - 188 x^{16} + 227 x^{15} - 571 x^{14} - 633 x^{13} + 412 x^{12} - 2156 x^{11} + 1703 x^{10} + 2628 x^{9} + 1031 x^{8} + 1528 x^{7} - 391 x^{6} + 241 x^{5} - 147 x^{4} + 21 x^{3} - 10 x^{2} - x + 1$ |
$21$ |
[7,7] |
$-\,31^{7}\cdot 577^{9}$ |
$2$ |
$47.9161181809$ |
$133.74228949737625$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$13$ |
$3294250109.26$ |
| 21.21.110...464.1 |
$x^{21} - x^{20} - 49 x^{19} + 49 x^{18} + 928 x^{17} - 894 x^{16} - 8860 x^{15} + 7979 x^{14} + 46924 x^{13} - 38237 x^{12} - 141310 x^{11} + 99810 x^{10} + 233828 x^{9} - 134152 x^{8} - 188281 x^{7} + 79711 x^{6} + 52846 x^{5} - 17134 x^{4} - 3010 x^{3} + 526 x^{2} + 50 x - 1$ |
$21$ |
[21,0] |
$2^{14}\cdot 37^{7}\cdot 577^{9}$ |
$3$ |
$80.6829250492$ |
$231.93988227213381$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$20$ |
$30696176966900$ |
| 21.21.234...333.1 |
$x^{21} - 6 x^{20} - 37 x^{19} + 251 x^{18} + 486 x^{17} - 4101 x^{16} - 2503 x^{15} + 33963 x^{14} + 600 x^{13} - 155515 x^{12} + 45616 x^{11} + 397419 x^{10} - 191382 x^{9} - 530658 x^{8} + 335989 x^{7} + 293449 x^{6} - 253693 x^{5} - 5734 x^{4} + 47660 x^{3} - 14944 x^{2} + 1819 x - 79$ |
$21$ |
[21,0] |
$229^{7}\cdot 577^{9}$ |
$2$ |
$93.3196046495$ |
$363.5010316353999$ |
|
|
? |
$S_3\times D_7$ (as 21T8) |
trivial |
$2$ |
$20$ |
$108385002485000$ |
