| 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 |
| 22.2.716...264.1 |
$x^{22} + 4 x^{20} + x^{18} - 20 x^{16} - 7 x^{14} + 93 x^{12} + 46 x^{10} - 121 x^{8} - 80 x^{6} - 34 x^{4} - 9 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$16.6222822507$ |
|
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$11$ |
$38833.928533$ |
| 22.2.286...056.1 |
$x^{22} - 5 x^{20} + 9 x^{18} - 6 x^{16} - 12 x^{14} + 37 x^{12} - 45 x^{10} + 75 x^{8} - 54 x^{6} - 17 x^{4} + 44 x^{2} - 16$ |
$22$ |
[2,10] |
$2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$17.7034135973$ |
|
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$11$ |
$97800.0774856$ |
| 22.6.184...625.1 |
$x^{22} - 7 x^{21} + 16 x^{20} - 3 x^{19} - 51 x^{18} + 101 x^{17} - 62 x^{16} - 50 x^{15} + 49 x^{14} + 124 x^{13} - 271 x^{12} + 166 x^{11} + 113 x^{10} - 102 x^{9} - 51 x^{8} - 34 x^{7} + 128 x^{6} - 78 x^{5} - 37 x^{4} + 36 x^{3} + 14 x^{2} - 8 x + 1$ |
$22$ |
[6,8] |
$5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2}$ |
$5$ |
$19.2655473485$ |
$89805.47415981455$ |
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$416442.121837$ |
| 22.6.458...896.1 |
$x^{22} - 12 x^{20} + 59 x^{18} - 154 x^{16} + 229 x^{14} - 193 x^{12} + 96 x^{10} - 57 x^{8} + 54 x^{6} - 24 x^{4} + x^{2} - 1$ |
$22$ |
[6,8] |
$2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$20.081203729$ |
|
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$827089.731554$ |
| 22.6.635...296.1 |
$x^{22} + 111 x^{20} + 4230 x^{18} + 329346 x^{16} - 2553795 x^{14} - 1664102961 x^{12} - 50639346936 x^{10} + 35043156036 x^{8} + 17771158853280 x^{6} + 85652947987596 x^{4} - 1530431923623624 x^{2} - 6261750295213284$ |
$22$ |
[6,8] |
$2^{28}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$882.254701417$ |
$13630.641297418244$ |
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$21761544372100000000000000$ |
| 22.10.254...184.1 |
$x^{22} - 4 x^{21} - 92 x^{20} + 978 x^{19} - 23031 x^{18} + 208542 x^{17} + 3327324 x^{16} - 36397800 x^{15} - 19963545 x^{14} - 406653528 x^{13} - 16539946488 x^{12} + 256034067942 x^{11} + 682357346031 x^{10} - 13494358927986 x^{9} + 9822827363220 x^{8} + 261815058820176 x^{7} - 813912422758992 x^{6} - 647257611403968 x^{5} + 8751031478070272 x^{4} - 24165278101734848 x^{3} + 30990808995877088 x^{2} - 13115399746724928 x - 2634468582334464$ |
$22$ |
[10,6] |
$2^{30}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$939.63750836$ |
$16209.655612939698$ |
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$15$ |
$739930020231000000000000000$ |
| 22.14.127...344.1 |
$x^{22} - 242454 x^{20} - 66254755944 x^{18} + 9988149125214624 x^{16} + 2412251307077297217168 x^{14} - 97126283753436220637656848 x^{12} - 36043439335840553783024429840880 x^{10} - 968324930877205693808500678923025440 x^{8} + 411693823788000055227773052463075223008512 x^{6} - 14674638475171337576102371060253129696887988224 x^{4} + 164949721485379801300637463025582558350584505753600 x^{2} - 571411117069770362003780702945732790998630818613760000$ |
$22$ |
[14,4] |
$2^{44}\cdot 3^{28}\cdot 7^{4}\cdot 13^{10}\cdot 23^{4}\cdot 137^{16}\cdot 2161^{10}$ |
$7$ |
$153679.147054$ |
|
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
not computed |
$2$ |
$17$ |
|
