| 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 |
| 22.0.253...304.1 |
$x^{22} - 132 x^{20} + 6006 x^{18} - 3432 x^{17} - 8404 x^{16} + 99528 x^{15} - 3347223 x^{14} - 2157848 x^{13} + 19467756 x^{12} + 3593532 x^{11} + 417479403 x^{10} + 660477972 x^{9} + 1786415928 x^{8} + 5675962688 x^{7} + 12184182186 x^{6} + 97343192496 x^{5} + 245071592040 x^{4} + 417345567804 x^{3} + 819274473963 x^{2} + 824171054652 x + 301353699564$ |
$22$ |
[0,11] |
$-\,2^{32}\cdot 3^{26}\cdot 11^{33}$ |
$3$ |
$366.286922497$ |
|
|
|
|
$\PSL(2,11)\wr C_2$ (as 22T40) |
trivial |
$2$ |
$10$ |
$1688335612100000000000$ |
| 22.0.253...304.2 |
$x^{22} - 132 x^{20} - 704 x^{19} + 6006 x^{18} + 75108 x^{17} + 96844 x^{16} - 2430252 x^{15} - 14707143 x^{14} - 5388944 x^{13} + 269725764 x^{12} + 1138506336 x^{11} + 1565449963 x^{10} - 136538820 x^{9} + 654683568 x^{8} + 9370157236 x^{7} + 24597721434 x^{6} + 81641723064 x^{5} + 253947197328 x^{4} + 439828133976 x^{3} + 447281514603 x^{2} + 254541143736 x + 67074533460$ |
$22$ |
[0,11] |
$-\,2^{32}\cdot 3^{26}\cdot 11^{33}$ |
$3$ |
$366.286922497$ |
|
|
|
|
$\PSL(2,11)\wr C_2$ (as 22T40) |
trivial |
$2$ |
$10$ |
$1688335612099639600000$ |
| 22.6.427...888.1 |
$x^{22} - 506 x^{19} - 462 x^{18} - 9042 x^{17} + 82500 x^{16} + 39402 x^{15} + 1841301 x^{14} - 5020334 x^{13} + 6526476 x^{12} - 101103984 x^{11} + 89570008 x^{10} - 597596736 x^{9} + 706449216 x^{8} - 756792960 x^{7} + 357855696 x^{6} + 378541152 x^{5} - 3841506240 x^{4} + 2102474880 x^{3} + 2415638016 x^{2} - 343056384 x - 73875456$ |
$22$ |
[6,8] |
$2^{28}\cdot 3^{29}\cdot 11^{33}$ |
$3$ |
$375.103119711$ |
|
|
|
|
$\PSL(2,11)\wr C_2$ (as 22T40) |
trivial |
$2$ |
$13$ |
$162785860272000000000000$ |
| 22.6.427...888.2 |
$x^{22} - 814 x^{19} - 462 x^{18} - 23826 x^{17} + 37884 x^{16} - 136422 x^{15} - 250371 x^{14} + 1847978 x^{13} - 9071964 x^{12} + 18960516 x^{11} - 21069488 x^{10} - 94197048 x^{9} + 368260464 x^{8} - 900049392 x^{7} + 521859888 x^{6} + 1681618752 x^{5} - 3705402624 x^{4} - 1838149632 x^{3} + 4104080640 x^{2} + 1353977856 x - 446128128$ |
$22$ |
[6,8] |
$2^{28}\cdot 3^{29}\cdot 11^{33}$ |
$3$ |
$375.103119711$ |
|
|
|
|
$\PSL(2,11)\wr C_2$ (as 22T40) |
trivial |
$2$ |
$13$ |
$162785860271644770000000$ |
