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 |
22.0.645...000.1 |
$x^{22} - 9 x^{21} + 56 x^{20} - 220 x^{19} + 580 x^{18} - 2264 x^{17} + 4416 x^{16} - 1384 x^{15} - 10860 x^{14} + 89440 x^{13} - 29880 x^{12} - 76000 x^{11} + 2534220 x^{10} - 7594460 x^{9} + 27154440 x^{8} - 60342304 x^{7} + 148813536 x^{6} - 272410304 x^{5} + 488764480 x^{4} - 632907520 x^{3} + 679729856 x^{2} - 426298944 x + 185673856$ |
$22$ |
[0,11] |
$-\,2^{36}\cdot 3^{17}\cdot 5^{37}$ |
$3$ |
$108.84778759$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
trivial |
$2$ |
$10$ |
$685314816230000$ |
22.6.193...000.1 |
$x^{22} - 8 x^{21} + 2 x^{20} + 230 x^{19} - 1505 x^{18} + 6870 x^{17} - 27520 x^{16} + 77780 x^{15} - 68060 x^{14} - 492220 x^{13} + 2296746 x^{12} - 3440848 x^{11} - 3621813 x^{10} + 19400180 x^{9} - 9455860 x^{8} - 50400306 x^{7} + 24093413 x^{6} + 195342878 x^{5} - 239853960 x^{4} + 24810140 x^{3} - 38189098 x^{2} + 44518604 x - 445526$ |
$22$ |
[6,8] |
$2^{36}\cdot 3^{18}\cdot 5^{37}$ |
$3$ |
$114.421315327$ |
$270.8346732868732$ |
|
|
|
$C_2\times M_{11}$ (as 22T26) |
trivial |
$2$ |
$13$ |
$3889643769660000$ |
22.0.322...000.1 |
$x^{22} - 7 x^{21} + 16 x^{20} + 65 x^{19} - 110 x^{18} - 1207 x^{17} + 4474 x^{16} + 18023 x^{15} - 94235 x^{14} + 29090 x^{13} + 996574 x^{12} - 2737168 x^{11} + 1364044 x^{10} + 9322580 x^{9} - 10371020 x^{8} - 48179488 x^{7} + 113742016 x^{6} + 41399312 x^{5} - 165872880 x^{4} + 344430720 x^{3} + 383317056 x^{2} - 792787392 x + 281693376$ |
$22$ |
[0,11] |
$-\,2^{36}\cdot 3^{17}\cdot 5^{38}$ |
$3$ |
$117.1091880622713$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
trivial |
$2$ |
$10$ |
$2579673009359379.0$ |
22.6.165...000.1 |
$x^{22} - 2 x^{21} - 31 x^{20} + 220 x^{19} - 355 x^{18} - 2402 x^{17} + 18749 x^{16} - 57548 x^{15} + 33215 x^{14} + 506450 x^{13} - 2619213 x^{12} + 7205376 x^{11} - 11977167 x^{10} + 7869510 x^{9} + 14684865 x^{8} - 47083716 x^{7} + 42183012 x^{6} + 14211456 x^{5} - 36308880 x^{4} + 10498140 x^{3} + 7450218 x^{2} - 6904116 x - 307638$ |
$22$ |
[6,8] |
$2^{44}\cdot 3^{17}\cdot 5^{37}$ |
$3$ |
$140.050627518$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
trivial |
$2$ |
$13$ |
$56428741249600000$ |
22.6.826...000.1 |
$x^{22} - 2 x^{21} - 79 x^{20} + 380 x^{19} + 1815 x^{18} - 17782 x^{17} + 12559 x^{16} + 300208 x^{15} - 918120 x^{14} - 1643440 x^{13} + 9472056 x^{12} + 4599568 x^{11} - 60806344 x^{10} + 9745400 x^{9} + 232992600 x^{8} - 103064800 x^{7} - 536710145 x^{6} + 224268370 x^{5} + 468709295 x^{4} - 209497020 x^{3} - 89249751 x^{2} + 216627102 x + 91862289$ |
$22$ |
[6,8] |
$2^{44}\cdot 3^{17}\cdot 5^{38}$ |
$3$ |
$150.68028151410968$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
trivial |
$2$ |
$13$ |
$48394083230572110$ |
22.0.247...000.1 |
$x^{22} + 95 x^{20} + 2125 x^{18} + 20375 x^{16} + 65875 x^{14} - 662275 x^{12} - 7146125 x^{10} - 8434375 x^{8} + 233350000 x^{6} + 1788375000 x^{4} + 4051050000 x^{2} + 3422250000$ |
$22$ |
[0,11] |
$-\,2^{44}\cdot 3^{18}\cdot 5^{38}$ |
$3$ |
$158.39583317571058$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
$[2, 2, 2]$ |
$2$ |
$10$ |
$5683324929970202.0$ |
22.22.270...992.1 |
$x^{22} - 2 x^{21} - 5937 x^{20} + 23644 x^{19} + 14380087 x^{18} - 80894442 x^{17} - 18670093311 x^{16} + 129387514176 x^{15} + 14373105061386 x^{14} - 113148936395428 x^{13} - 6854671084823338 x^{12} + 58111620792538152 x^{11} + 2046072696561503990 x^{10} - 17973347443377019012 x^{9} - 374677880757551635638 x^{8} + 3306560545446575136576 x^{7} + 39636165734182768698009 x^{6} - 342468308954578377542658 x^{5} - 2108367836583878570071433 x^{4} + 17661153751544098470667084 x^{3} + 36519687428375669184589167 x^{2} - 338768850670953788929792826 x + 398597520143579143607377753$ |
$22$ |
[22,0] |
$2^{54}\cdot 3^{21}\cdot 337^{8}\cdot 310501^{8}$ |
$4$ |
$12899.643188056109$ |
|
|
|
|
$C_2\times M_{11}$ (as 22T26) |
not computed |
$2$ |
$21$ |
|
22.0.108...968.1 |
$x^{22} - 2 x^{21} - 2697 x^{20} - 10124 x^{19} + 2953363 x^{18} + 25956006 x^{17} - 995429163 x^{16} - 24258875760 x^{15} - 397958445798 x^{14} + 2025646395260 x^{13} + 256357819732118 x^{12} + 8974610793563736 x^{11} + 22753842630269174 x^{10} - 2420390220250614148 x^{9} + 14743319721784347354 x^{8} - 1814365511527586805552 x^{7} + 11781955472239770131637 x^{6} + 18716320530457096142982 x^{5} + 1873778694390872152244131 x^{4} + 43569900142361465974349524 x^{3} - 223044399573065807939428185 x^{2} - 1262953941990121085966551586 x + 14484088526897882877702983329$ |
$22$ |
[0,11] |
$-\,2^{56}\cdot 3^{21}\cdot 337^{8}\cdot 310501^{8}$ |
$4$ |
$13738.650034394072$ |
|
✓ |
|
|
$C_2\times M_{11}$ (as 22T26) |
not computed |
$2$ |
$10$ |
|