| 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 |
| 22.4.645...000.1 |
$x^{22} - 11 x^{21} + 5 x^{20} + 335 x^{19} - 810 x^{18} - 4452 x^{17} + 16362 x^{16} + 27510 x^{15} - 149325 x^{14} - 80365 x^{13} + 783995 x^{12} + 42265 x^{11} - 2559710 x^{10} + 447060 x^{9} + 5251710 x^{8} - 1715814 x^{7} - 6547836 x^{6} + 4250280 x^{5} + 4685800 x^{4} - 7571000 x^{3} - 3152200 x^{2} + 6276200 x + 3414000$ |
$22$ |
[4,9] |
$-\,2^{36}\cdot 3^{17}\cdot 5^{37}$ |
$3$ |
$108.84778759$ |
$290.08437852363267$ |
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
trivial |
$2$ |
$12$ |
$46335294924500000$ |
| 22.2.193...000.1 |
$x^{22} - 8 x^{21} + 33 x^{20} - 200 x^{19} + 985 x^{18} - 3690 x^{17} + 12030 x^{16} - 28920 x^{15} + 43605 x^{14} + 157400 x^{13} - 1631281 x^{12} + 8675988 x^{11} - 35721373 x^{10} + 126155450 x^{9} - 382410030 x^{8} + 1013263932 x^{7} - 2350280781 x^{6} + 4622082636 x^{5} - 7118046395 x^{4} + 7748137180 x^{3} - 4988648001 x^{2} + 1044563818 x + 545722732$ |
$22$ |
[2,10] |
$2^{36}\cdot 3^{18}\cdot 5^{37}$ |
$3$ |
$114.421315327$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
trivial |
$2$ |
$11$ |
$345110169299000$ |
| 22.2.344...000.1 |
$x^{22} - 6 x^{21} + 9 x^{20} + 40 x^{19} + 45 x^{18} - 894 x^{17} + 419 x^{16} + 11784 x^{15} - 41070 x^{14} + 181440 x^{13} - 999564 x^{12} + 3332244 x^{11} - 10073016 x^{10} + 39717720 x^{9} - 131087040 x^{8} + 291509856 x^{7} - 493491996 x^{6} + 722343744 x^{5} - 613517940 x^{4} - 553234320 x^{3} + 2204807976 x^{2} - 2277211536 x + 827950104$ |
$22$ |
[2,10] |
$2^{40}\cdot 3^{16}\cdot 5^{37}$ |
$3$ |
$117.453240367$ |
$304.0016421307835$ |
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
trivial |
$2$ |
$11$ |
$1700186456810000$ |
| 22.0.247...000.1 |
$x^{22} + 44 x^{20} + 630 x^{18} + 8460 x^{16} + 76305 x^{14} + 643608 x^{12} + 3617232 x^{10} + 19958520 x^{8} + 82688640 x^{6} + 387467520 x^{4} + 1977939216 x^{2} + 3692749824$ |
$22$ |
[0,11] |
$-\,2^{42}\cdot 3^{18}\cdot 5^{36}$ |
$3$ |
$128.479743757$ |
$410.24126234069195$ |
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
$[2]$ |
$2$ |
$10$ |
$13913504688600000$ |
| 22.6.413...000.1 |
$x^{22} - 28 x^{20} + 1000 x^{18} - 30600 x^{16} + 426900 x^{14} - 5928240 x^{12} + 39923520 x^{10} - 175764000 x^{8} + 485640000 x^{6} - 487920000 x^{4} + 156648000 x^{2} - 31104000$ |
$22$ |
[6,8] |
$2^{42}\cdot 3^{17}\cdot 5^{37}$ |
$3$ |
$131.497863234$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
trivial |
$2$ |
$13$ |
$5705591541650000$ |
| 22.12.223...160.1 |
$x^{22} - 15 x^{20} - 5446 x^{18} + 31824 x^{16} + 8932590 x^{14} + 25606542 x^{12} - 4324351728 x^{10} - 33068943924 x^{8} + 351858173934 x^{6} + 2196660144654 x^{4} - 6084443980476 x^{2} + 151269407160$ |
$22$ |
[12,5] |
$-\,2^{71}\cdot 3^{21}\cdot 5\cdot 113\cdot 337^{8}\cdot 310501^{8}\cdot 11155561$ |
$7$ |
$61464.6503354$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$16$ |
|
| 22.14.600...784.1 |
$x^{22} - 136 x^{20} + 2859 x^{18} + 269688 x^{16} - 10363368 x^{14} - 66023304 x^{12} + 5691932352 x^{10} - 33761599008 x^{8} - 556843607163 x^{6} + 4672121576416 x^{4} + 4008220307087 x^{2} - 32887027192104$ |
$22$ |
[14,4] |
$2^{71}\cdot 3^{20}\cdot 337^{8}\cdot 947\cdot 310501^{8}\cdot 53591959$ |
$6$ |
$64285.9108067$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$17$ |
|
| 22.18.202...496.1 |
$x^{22} - 59199 x^{20} + 355785867 x^{18} + 15574863457179 x^{16} - 243890588632340310 x^{14} + 980617589843794278834 x^{12} + 3104638990661417055111462 x^{10} - 34961363048645624190273856458 x^{8} + 91888023235228572081111273993546 x^{6} - 75419055111706596835859501211384870 x^{4} + 5713137723447682436765249279773097994 x^{2} - 21260787460376367360486668899081431150$ |
$22$ |
[18,2] |
$2^{69}\cdot 3^{22}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607$ |
$7$ |
$67934.91348618311$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$19$ |
|
| 22.16.277...568.1 |
$x^{22} - 180 x^{20} + 9179 x^{18} + 58284 x^{16} - 16217640 x^{14} + 321816792 x^{12} + 2957044992 x^{10} - 135890353824 x^{8} + 871502095749 x^{6} + 4468447202724 x^{4} - 44093388187521 x^{2} + 46916659556700$ |
$22$ |
[16,3] |
$-\,2^{70}\cdot 3^{21}\cdot 67\cdot 337^{8}\cdot 2851\cdot 310501^{8}\cdot 818717$ |
$7$ |
$68918.5515227$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$18$ |
|
| 22.8.315...416.1 |
$x^{22} - 11 x^{21} + 73 x^{20} - 345 x^{19} - 4261 x^{18} + 45987 x^{17} - 307032 x^{16} + 1383522 x^{15} + 3961947 x^{14} - 48148705 x^{13} + 366194477 x^{12} - 1522409545 x^{11} + 1221051993 x^{10} + 6576607873 x^{9} - 104670123606 x^{8} + 364667664168 x^{7} - 921763556307 x^{6} + 1531016892369 x^{5} + 1216236277569 x^{4} - 4579083727977 x^{3} + 13843027641789 x^{2} - 11356029443979 x + 7476951174594$ |
$22$ |
[8,7] |
$-\,2^{48}\cdot 3^{20}\cdot 79\cdot 337^{8}\cdot 25537\cdot 310501^{8}\cdot 1108640890417$ |
$7$ |
$69320.7820501$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$14$ |
|
| 22.18.359...104.1 |
$x^{22} - 257 x^{20} + 24474 x^{18} - 973488 x^{16} + 4911342 x^{14} + 833458818 x^{12} - 24773125392 x^{10} + 177479869188 x^{8} + 2609466379182 x^{6} - 46742377664590 x^{4} + 197759461441604 x^{2} - 49242609059256$ |
$22$ |
[18,2] |
$2^{73}\cdot 3^{20}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607$ |
$7$ |
$69735.0463084$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$19$ |
|
| 22.8.584...320.1 |
$x^{22} + 40 x^{20} - 4821 x^{18} - 209496 x^{16} + 5285400 x^{14} + 302815992 x^{12} + 922756032 x^{10} - 93270702624 x^{8} - 1132846722171 x^{6} - 2066536069936 x^{4} + 13681132452239 x^{2} + 35545793447880$ |
$22$ |
[8,7] |
$-\,2^{71}\cdot 3^{21}\cdot 5\cdot 337^{8}\cdot 1543\cdot 310501^{8}\cdot 21330377$ |
$7$ |
$71289.4345156$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$14$ |
|
| 22.14.121...176.1 |
$x^{22} - 158 x^{20} + 5799 x^{18} + 192426 x^{16} - 14130840 x^{14} + 106875912 x^{12} + 5499758880 x^{10} - 91451924736 x^{8} - 54779058171 x^{6} + 6739137357122 x^{4} - 19818898708405 x^{2} - 18485391608046$ |
$22$ |
[14,4] |
$2^{71}\cdot 3^{20}\cdot 11\cdot 337^{8}\cdot 4789\cdot 310501^{8}\cdot 19494793$ |
$7$ |
$73702.8497631$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$17$ |
|
| 22.6.136...216.1 |
$x^{22} + 84 x^{20} - 2341 x^{18} - 343692 x^{16} - 3803688 x^{14} + 333658776 x^{12} + 9072108672 x^{10} + 5363172192 x^{8} - 2056157959803 x^{6} - 22774387512564 x^{4} - 77942112687873 x^{2} - 36916858667964$ |
$22$ |
[6,8] |
$2^{68}\cdot 3^{21}\cdot 11\cdot 31\cdot 37\cdot 337^{8}\cdot 310501^{8}\cdot 243830141$ |
$8$ |
$74093.5802868$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$13$ |
|
| 22.20.236...680.1 |
$x^{22} - 400 x^{20} + 67179 x^{18} - 6153936 x^{16} + 332234520 x^{14} - 10449620808 x^{12} + 161768261952 x^{10} + 150453098976 x^{8} - 47964749150331 x^{6} + 697620189720184 x^{4} - 3355033131829681 x^{2} + 638422240164720$ |
$22$ |
[20,1] |
$-\,2^{70}\cdot 3^{21}\cdot 5\cdot 11\cdot 29\cdot 43\cdot 337^{8}\cdot 310501^{8}\cdot 193926709$ |
$9$ |
$84342.7976005$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$20$ |
|
| 22.22.198...256.1 |
$x^{22} - 587 x^{20} + 151074 x^{18} - 22444968 x^{16} + 2131486062 x^{14} - 135179152602 x^{12} + 5798322147168 x^{10} - 166188568269012 x^{8} + 3053662171928622 x^{6} - 32824260622235770 x^{4} + 166011843276804404 x^{2} - 162477537538472376$ |
$22$ |
[22,0] |
$2^{71}\cdot 3^{21}\cdot 11^{2}\cdot 337^{8}\cdot 1847\cdot 14387\cdot 17401\cdot 310501^{8}$ |
$8$ |
$92916.2418907$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$21$ |
|
| 22.22.244...024.1 |
$x^{22} - 576 x^{20} + 145259 x^{18} - 21111552 x^{16} + 1957294872 x^{14} - 120874641864 x^{12} + 5030770408512 x^{10} - 139151595045408 x^{8} + 2444260894986117 x^{6} - 24604405843720824 x^{4} + 108887749553059407 x^{2} - 26396816028057984$ |
$22$ |
[22,0] |
$2^{71}\cdot 3^{21}\cdot 337^{8}\cdot 653\cdot 46723\cdot 310501^{8}\cdot 2253079$ |
$7$ |
$93789.9588324$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$21$ |
|
| 22.4.380...144.1 |
$x^{22} + 304 x^{20} + 36459 x^{18} + 2066928 x^{16} + 40935192 x^{14} - 1320559944 x^{12} - 86702793408 x^{10} - 1392387544608 x^{8} + 9697659463557 x^{6} + 538828326720056 x^{4} + 5159145077989967 x^{2} + 10287371329244976$ |
$22$ |
[4,9] |
$-\,2^{70}\cdot 3^{21}\cdot 337^{8}\cdot 2707\cdot 310501^{8}\cdot 79172602891$ |
$6$ |
$95701.9013625$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$12$ |
|
| 22.2.515...576.1 |
$x^{22} + 513 x^{20} + 114074 x^{18} + 14371632 x^{16} + 1122151662 x^{14} + 55486050798 x^{12} + 1677095605968 x^{10} + 26575785014988 x^{8} + 62534541123822 x^{6} - 4178116504369170 x^{4} - 43296735359689596 x^{2} - 3484724793731976$ |
$22$ |
[2,10] |
$2^{71}\cdot 3^{21}\cdot 211\cdot 337^{8}\cdot 310501^{8}\cdot 688136807609$ |
$6$ |
$97032.4762052$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$11$ |
|
| 22.2.515...576.2 |
$x^{22} + 291683 x^{20} + 33501422709 x^{18} + 1977876739665132 x^{16} + 65381330401848593226 x^{14} + 1215336754705013042214354 x^{12} + 11595941116691490694218710682 x^{10} + 36704973741016227116866560785916 x^{8} - 142239130451357264435620850834521758 x^{6} - 685947372298190601797182903175363707534 x^{4} - 691962597113360333890871166329989971128786 x^{2} - 56045264606963830837821634605099837836378400$ |
$22$ |
[2,10] |
$2^{71}\cdot 3^{21}\cdot 211\cdot 337^{8}\cdot 310501^{8}\cdot 688136807609$ |
$6$ |
$97032.47620515806$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$11$ |
|
| 22.0.614...824.1 |
$x^{22} + 656 x^{20} + 190059 x^{18} + 31982160 x^{16} + 3455500056 x^{14} + 249908957112 x^{12} + 12216440211264 x^{10} + 397142176666080 x^{8} + 8187635841570693 x^{6} + 96794448620299288 x^{4} + 522455049623219279 x^{2} + 597908782748023056$ |
$22$ |
[0,11] |
$-\,2^{68}\cdot 3^{20}\cdot 17\cdot 97\cdot 337^{8}\cdot 8297\cdot 11273\cdot 26921\cdot 310501^{8}$ |
$9$ |
$97808.4519295$ |
|
✓ |
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$10$ |
|
