| 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 |
| 22.2.275...000.1 |
$x^{22} + 78 x^{20} + 2355 x^{18} + 30360 x^{16} + 156915 x^{14} + 293802 x^{12} + 1279641 x^{10} + 795000 x^{8} - 582480 x^{6} + 170360 x^{4} + 14292 x^{2} - 5184$ |
$22$ |
[2,10] |
$2^{42}\cdot 3^{16}\cdot 5^{36}$ |
$3$ |
$116.267946536$ |
$448.95757350728394$ |
|
|
|
$C_2^{10}.M_{11}$ (as 22T43) |
trivial |
$2$ |
$11$ |
$4373557224090000$ |
| 22.6.110...000.1 |
$x^{22} + 22 x^{20} + 575 x^{18} + 8000 x^{16} + 66375 x^{14} + 216150 x^{12} + 77925 x^{10} - 1702500 x^{8} - 1800000 x^{6} + 1125000 x^{4} + 7312500 x^{2} - 2250000$ |
$22$ |
[6,8] |
$2^{44}\cdot 3^{16}\cdot 5^{36}$ |
$3$ |
$123.830140446$ |
|
|
|
|
$C_2^{10}.M_{11}$ (as 22T43) |
trivial |
$2$ |
$13$ |
$3102579979940000$ |
| 22.6.247...000.1 |
$x^{22} - x^{21} - 21 x^{20} + 80 x^{19} + 190 x^{18} - 2730 x^{17} - 2370 x^{16} + 23040 x^{15} - 11685 x^{14} - 139255 x^{13} + 66637 x^{12} + 883188 x^{11} - 858962 x^{10} - 5154490 x^{9} + 11455530 x^{8} - 94992 x^{7} - 23559708 x^{6} + 24631212 x^{5} + 1602700 x^{4} - 21497200 x^{3} + 16049640 x^{2} + 8247560 x - 1432040$ |
$22$ |
[6,8] |
$2^{42}\cdot 3^{18}\cdot 5^{36}$ |
$3$ |
$128.479743757$ |
|
|
|
|
$C_2^{10}.M_{11}$ (as 22T43) |
trivial |
$2$ |
$13$ |
$24347082785000000$ |
| 22.10.210...000.1 |
$x^{22} + 1521110995119 x^{20} + 20767967363363151457665 x^{18} - 125802676272554404269617160982350 x^{16} - 447129861314250111523595651626294337559000 x^{14} + 2211187005788657175999069028194179567572695016920000 x^{12} + 495161089736201224478016513692993953268704949758149081450000 x^{10} - 6532269446805556223473454007587119713902772265719196261716243847500000 x^{8} + 880101110859184651857903730474356017770939048207067136486977359706942040000000 x^{6} + 5695692754570027594526557200758139973678062841883039454997024866872864512936560150000000 x^{4} - 593268499597857685637766137050940784311360565636847362570893397339081071862088416668321250000000 x^{2} - 1495722903681177175207908834306985386050749026948136139791810294784018587329257867815333630665502500000000$ |
$22$ |
[10,6] |
$2^{72}\cdot 3^{22}\cdot 5^{10}\cdot 113^{10}\cdot 337^{8}\cdot 310501^{8}\cdot 11155561^{10}$ |
$7$ |
$680610426.613$ |
|
|
|
? |
$C_2^{10}.M_{11}$ (as 22T43) |
not computed |
$2$ |
$15$ |
|
| 22.14.943...176.1 |
$x^{22} - 4 x^{21} - 19816444360202 x^{20} - 130939653580494 x^{19} + 25786503236037554878425992 x^{18} + 5726614008231433361943000846 x^{17} + 1853199936361063324045988574016949756145 x^{16} - 38883408353642848687085741543497552063968 x^{15} - 15060234044348562983945017165467327796261964211831528 x^{14} - 199039852412494337461782647853600174129709039479701632 x^{13} + 40187571918038865471053915896336401254183754575711331365551900336 x^{12} + 2455095669618055435031158095789331634717470957031477209472795810240 x^{11} - 19565985868689197678390309973604843241222107734303067076292444689720374688976 x^{10} - 4853357376174371561484596079213957389612328381542532083455497824576580839223776 x^{9} - 40377896107578898581991957538317315013759727463568542176019239999961418992134152627638920 x^{8} - 1923084011887330958490185564498498689673058961638112728382587739188796106386934276380187904 x^{7} + 9344903153423008228537372825531905816434608434849238704654174673373278192619480961750957827787387837 x^{6} + 2150076913827860229815889987714521394730465395505792314178494356305081116586224340126294401234807386796 x^{5} + 9562222520630242259352128792515493185930222220514497587645269371884600757140812122295217552865088194604235770934 x^{4} + 1627324957935026207498329761483086598590718808278355719693715873485565239319775609483592813559885005175464046233482 x^{3} + 295133295107046583778671220679241283682170497750671886252850596710789348375767277328857277745870833992825928359747354263392 x^{2} + 421472200000400608030247269473317696498746747336596619059268244253465866998402109100984889845727726111427124833188610301750 x - 132861687629623581764448976155035492634283376290875233405879877879900232451476429614452651850733230795574481761788312980099558803526275$ |
$22$ |
[14,4] |
$2^{64}\cdot 3^{22}\cdot 337^{8}\cdot 947^{10}\cdot 310501^{8}\cdot 53591959^{10}$ |
$6$ |
$1365244084.2786899$ |
|
|
|
|
$C_2^{10}.M_{11}$ (as 22T43) |
not computed |
$2$ |
$17$ |
|
| 22.14.268...784.1 |
$x^{22} - 13804431167056 x^{20} + 29455972774636519059028044 x^{18} + 282033335825689492595606193310007218368 x^{16} - 1100067537115825097282039898823065852802526737569408 x^{14} - 711369580334732818426577644309882828779774928375610743409128704 x^{12} + 6224971581116867291176830299635009030608381084723679035467660012998285012992 x^{10} - 3747833231991359307927309897387471198885933309684020485859542287332808873765923846934528 x^{8} - 6274369569526916448536833950155270998368078365193513543624088680948481195760518524041106824138496768 x^{6} + 5343558891203926971053678141516280096820104179732811762443202895791628733302502206317811912655111486804391018496 x^{4} + 465315646285731804566448193725361044248288059478367061599274499469392698960388352711250887836367396465243767319244482010112 x^{2} - 387525510081628637297743170535017129158275865687798305019045138474571366001139953640250564464680282754821621623700592281054857750134784$ |
$22$ |
[14,4] |
$2^{72}\cdot 3^{20}\cdot 337^{8}\cdot 947^{10}\cdot 310501^{8}\cdot 53591959^{10}$ |
$6$ |
$1589648471.61$ |
|
|
|
? |
$C_2^{10}.M_{11}$ (as 22T43) |
not computed |
$2$ |
$17$ |
|
| 22.6.465...736.1 |
$x^{22} + 44093388187521 x^{20} + 209644616157290336872450800 x^{18} - 1918326833766516877145612304640202610000 x^{16} - 14033625357672757890962248232195405624570831712000000 x^{14} - 14327363001042340287658373126532762994707342768400250803200000000 x^{12} + 73155017113516899879646403705978634052064727703137418176016931767440000000000 x^{10} + 172961783005919316733286895245898258178180718110899199234964810104670395301160000000000000 x^{8} + 29163452098994916756535843681511546182067427493883528300264411710594464387592978997173200000000000000 x^{6} - 215482514009663496075841906438049192600636056827517073619648074832500266214861368952421191535957390000000000000000 x^{4} - 198251395036319826765137880268363506213709892664773937814853717831634869375711794380750206495940054252200460000000000000000000 x^{2} - 51673851153110341911101636537143872524838733712511652216813045532878318310449694003880719633962468700454539909239644900000000000000000000$ |
$22$ |
[6,8] |
$2^{70}\cdot 3^{22}\cdot 67^{10}\cdot 337^{8}\cdot 2851^{10}\cdot 310501^{8}\cdot 818717^{10}$ |
$7$ |
$2750877871.52$ |
|
|
|
? |
$C_2^{10}.M_{11}$ (as 22T43) |
not computed |
$2$ |
$13$ |
|
