Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 19 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.4.645700815000000000000000000000000000000000000.1	x^22 - 11x^21 + 5x^20 + 335x^19 - 810x^18 - 4452x^17 + 16362x^16 + 27510x^15 - 149325x^14 - 80365x^13 + 783995x^12 + 42265x^11 - 2559710x^10 + 447060x^9 + 5251710x^8 - 1715814x^7 - 6547836x^6 + 4250280x^5 + 4685800x^4 - 7571000x^3 - 3152200x^2 + 6276200x + 3414000	\( -\,2^{36}\cdot 3^{17}\cdot 5^{37} \)	22T44	Trivial (GRH)
22.2.1937102445000000000000000000000000000000000000.1	x^22 - 8x^21 + 33x^20 - 200x^19 + 985x^18 - 3690x^17 + 12030x^16 - 28920x^15 + 43605x^14 + 157400x^13 - 1631281x^12 + 8675988x^11 - 35721373x^10 + 126155450x^9 - 382410030x^8 + 1013263932x^7 - 2350280781x^6 + 4622082636x^5 - 7118046395x^4 + 7748137180x^3 - 4988648001x^2 + 1044563818x + 545722732	\( 2^{36}\cdot 3^{18}\cdot 5^{37} \)	22T44	Trivial (GRH)
22.2.3443737680000000000000000000000000000000000000.1	x^22 - 6x^21 + 9x^20 + 40x^19 + 45x^18 - 894x^17 + 419x^16 + 11784x^15 - 41070x^14 + 181440x^13 - 999564x^12 + 3332244x^11 - 10073016x^10 + 39717720x^9 - 131087040x^8 + 291509856x^7 - 493491996x^6 + 722343744x^5 - 613517940x^4 - 553234320x^3 + 2204807976x^2 - 2277211536x + 827950104	\( 2^{40}\cdot 3^{16}\cdot 5^{37} \)	22T44	Trivial (GRH)
22.0.24794911296000000000000000000000000000000000000.1	x^22 + 44x^20 + 630x^18 + 8460x^16 + 76305x^14 + 643608x^12 + 3617232x^10 + 19958520x^8 + 82688640x^6 + 387467520x^4 + 1977939216x^2 + 3692749824	\( -\,2^{42}\cdot 3^{18}\cdot 5^{36} \)	22T44	$[2]$ (GRH)
22.6.41324852160000000000000000000000000000000000000.1	x^22 - 28x^20 + 1000x^18 - 30600x^16 + 426900x^14 - 5928240x^12 + 39923520x^10 - 175764000x^8 + 485640000x^6 - 487920000x^4 + 156648000x^2 - 31104000	\( 2^{42}\cdot 3^{17}\cdot 5^{37} \)	22T44	Trivial (GRH)
22.12.2237479871188499870613354915145778127677091451853959466606041823244675621995663555455152169522515054428160.1	x^22 - 15x^20 - 5446x^18 + 31824x^16 + 8932590x^14 + 25606542x^12 - 4324351728x^10 - 33068943924x^8 + 351858173934x^6 + 2196660144654x^4 - 6084443980476x^2 + 151269407160	\( -\,2^{71}\cdot 3^{21}\cdot 5\cdot 113\cdot 337^{8}\cdot 310501^{8}\cdot 11155561 \)	22T44	n/a
22.14.6005478695920935077275180178728170344905283779505833696386712583652456011831687867181255322542385643126784.1	x^22 - 136x^20 + 2859x^18 + 269688x^16 - 10363368x^14 - 66023304x^12 + 5691932352x^10 - 33761599008x^8 - 556843607163x^6 + 4672121576416x^4 + 4008220307087x^2 - 32887027192104	\( 2^{71}\cdot 3^{20}\cdot 337^{8}\cdot 947\cdot 310501^{8}\cdot 53591959 \)	22T44	n/a
22.16.27758443257594324914983363876184067664865764900320098627846512840261521316613154967560690069271834754285568.1	x^22 - 180x^20 + 9179x^18 + 58284x^16 - 16217640x^14 + 321816792x^12 + 2957044992x^10 - 135890353824x^8 + 871502095749x^6 + 4468447202724x^4 - 44093388187521x^2 + 46916659556700	\( -\,2^{70}\cdot 3^{21}\cdot 67\cdot 337^{8}\cdot 2851\cdot 310501^{8}\cdot 818717 \)	22T44	n/a
22.8.31549754154938736139605034462596274469412770924031278962771396260567384323209653421425695172275073152188416.1	x^22 - 11x^21 + 73x^20 - 345x^19 - 4261x^18 + 45987x^17 - 307032x^16 + 1383522x^15 + 3961947x^14 - 48148705x^13 + 366194477x^12 - 1522409545x^11 + 1221051993x^10 + 6576607873x^9 - 104670123606x^8 + 364667664168x^7 - 921763556307x^6 + 1531016892369x^5 + 1216236277569x^4 - 4579083727977x^3 + 13843027641789x^2 - 11356029443979x + 7476951174594	\( -\,2^{48}\cdot 3^{20}\cdot 79\cdot 337^{8}\cdot 25537\cdot 310501^{8}\cdot 1108640890417 \)	22T44	n/a
22.18.35968643551695332182677064543344800913941547158154336510998469613936975508099279042617383314590716452143104.1	x^22 - 257x^20 + 24474x^18 - 973488x^16 + 4911342x^14 + 833458818x^12 - 24773125392x^10 + 177479869188x^8 + 2609466379182x^6 - 46742377664590x^4 + 197759461441604x^2 - 49242609059256	\( 2^{73}\cdot 3^{20}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607 \)	22T44	n/a
22.8.58418948490087900856198784513049139500595201522971777317979130633702859321491007685912328702163396402872320.1	x^22 + 40x^20 - 4821x^18 - 209496x^16 + 5285400x^14 + 302815992x^12 + 922756032x^10 - 93270702624x^8 - 1132846722171x^6 - 2066536069936x^4 + 13681132452239x^2 + 35545793447880	\( -\,2^{71}\cdot 3^{21}\cdot 5\cdot 337^{8}\cdot 1543\cdot 310501^{8}\cdot 21330377 \)	22T44	n/a
22.14.121521793204922702401925547871513287519587064054154046165862083482052135980296415200485327438880728653234176.1	x^22 - 158x^20 + 5799x^18 + 192426x^16 - 14130840x^14 + 106875912x^12 + 5499758880x^10 - 91451924736x^8 - 54779058171x^6 + 6739137357122x^4 - 19818898708405x^2 - 18485391608046	\( 2^{71}\cdot 3^{20}\cdot 11\cdot 337^{8}\cdot 4789\cdot 310501^{8}\cdot 19494793 \)	22T44	n/a
22.6.136512613038986913742008486695416726751511776495295634952214697836102284383214104319797066438605390496137216.1	x^22 + 84x^20 - 2341x^18 - 343692x^16 - 3803688x^14 + 333658776x^12 + 9072108672x^10 + 5363172192x^8 - 2056157959803x^6 - 22774387512564x^4 - 77942112687873x^2 - 36916858667964	\( 2^{68}\cdot 3^{21}\cdot 11\cdot 31\cdot 37\cdot 337^{8}\cdot 310501^{8}\cdot 243830141 \)	22T44	n/a
22.20.2360782888136677539846811675588590672634700789304705468856315278608937941898270750476788224860384348791111680.1	x^22 - 400x^20 + 67179x^18 - 6153936x^16 + 332234520x^14 - 10449620808x^12 + 161768261952x^10 + 150453098976x^8 - 47964749150331x^6 + 697620189720184x^4 - 3355033131829681x^2 + 638422240164720	\( -\,2^{70}\cdot 3^{21}\cdot 5\cdot 11\cdot 29\cdot 43\cdot 337^{8}\cdot 310501^{8}\cdot 193926709 \)	22T44	n/a
22.22.19861680445136995514566695021635141826242824408734364859334714399782912213082611059290887677605650017346912256.1	x^22 - 587x^20 + 151074x^18 - 22444968x^16 + 2131486062x^14 - 135179152602x^12 + 5798322147168x^10 - 166188568269012x^8 + 3053662171928622x^6 - 32824260622235770x^4 + 166011843276804404x^2 - 162477537538472376	\( 2^{71}\cdot 3^{21}\cdot 11^{2}\cdot 337^{8}\cdot 1847\cdot 14387\cdot 17401\cdot 310501^{8} \)	22T44	n/a
22.22.24402796323422549444668858510960358552762329591784234782163089041212069572638422789466222769600101521528193024.1	x^22 - 576x^20 + 145259x^18 - 21111552x^16 + 1957294872x^14 - 120874641864x^12 + 5030770408512x^10 - 139151595045408x^8 + 2444260894986117x^6 - 24604405843720824x^4 + 108887749553059407x^2 - 26396816028057984	\( 2^{71}\cdot 3^{21}\cdot 337^{8}\cdot 653\cdot 46723\cdot 310501^{8}\cdot 2253079 \)	22T44	n/a
22.4.38041046614734606844466182382827953894774429871771088765931049023543756062067815864066521884753399513448710144.1	x^22 + 304x^20 + 36459x^18 + 2066928x^16 + 40935192x^14 - 1320559944x^12 - 86702793408x^10 - 1392387544608x^8 + 9697659463557x^6 + 538828326720056x^4 + 5159145077989967x^2 + 10287371329244976	\( -\,2^{70}\cdot 3^{21}\cdot 337^{8}\cdot 2707\cdot 310501^{8}\cdot 79172602891 \)	22T44	n/a
22.2.51543810007530364950738948681743384761753476096510835701363261292919242474159040085359431452872546884912152576.1	x^22 + 513x^20 + 114074x^18 + 14371632x^16 + 1122151662x^14 + 55486050798x^12 + 1677095605968x^10 + 26575785014988x^8 + 62534541123822x^6 - 4178116504369170x^4 - 43296735359689596x^2 - 3484724793731976	\( 2^{71}\cdot 3^{21}\cdot 211\cdot 337^{8}\cdot 310501^{8}\cdot 688136807609 \)	22T44	n/a
22.0.61415850852267200397515695951218522185201753278017240901376750286638166845798793940070572804439992043594317824.1	x^22 + 656x^20 + 190059x^18 + 31982160x^16 + 3455500056x^14 + 249908957112x^12 + 12216440211264x^10 + 397142176666080x^8 + 8187635841570693x^6 + 96794448620299288x^4 + 522455049623219279x^2 + 597908782748023056	\( -\,2^{68}\cdot 3^{20}\cdot 17\cdot 97\cdot 337^{8}\cdot 8297\cdot 11273\cdot 26921\cdot 310501^{8} \)	22T44	n/a