Global number field search results

Further refine search

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

Results (displaying all 31 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.4.931263224878297608080470016.1	x^22 - 4x^21 + 5x^20 + 4x^19 - 26x^18 + 31x^17 + 15x^16 - 79x^15 + 76x^14 + 60x^13 - 153x^12 + 84x^11 + 83x^10 - 192x^9 + 24x^8 + 58x^7 - 150x^6 + 30x^5 + 19x^4 - 23x^3 + 6x^2 + 29x + 1	\( -\,2^{12}\cdot 11^{7}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.4.951194438369517944038992707.1	x^22 - 11x^21 + 66x^20 - 275x^19 + 879x^18 - 2268x^17 + 4871x^16 - 8878x^15 + 13903x^14 - 18847x^13 + 22192x^12 - 22691x^11 + 20056x^10 - 15173x^9 + 9644x^8 - 4974x^7 + 1932x^6 - 448x^5 - 27x^4 + 71x^3 - 24x^2 + x + 1	\( -\,139\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}\cdot 9473 \)	22T53	Trivial (GRH)
22.4.969538443288973935184255159.1	x^22 - x^21 + 3x^20 + 3x^18 + 5x^17 + 7x^16 + 4x^15 + 12x^14 - 17x^13 - 35x^11 - 28x^10 - 29x^9 - 20x^8 - 6x^7 - 11x^6 - 26x^5 - 22x^4 - 11x^3 - 4x^2 + 9x - 1	\( -\,173\cdot 7043\cdot 28208540809^{2} \)	22T53	Trivial (GRH)
22.4.1533107758369291702785569375.1	x^22 - 2x^21 + 7x^20 - 20x^19 + 38x^18 - 74x^17 + 107x^16 - 167x^15 + 185x^14 - 284x^13 + 308x^12 - 417x^11 + 466x^10 - 462x^9 + 446x^8 - 292x^7 + 170x^6 - 55x^5 - 7x^4 + 11x^3 - 8x^2 + x + 1	\( -\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997 \)	22T52	Trivial (GRH)
22.4.1897242698910438481935564683.1	x^22 - x^21 + x^20 + x^19 + x^18 + 5x^17 - 11x^16 + 6x^15 + 19x^14 - 22x^13 - 4x^12 + 6x^11 + 13x^10 + 26x^9 - 75x^8 - 11x^7 + 101x^6 - 32x^5 - 59x^4 + 28x^3 + 15x^2 - 6x - 1	\( -\,47147\cdot 200601609583^{2} \)	22T53	Trivial (GRH)
22.4.25502334351981396972252168823.1	x^22 - x^21 - 4x^20 + 5x^19 + 9x^18 - 14x^17 - 15x^16 + 28x^15 + 20x^14 - 44x^13 - 20x^12 + 55x^11 + 15x^10 - 55x^9 - 9x^8 + 45x^7 + x^6 - 28x^5 + 2x^4 + 12x^3 - 2x^2 - 3x + 1	\( -\,13\cdot 769\cdot 941\cdot 27630898417\cdot 98112787247 \)	22T59	Trivial (GRH)
22.4.120805734981681461698275794063.1	x^22 - 3x^21 + 2x^20 + 6x^19 - 15x^18 + 11x^17 + 10x^16 - 31x^15 + 28x^14 + 2x^13 - 32x^12 + 35x^11 - 11x^10 - 16x^9 + 25x^8 - 14x^7 - 4x^6 + 10x^5 - 8x^4 + 2x^3 + 2x^2 - 2x + 1	\( -\,13\cdot 9292748844744727822944291851 \)	22T59	Trivial (GRH)
22.4.1562900555060447098970765787136.1	x^22 + 10x^20 + 41x^18 + 85x^16 + 79x^14 - 14x^12 - 98x^10 - 74x^8 - 3x^6 + 22x^4 + 9x^2 + 1	\( -\,2^{22}\cdot 610429790897^{2} \)	22T53	Trivial (GRH)
22.4.1562900555060447098970765787136.2	x^22 - 7x^20 + 15x^18 - 4x^16 - 28x^14 + 36x^12 + 7x^10 - 49x^8 - 5x^6 + 24x^4 + 10x^2 + 1	\( -\,2^{22}\cdot 610429790897^{2} \)	22T53	Trivial (GRH)
22.4.12168778905430087144801751269376.1	x^22 - 2x^21 - x^20 + 10x^19 - 11x^18 - 10x^17 + 34x^16 - 18x^15 - 34x^14 + 50x^13 + x^12 - 52x^11 + 28x^10 + 28x^9 - 36x^8 - 2x^7 + 23x^6 - 8x^5 - 6x^4 + 6x^3 - x^2 - 2x + 1	\( -\,2^{33}\cdot 1416632312516459164303 \)	22T57	Trivial (GRH)
22.4.31964561289410824381582196867072.1	x^22 - 2x^21 + 3x^20 - 2x^19 - 3x^18 + 6x^17 - 10x^16 + 6x^15 + 2x^14 - 6x^13 + 13x^12 - 4x^11 + 4x^9 - 8x^8 - 2x^7 - x^6 - 4x^5 + 2x^4 + 2x^3 + x^2 + 2x - 1	\( -\,2^{33}\cdot 235475711\cdot 15802753811681 \)	22T57	Trivial (GRH)
22.4.178176446876650757881387571453423.1	x^22 - 3x^21 - 4x^20 + 21x^19 - 34x^18 - 64x^17 + 209x^16 - 79x^15 - 626x^14 + 986x^13 + 469x^12 - 2461x^11 + 890x^10 + 2535x^9 - 360x^8 - 4500x^7 - 1390x^6 + 7497x^5 - 2384x^4 - 6847x^3 + 1939x^2 + 3881x - 2897	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.4.315595142827230969392399757869056.1	x^22 + 12x^20 + 58x^18 + 144x^16 + 193x^14 + 130x^12 + 21x^10 - 40x^8 - 45x^6 - 18x^4 + 1	\( -\,2^{22}\cdot 8674315276967^{2} \)	22T53	Trivial (GRH)
22.4.316932538277153190033818958954496.1	x^22 + 14x^20 + 84x^18 + 285x^16 + 607x^14 + 843x^12 + 745x^10 + 363x^8 + 45x^6 - 29x^4 - 6x^2 + 1	\( -\,2^{22}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2} \)	22T53	Trivial (GRH)
22.4.529866739430089519756710630129664.1	x^22 + 3x^20 + 23x^18 - 39x^16 + 58x^14 + 58x^12 - 275x^10 + 455x^8 - 258x^6 + 12x^4 + 12x^2 + 1	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.4.529866739430089519756710630129664.2	x^22 - 3x^20 - x^18 + 4x^16 + 12x^14 - 14x^12 - 6x^10 + 6x^8 - 8x^6 + 11x^4 - 6x^2 + 1	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.4.7198079267989980836471065337135104.1	x^22 + 17x^20 + 100x^18 + 265x^16 + 265x^14 - 217x^12 - 833x^10 - 861x^8 - 405x^6 - 79x^4 - x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.4.33833812608216375123231853716176896.1	x^22 + 16x^20 + 105x^18 + 363x^16 + 700x^14 + 709x^12 + 248x^10 - 146x^8 - 135x^6 - 20x^4 + 5x^2 + 1	\( -\,2^{22}\cdot 2053^{2}\cdot 43747835269^{2} \)	22T53	Trivial (GRH)
22.4.39034415726392643532837005585022976.1	x^22 + 15x^20 + 91x^18 + 279x^16 + 417x^14 + 130x^12 - 453x^10 - 544x^8 - 66x^6 + 185x^4 + 75x^2 + 1	\( -\,2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2} \)	22T53	Trivial (GRH)
22.4.1539829330034588067972966835892211043.1	x^22 - 11x^21 + 72x^20 - 335x^19 + 1211x^18 - 3546x^17 + 8610x^16 - 17574x^15 + 30322x^14 - 44228x^13 + 54150x^12 - 54734x^11 + 44075x^10 - 25887x^9 + 7693x^8 + 4031x^7 - 7645x^6 + 6006x^5 - 3064x^4 + 1060x^3 - 235x^2 + 28x - 1	\( -\,151\cdot 757\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.4.56501459388151144478039723653407440896.1	x^22 + 14x^20 + 48x^18 - 43x^16 - 492x^14 - 675x^12 + 603x^10 + 2355x^8 + 2294x^6 + 937x^4 + 136x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.4.1620949848995907632875795273183398788595712.1	x^22 + 22x^20 - 44x^19 + 308x^18 - 682x^17 + 5148x^16 - 4884x^15 + 20746x^14 - 37576x^13 + 458128x^12 + 582788x^11 + 2492600x^10 - 5616732x^9 + 12766776x^8 + 72829196x^7 + 27797264x^6 - 125806824x^5 - 187011000x^4 - 118806292x^3 - 39878476x^2 - 6794304x - 306180	\( -\,2^{22}\cdot 7^{15}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.4.46938516011269707747849773730468750000000000.1	x^22 + 48x^20 + 915x^18 + 8805x^16 + 44865x^14 + 113886x^12 + 96498x^10 - 129690x^8 - 305910x^6 - 179685x^4 - 26136x^2 + 3267	\( -\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.4.62584688015026276997133031640625000000000000.1	x^22 + 35x^20 + 145x^18 - 6780x^16 - 104715x^14 - 644565x^12 - 2013750x^10 - 3324525x^8 - 2834100x^6 - 1163300x^4 - 180475x^2 + 400	\( -\,2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
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)
22.4.4129233136056857981979443884256982828952059904.1	x^22 + 13x^20 - 636x^18 - 14672x^16 - 99474x^14 - 107348x^12 + 1163186x^10 + 3657772x^8 + 4010549x^6 + 1905711x^4 + 380936x^2 + 26569	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[2]$ (GRH)
22.4.4129233136056857981979443884256982828952059904.2	x^22 + 36x^20 + 304x^18 - 824x^16 - 20222x^14 - 83254x^12 - 86677x^10 + 173346x^8 + 424981x^6 + 275162x^4 + 53257x^2 + 81	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[2]$ (GRH)
22.4.66629645503270637631815521928756480198707930726986474039437748911210496.1	x^22 + 14x^20 + 49x^18 - 84x^16 - 873x^14 - 2112x^12 - 2265x^10 - 576x^8 + 1248x^6 + 1432x^4 + 632x^2 + 64	\( -\,2^{48}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16} \)	22T52	Trivial (GRH)
22.4.2873403462328546247872044383177623208569279512601291692950752921795952640.1	x^22 + 30x^20 + 369x^18 + 2328x^16 + 6999x^14 - 828x^12 - 83625x^10 - 301428x^8 - 506304x^6 - 378264x^4 - 11592x^2 + 99360	\( -\,2^{45}\cdot 3^{29}\cdot 5\cdot 7^{4}\cdot 23^{5}\cdot 137^{16} \)	22T52	$[2, 2]$ (GRH)
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
22.4.89814816729714094690034635615977259767382470415665884551559211803518872278540698479285989313375051412956223992468516612438569815867619968291363094528.1	x^22 + 350979911981x^20 + 31531275754154229225223x^18 - 1008475776612104694791025230553140x^16 - 322210865092605626920894378672118911225727924x^14 - 19529018819360050704565836683305706609504623505697529548x^12 - 410234603418031762383384462130197113631475314083796487142186400646x^10 + 5390789668257352445984987416818769498331207874384440256448010938109751829528x^8 + 451768370856126860241308044208349162281195558160970550493108599901855572804705581749739x^6 + 9424011074022261152946034414793624539687127146424963172213534510497787303562636588544545074514647x^4 + 85250981988906328919751592540467398125516301996518291421959573140028237511664288009433412817980612093390615x^2 + 283387806180923778139516911237181187298863566502351586888060171469808217840060096000563691256839885538552395504212243	\( -\,2^{22}\cdot 151^{11}\cdot 2311^{11}\cdot 24910163^{11} \)	22T50	n/a