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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.13826007828239234871378695182440742234972683.1	x^22 - x^21 + 116x^20 - 116x^19 + 5866x^18 - 5866x^17 + 169741x^16 - 169741x^15 + 3102241x^14 - 3102241x^13 + 37314741x^12 - 37314741x^11 + 298939741x^10 - 298939741x^9 + 1583705366x^8 - 1583705366x^7 + 5438002241x^6 - 5438002241x^5 + 11861830366x^4 - 11861830366x^3 + 16803236616x^2 - 16803236616x + 17926283491	\( -\,3^{11}\cdot 7^{11}\cdot 23^{21} \)	$C_{22}$ (as 22T1)	$[2, 1433434]$ (GRH)
22.0.43604905791095263021253936224725999514116031.1	x^22 - 9x^21 + 103x^20 - 633x^19 + 4455x^18 - 21547x^17 + 115721x^16 - 463428x^15 + 2047836x^14 - 6940762x^13 + 26133577x^12 - 75415028x^11 + 246269894x^10 - 601120919x^9 + 1716577617x^8 - 3469345651x^7 + 8681282523x^6 - 13884271574x^5 + 30359360950x^4 - 34852602875x^3 + 66136100859x^2 - 41797446694x + 68117781041	\( -\,23^{20}\cdot 31^{11} \)	$C_{22}$ (as 22T1)	$[3128667]$ (GRH)
22.0.60063165247472201954266758470414053725437952.1	x^22 + 138x^20 + 8280x^18 + 283176x^16 + 6080832x^14 + 85131648x^12 + 781208064x^10 + 4603547520x^8 + 16572771072x^6 + 33145542144x^4 + 30595885056x^2 + 8344332288	\( -\,2^{33}\cdot 3^{11}\cdot 23^{21} \)	$C_{22}$ (as 22T1)	$[2, 3189916]$ (GRH)
22.0.165693399436195066245409511458333024560546875.1	x^22 - 9x^21 + 114x^20 - 723x^19 + 5545x^18 - 27862x^17 + 161687x^16 - 673652x^15 + 3199234x^14 - 11272660x^13 + 45446261x^12 - 136089890x^11 + 474573050x^10 - 1198919315x^9 + 3649189205x^8 - 7608385175x^7 + 20266939465x^6 - 33305104255x^5 + 77468338075x^4 - 90946009745x^3 + 183517941560x^2 - 117944870669x + 204320499769	\( -\,5^{11}\cdot 7^{11}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[6263182]$ (GRH)
22.0.948015833262595128634255168492301209005419806211.1	x^22 - 9x^21 + 8x^20 + 69x^19 + 341x^18 - 1536x^17 - 1667x^16 + 252x^15 + 45513x^14 + 12225x^13 + 72521x^12 - 276013x^11 + 757511x^10 + 840645x^9 + 11788951x^8 + 27209924x^7 + 94723994x^6 + 160917509x^5 + 349577039x^4 + 428625612x^3 + 683809164x^2 + 522560028x + 589202287	\( -\,11^{11}\cdot 67^{20} \)	$C_{22}$ (as 22T1)	$[23, 117139]$ (GRH)
22.0.1912320645087103459758821027834145013889251672064.1	x^22 + 134x^20 + 6968x^18 + 181704x^16 + 2564224x^14 + 19630464x^12 + 77539904x^10 + 145088768x^8 + 131212800x^6 + 54371840x^4 + 8027136x^2 + 137216	\( -\,2^{33}\cdot 67^{21} \)	$C_{22}$ (as 22T1)	$[1397102]$ (GRH)
22.0.1922554115559596594815766124679345986918150636343.1	x^22 - 9x^21 - 23x^20 + 427x^19 - 333x^18 - 8101x^17 + 19825x^16 + 54452x^15 - 199899x^14 - 268055x^13 + 1619754x^12 - 923591x^11 - 3715861x^10 + 3187790x^9 + 19675195x^8 - 56103742x^7 + 59561975x^6 - 21663766x^5 + 150503099x^4 - 437293737x^3 + 963528183x^2 - 867599298x + 639704333	\( -\,7^{11}\cdot 89^{20} \)	$C_{22}$ (as 22T1)	$[1084931]$ (GRH)
22.0.2064059898366606610712682200765411384896320962560.1	x^22 + 44x^20 + 858x^18 + 9768x^16 + 71984x^14 + 359744x^12 + 1241240x^10 + 2950112x^8 + 4723312x^6 + 4842816x^4 + 2857888x^2 + 734760	\( -\,2^{43}\cdot 5\cdot 7^{10}\cdot 11^{22}\cdot 13\cdot 157 \)	22T37	$[2, 2, 499520]$ (GRH)
22.0.8351990464247387275322638622384170627163060436992.1	x^22 - 2x^21 - 57x^20 + 78x^19 + 1486x^18 - 1192x^17 - 19345x^16 + 8722x^15 + 166656x^14 - 5440x^13 - 680544x^12 - 318952x^11 + 1977573x^10 + 2955478x^9 + 10118056x^8 - 4737470x^7 + 447202x^6 + 4776110x^5 + 248446153x^4 + 188456410x^3 + 890303175x^2 + 263009438x + 762593971	\( -\,2^{33}\cdot 89^{20} \)	$C_{22}$ (as 22T1)	$[1293259]$ (GRH)
22.0.171107316284804096938603185096461792835715406634527.1	x^22 - x^21 + 136x^20 - 141x^19 + 6933x^18 - 11219x^17 + 176727x^16 - 447777x^15 + 2849200x^14 - 9627703x^13 + 31913346x^12 - 114648803x^11 + 293038974x^10 - 732575214x^9 + 2085803018x^8 - 3042652387x^7 + 8079316286x^6 - 13226651538x^5 + 17433518072x^4 - 19326356701x^3 + 19500553636x^2 - 6880449063x + 7438698677	\( -\,7^{11}\cdot 89^{21} \)	$C_{22}$ (as 22T1)	$[6596678]$ (GRH)
22.0.1680332897640332021620975129530177197841148968789147.1	x^22 - x^21 + 91x^20 - 140x^19 + 5866x^18 - 6595x^17 + 171038x^16 + 105438x^15 + 3197216x^14 + 5217907x^13 + 46857656x^12 + 117294960x^11 + 496574452x^10 + 1287274232x^9 + 4044314069x^8 + 9224730377x^7 + 18936907588x^6 + 27784386063x^5 + 32870636944x^4 + 26173775028x^3 + 15505412182x^2 + 4564257710x + 939238609	\( -\,3^{11}\cdot 199^{20} \)	$C_{22}$ (as 22T1)	$[3608231]$ (GRH)
22.0.39785189666798958828616586618395684610035295457378304.1	x^22 + 181x^20 + 13028x^18 + 490585x^16 + 10635319x^14 + 137334967x^12 + 1056115843x^10 + 4729178714x^8 + 11925395238x^6 + 15697884460x^4 + 8830679464x^2 + 939238609	\( -\,2^{22}\cdot 199^{20} \)	$C_{22}$ (as 22T1)	$[2097569]$ (GRH)
22.0.11654522436820240107274506932479072962338428405475204819.1	x^22 - x^21 + 10x^20 - 130x^19 + 1885x^18 - 3051x^17 + 19486x^16 - 173956x^15 + 1407458x^14 - 2060852x^13 - 21380891x^12 + 232972284x^11 - 992590046x^10 + 2186797028x^9 + 1727107332x^8 - 33713397579x^7 + 156515778679x^6 - 463698132550x^5 + 1062844895210x^4 - 1843489099333x^3 + 2553256282724x^2 - 2451856901550x + 1515754471721	\( -\,419^{21} \)	$C_{22}$ (as 22T1)	$[5829723]$ (GRH)