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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
23.23.6111571184724799803076702357055363809.1	x^23 - x^22 - 22x^21 + 21x^20 + 210x^19 - 190x^18 - 1140x^17 + 969x^16 + 3876x^15 - 3060x^14 - 8568x^13 + 6188x^12 + 12376x^11 - 8008x^10 - 11440x^9 + 6435x^8 + 6435x^7 - 3003x^6 - 2002x^5 + 715x^4 + 286x^3 - 66x^2 - 12x + 1	\( 47^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.140063703503689367173618364344202364099995564521.1	x^23 - x^22 - 66x^21 + 147x^20 + 1630x^19 - 5648x^18 - 16457x^17 + 92686x^16 + 18441x^15 - 709360x^14 + 832638x^13 + 2239299x^12 - 5679764x^11 - 156443x^10 + 12673530x^9 - 11318727x^8 - 6468097x^7 + 14166332x^6 - 3186420x^5 - 5386949x^4 + 2918745x^3 + 436718x^2 - 516219x + 63941	\( 139^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.1260708975389644854773397594813026107886327713657.1	x^23 - 11x^22 - 49x^21 + 847x^20 + 333x^19 - 27195x^18 + 26294x^17 + 472463x^16 - 807088x^15 - 4813093x^14 + 11025393x^13 + 28842666x^12 - 85904881x^11 - 92539623x^10 + 401542378x^9 + 86961683x^8 - 1107595373x^7 + 357772746x^6 + 1662322180x^5 - 1168158873x^4 - 1079773672x^3 + 1139070319x^2 + 85927891x - 235248461	\( 23593^{11} \)	$D_{23}$ (as 23T2)	Trivial (GRH)
23.23.208804679998479120343550329105670000000000000000000000.1	x^23 - 115x^21 + 5750x^19 - 163875x^17 + 2932500x^15 - 34212500x^13 + 261625000x^11 - 1284765625x^9 + 3854296875x^7 - 6423828125x^5 + 4941406250x^3 - 1123046875x - 218280250	\( 2^{22}\cdot 5^{22}\cdot 23^{23} \)	$F_{23}$ (as 23T4)	Trivial (GRH)
23.23.542693874230042671882983450092579839839306394717839529.1	x^23 - x^22 - 132x^21 + 269x^20 + 6722x^19 - 19118x^18 - 167488x^17 + 601226x^16 + 2127300x^15 - 9664345x^14 - 12698450x^13 + 83446410x^12 + 19888027x^11 - 390244377x^10 + 110929757x^9 + 994369765x^8 - 511651057x^7 - 1370318108x^6 + 775297206x^5 + 972267257x^4 - 466392148x^3 - 312747839x^2 + 85444683x + 38737459	\( 277^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.39941131008096550428701851231676209894223228004485139129721.1	x^23 - x^22 - 220x^21 + 87x^20 + 19764x^19 + 7502x^18 - 942100x^17 - 1247222x^16 + 25503060x^15 + 62076437x^14 - 368245290x^13 - 1464919087x^12 + 1795768610x^11 + 16428532486x^10 + 16509241674x^9 - 60887740509x^8 - 181108379413x^7 - 148388500129x^6 + 88587002490x^5 + 252590462192x^4 + 171337144724x^3 + 31220491402x^2 - 10221385976x - 3012210881	\( 461^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.824185149135487077883465900577270766354751717380230010246241.1	x^23 - 253x^21 - 161x^20 + 26335x^19 + 33028x^18 - 1467515x^17 - 2734079x^16 + 47658093x^15 + 118763283x^14 - 910024555x^13 - 2931964974x^12 + 9516128606x^11 + 41347298260x^10 - 39738537224x^9 - 313669878607x^8 - 104709853475x^7 + 1076728692839x^6 + 1230914947669x^5 - 913297744524x^4 - 1823221987393x^3 - 124828056170x^2 + 645413252986x + 157112485811	\( 23^{44} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.12687910093209570367523581223700258577242701778943851443146801.1	x^23 - x^22 - 286x^21 + 61x^20 + 32489x^19 + 14967x^18 - 1928206x^17 - 2239956x^16 + 65439786x^15 + 128285990x^14 - 1279328514x^13 - 3758213062x^12 + 12892455511x^11 + 58719404143x^10 - 31105194350x^9 - 448954503771x^8 - 491325793721x^7 + 1084631540509x^6 + 3053149451318x^5 + 2305895458302x^4 - 281144721703x^3 - 1007901237378x^2 - 154197339893x + 118359867167	\( 599^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.281289734904574222488347652007286105552626963997840714384801792.1	x^23 - 299x^21 + 38870x^19 - 2880267x^17 + 134008212x^15 - 4064915764x^13 + 80820089896x^11 - 1031899362065x^9 + 8048815024107x^7 - 34878198437797x^5 + 69756396875594x^3 - 41219689062851x - 12722733426052	\( 2^{22}\cdot 13^{22}\cdot 23^{23} \)	$F_{23}$ (as 23T4)	Trivial (GRH)
23.23.294114910567428962511991419268717959339196150815159804184604281.1	x^23 - x^22 - 330x^21 + 491x^20 + 46010x^19 - 87998x^18 - 3534734x^17 + 8097381x^16 + 163274386x^15 - 432276476x^14 - 4617725871x^13 + 13958868541x^12 + 76934101895x^11 - 269759119969x^10 - 654647210801x^9 + 2901393808025x^8 + 1396549312920x^7 - 14112769866979x^6 + 10842020004862x^5 + 12214116095559x^4 - 17293268074281x^3 + 3381350907752x^2 + 1669609496979x - 220900980203	\( 691^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.16151009482177927765006229664562804196212236775629575713829087641.1	x^23 - x^22 - 396x^21 + 517x^20 + 58242x^19 - 89048x^18 - 4136665x^17 + 6675371x^16 + 155317993x^15 - 248917597x^14 - 3168505860x^13 + 4803054368x^12 + 34789513687x^11 - 47690452504x^10 - 193631555469x^9 + 225956060874x^8 + 483028561517x^7 - 415966978205x^6 - 465412635150x^5 + 267147031000x^4 + 115014666875x^3 - 62643096875x^2 - 1127109375x + 2017578125	\( 829^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)
23.23.477949960252640343082669666642744217085836889062320413931701625489.1	x^23 - x^22 - 462x^21 + 519x^20 + 78046x^19 - 96292x^18 - 6163501x^17 + 7373917x^16 + 250455980x^15 - 290053856x^14 - 5501340108x^13 + 6875865393x^12 + 66926124686x^11 - 96263348909x^10 - 438046106473x^9 + 740824871406x^8 + 1383038185176x^7 - 2863260767644x^6 - 1570567685623x^5 + 5193710248505x^4 - 862947136357x^3 - 3368621429671x^2 + 2154713129200x - 341763031283	\( 967^{22} \)	$C_{23}$ (as 23T1)	Trivial (GRH)