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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
25.25.338813178901720135627329000271856784820556640625.1	x^25 - 50x^23 + 1025x^21 - 11250x^19 - 125x^18 + 72525x^17 + 3100x^16 - 283885x^15 - 28375x^14 + 674550x^13 + 121800x^12 - 942450x^11 - 261005x^10 + 718625x^9 + 269475x^8 - 258425x^7 - 117125x^6 + 33010x^5 + 16625x^4 - 1100x^3 - 650x^2 - 50x - 1	\( 5^{68} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.1269734648531914468903714880493455422104626762401.1	x^25 - x^24 - 48x^23 + 43x^22 + 946x^21 - 752x^20 - 9993x^19 + 6962x^18 + 62052x^17 - 37341x^16 - 234195x^15 + 119366x^14 + 538390x^13 - 226505x^12 - 737819x^11 + 249907x^10 + 571793x^9 - 151052x^8 - 224456x^7 + 42136x^6 + 35494x^5 - 2561x^4 - 1633x^3 + 57x^2 + 19x - 1	\( 101^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.19744527036368077698033828496963106435582783749713601.1	x^25 - x^24 - 72x^23 + 161x^22 + 1991x^21 - 6935x^20 - 23789x^19 + 131523x^18 + 59219x^17 - 1219472x^16 + 1274267x^15 + 5134575x^14 - 12138942x^13 - 4263646x^12 + 39567816x^11 - 30337248x^10 - 42180110x^9 + 75903945x^8 - 9872226x^7 - 55689151x^6 + 38006340x^5 + 5737119x^4 - 14814116x^3 + 5029783x^2 - 190198x - 111103	\( 151^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.3909933000788329339715778837921617322655826705601954756001.1	x^25 - x^24 - 120x^23 + 87x^22 + 5789x^21 - 2591x^20 - 146272x^19 + 26182x^18 + 2128729x^17 + 143339x^16 - 18517488x^15 - 5136393x^14 + 96923558x^13 + 42784540x^12 - 299088119x^11 - 167117297x^10 + 510501238x^9 + 321873492x^8 - 408815960x^7 - 263064528x^6 + 88908581x^5 + 40531608x^4 - 2051852x^3 - 1066000x^2 + 23968x + 4768	\( 251^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.298858039306015483445329296147756574767800059094329115180169601.1	x^25 - x^24 - 192x^23 + 107x^22 + 15030x^21 - 1306x^20 - 632791x^19 - 221401x^18 + 15781195x^17 + 11305013x^16 - 242203703x^15 - 241493765x^14 + 2318100658x^13 + 2777496960x^12 - 13790113019x^11 - 18425686096x^10 + 49846712475x^9 + 71255379842x^8 - 103704806969x^7 - 155205497967x^6 + 110262430876x^5 + 171412082812x^4 - 45833333710x^3 - 73057285978x^2 + 6292934527x + 6307554361	\( 401^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.4931594142375771105480494098054585760878374959955311864606883374401.1	x^25 - x^24 - 288x^23 + 497x^22 + 34352x^21 - 78170x^20 - 2240723x^19 + 6111573x^18 + 88353827x^17 - 277220089x^16 - 2180920913x^15 + 7768392594x^14 + 33401169837x^13 - 136672173208x^12 - 297659219628x^11 + 1479506226130x^10 + 1250997120007x^9 - 9250584651357x^8 + 37235512027x^7 + 29123329385706x^6 - 15122977023774x^5 - 33560927016050x^4 + 26612300985025x^3 + 1442645425875x^2 - 4088955351250x + 666457915625	\( 601^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.198258780827351695791008735816797746301096570719885588203276967256801.1	x^25 - x^24 - 336x^23 + 75x^22 + 45899x^21 + 13061x^20 - 3362943x^19 - 1970280x^18 + 147831619x^17 + 113481379x^16 - 4123860033x^15 - 3703105216x^14 + 74859514573x^13 + 76261714738x^12 - 885235325980x^11 - 1019102628348x^10 + 6647166275045x^9 + 8667324085851x^8 - 29651886280369x^7 - 43871171250230x^6 + 67425341538954x^5 + 113659250436626x^4 - 51510706736207x^3 - 102219387211201x^2 + 8576334530877x + 17666045410357	\( 701^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.227936564389216769066972959924266550757465665810741484165191650390625.1	x^25 - 550x^23 + 124025x^21 - 14973750x^19 - 1073875x^18 + 1061415025x^17 + 292953100x^16 - 45696670635x^15 - 29496124625x^14 + 1195775125050x^13 + 1388600089800x^12 - 18216821941450x^11 - 32760226572755x^10 + 141336159619875x^9 + 373032643425475x^8 - 331978561284425x^7 - 1686835306391125x^6 - 1031805037461990x^5 + 1080219244517875x^4 + 1100312373931650x^3 - 5183853220150x^2 - 156124659276300x - 26153667939751	\( 5^{68}\cdot 11^{20} \)	$C_{25}$ (as 25T1)	$[5]$ (GRH)
25.25.227936564389216769066972959924266550757465665810741484165191650390625.2	x^25 - 550x^23 + 124025x^21 - 14973750x^19 - 468875x^18 + 1062231775x^17 + 127909100x^16 - 45741591885x^15 - 12878589625x^14 + 1194292723800x^13 + 607824841800x^12 - 18393612016450x^11 - 14200548281755x^10 + 158788744054875x^9 + 159805347014225x^8 - 710266705493675x^7 - 819704665921625x^6 + 1448128599562260x^5 + 1723030958622875x^4 - 1001465382017100x^3 - 1173337004132150x^2 - 200208626090550x - 9441969348251	\( 5^{68}\cdot 11^{20} \)	$C_{25}$ (as 25T1)	$[5]$ (GRH)
25.25.227936564389216769066972959924266550757465665810741484165191650390625.3	x^25 - 550x^23 + 124025x^21 - 14973750x^19 - 15125x^18 + 1062050275x^17 + 4126100x^16 - 45731609385x^15 - 415438375x^14 + 1194622146300x^13 + 22243405800x^12 - 18421283506450x^11 - 678182906005x^10 + 159208867549875x^9 + 9127440610475x^8 - 719226536302175x^7 - 22665313001375x^6 + 1547329331945760x^5 - 51166647560875x^4 - 1243323318639600x^3 + 164764650851350x^2 + 48016300765950x - 6753826844501	\( 5^{68}\cdot 11^{20} \)	$C_{25}$ (as 25T1)	n/a
25.25.227936564389216769066972959924266550757465665810741484165191650390625.4	x^25 - 550x^23 + 124025x^21 - 14973750x^19 - 2102375x^18 + 1060144525x^17 + 573527900x^16 - 45626793135x^15 - 57745934125x^14 + 1198081082550x^13 + 2710469962200x^12 - 17657242921450x^11 - 65075477797495x^10 + 96351540709875x^9 + 755653228638275x^8 + 707942320831075x^7 - 2724949254850625x^6 - 8413751638067490x^5 - 10066386119106625x^4 - 6004767748400850x^3 - 1749838739064350x^2 - 210794145955800x - 6151028734499	\( 5^{68}\cdot 11^{20} \)	$C_{25}$ (as 25T1)	$[5]$ (GRH)
25.25.1035996976866061687572354401200188865607516483497915359292674342768001.1	x^25 - x^24 - 360x^23 + 561x^22 + 50509x^21 - 71185x^20 - 3762281x^19 + 3222735x^18 + 167015969x^17 - 11071180x^16 - 4593891060x^15 - 3802678517x^14 + 76639409753x^13 + 134888109273x^12 - 701125573722x^11 - 2002221575510x^10 + 2498218571582x^9 + 13615398610851x^8 + 4915687383185x^7 - 37245464805375x^6 - 49405455102305x^5 + 13790562028053x^4 + 66222925208094x^3 + 41570931977659x^2 + 4021161749229x - 2175105944071	\( 751^{24} \)	$C_{25}$ (as 25T1)	Trivial (GRH)
25.25.11548169354972874033626020541245956538701891644459465169347822666168212890625.1	x^25 - 1010x^23 + 423695x^21 - 16564x^20 - 97018075x^19 + 16710955x^18 + 13422938380x^17 - 5485909940x^16 - 1175552933960x^15 + 845174650850x^14 + 66410531601355x^13 - 70461282259010x^12 - 2420450112730290x^11 + 3387202078316558x^10 + 55859212319178175x^9 - 95685155058299450x^8 - 780055746914306825x^7 + 1557503978250126535x^6 + 5979479311086497354x^5 - 13526430608091887250x^4 - 19803963163014939215x^3 + 50974370534094620880x^2 + 9050213705799566715x - 38485766521793272607	\( 5^{40}\cdot 101^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.11548169354972874033626020541245956538701891644459465169347822666168212890625.2	x^25 - 1010x^23 + 416120x^21 - 119786x^20 - 92851825x^19 + 77648295x^18 + 12625715080x^17 - 19563201060x^16 - 1103386742210x^15 + 2606214708525x^14 + 62777145784355x^13 - 204409768833865x^12 - 2266218619182215x^11 + 9743726823879892x^10 + 47457692171150925x^9 - 276485257390184925x^8 - 422037681808798000x^7 + 4274886158200428415x^6 - 1829877645315965021x^5 - 27984454640013654375x^4 + 45789263205923977660x^3 + 15474193591179457270x^2 - 41158441525542510360x - 16510160157919896943	\( 5^{40}\cdot 101^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.11548169354972874033626020541245956538701891644459465169347822666168212890625.3	x^25 - 1010x^23 + 393395x^21 - 82214x^20 - 77133700x^19 + 35193955x^18 + 8294519455x^17 - 5536293790x^16 - 504670619810x^15 + 425568926225x^14 + 17626167204980x^13 - 16758299601935x^12 - 359838520343665x^11 + 344954657261958x^10 + 4348657471082675x^9 - 3761130316961825x^8 - 30976450128926475x^7 + 21327357544787485x^6 + 125386209929929004x^5 - 57844425068056750x^4 - 260320879713631715x^3 + 54511774675262230x^2 + 207711763316129890x + 13895971453380343	\( 5^{40}\cdot 101^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.11548169354972874033626020541245956538701891644459465169347822666168212890625.4	x^25 - 1010x^23 + 408545x^21 - 82214x^20 - 88874950x^19 + 55116205x^18 + 11627188680x^17 - 14569481290x^16 - 960015631260x^15 + 1991258743100x^14 + 50484244881730x^13 - 154430289182685x^12 - 1631967413736815x^11 + 6999683430290308x^10 + 28657059461272800x^9 - 181562185323651575x^8 - 151479667998984250x^7 + 2459705659955183385x^6 - 2551473066213323146x^5 - 13215853303684560625x^4 + 32931106903916290285x^3 - 3546244457438956345x^2 - 54470348529213734710x + 42821375557427150093	\( 5^{40}\cdot 101^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.227611484625260901780055732479538161718013444811958834179677069187164306640625.1	x^25 - 1550x^23 + 985025x^21 - 335148750x^19 - 1321375x^18 + 66971873775x^17 + 1015873100x^16 - 8126381085385x^15 - 288253992125x^14 + 598759114519800x^13 + 36170557945800x^12 - 25990984386144450x^11 - 2042542765396255x^10 + 621114013802522375x^9 + 55973138695881225x^8 - 7291124562630257675x^7 - 1152117614947971625x^6 + 36464874055184939260x^5 + 7090953337926595375x^4 - 64048521279405896600x^3 - 7418028362553619150x^2 + 24592344442048304950x - 3211621783659145751	\( 5^{68}\cdot 31^{20} \)	$C_{25}$ (as 25T1)	n/a
25.25.227611484625260901780055732479538161718013444811958834179677069187164306640625.2	x^25 - 1550x^23 + 985025x^21 - 335148750x^19 - 77000125x^18 + 66876014025x^17 + 59197696100x^16 - 8111522824135x^15 - 16797346268375x^14 + 600140932816050x^13 + 2222178011701800x^12 - 24981626726799450x^11 - 150186181700207005x^10 + 394840637488502375x^9 + 4908918704216766225x^8 + 7170562108917464575x^7 - 50596670999271679375x^6 - 250276302703900127990x^5 - 481642554117131820875x^4 - 448031467429506142850x^3 - 180902906700178007650x^2 - 15239564267440452800x + 2343310686055630999	\( 5^{68}\cdot 31^{20} \)	$C_{25}$ (as 25T1)	n/a
25.25.227611484625260901780055732479538161718013444811958834179677069187164306640625.3	x^25 - 1550x^23 + 985025x^21 - 335148750x^19 - 38319875x^18 + 66941602275x^17 + 29460319900x^16 - 8121689002885x^15 - 8359365771625x^14 + 599195478192300x^13 + 1108880965450200x^12 - 25735760122584450x^11 - 73928366383086995x^10 + 560815730021192375x^9 + 2379329196310910025x^8 - 3547856441731801175x^7 - 29490586343949441125x^6 - 33914550662807657240x^5 + 33554962682608500875x^4 + 62488560763081705900x^3 - 5843218933392249350x^2 - 16035495984262633550x + 3224340405664787501	\( 5^{68}\cdot 31^{20} \)	$C_{25}$ (as 25T1)	n/a
25.25.227611484625260901780055732479538161718013444811958834179677069187164306640625.4	x^25 - 1550x^23 + 985025x^21 - 335148750x^19 - 5886125x^18 + 67015839525x^17 + 4525252900x^16 - 8133195776635x^15 - 1284040510375x^14 + 598125348233550x^13 + 172020628126200x^12 - 26022499540269450x^11 - 11487780086685245x^10 + 647652419463437375x^9 + 368288011589757525x^8 - 8867062293830230925x^7 - 5260769512829156375x^6 + 62279523875038372510x^5 + 30828560929555647125x^4 - 182032030329568110350x^3 - 50566067906613262850x^2 + 62045773461582216700x + 11183922944644501751	\( 5^{68}\cdot 31^{20} \)	$C_{25}$ (as 25T1)	n/a
25.25.179575427285891034426038718238151945439156258996386904982500709593296051025390625.1	x^25 - 1510x^23 - 3775x^22 + 886370x^21 + 3018339x^20 - 270641075x^19 - 841263280x^18 + 49405022580x^17 + 105209320215x^16 - 5707780707485x^15 - 4894370697225x^14 + 419257369310355x^13 - 167805809274915x^12 - 18968470528314790x^11 + 27514154918425942x^10 + 499106416403648175x^9 - 1134379073442882225x^8 - 6853500138332825725x^7 + 20399730914876360265x^6 + 37173715758686750029x^5 - 147538257096294486000x^4 - 4979093806744954890x^3 + 246479720085716115620x^2 - 27919634273568079160x - 86339316834042614143	\( 5^{40}\cdot 151^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.179575427285891034426038718238151945439156258996386904982500709593296051025390625.2	x^25 - 1510x^23 + 942995x^21 - 39864x^20 - 323623200x^19 + 33413280x^18 + 68008875655x^17 - 12107578640x^16 - 9187449588510x^15 + 2451791469600x^14 + 811235682491605x^13 - 303022226928760x^12 - 46443165424622140x^11 + 23546657206929408x^10 + 1664070940159066800x^9 - 1138986477909910400x^8 - 34528266093143880000x^7 + 32320580026255119360x^6 + 350695231837169327104x^5 - 462138311426913280000x^4 - 1078220626258959728640x^3 + 2164878525682671943680x^2 - 913727091195101839360x - 29654833162964959232	\( 5^{40}\cdot 151^{24} \)	$C_{25}$ (as 25T1)	$[5]$ (GRH)
25.25.179575427285891034426038718238151945439156258996386904982500709593296051025390625.3	x^25 - 1510x^23 - 3775x^22 + 886370x^21 + 4101311x^20 - 264336825x^19 - 1628643720x^18 + 45005546980x^17 + 333293260385x^16 - 4572304527685x^15 - 39654613098025x^14 + 272562107887855x^13 + 2854195063152865x^12 - 8366656352727740x^11 - 122615074701281442x^10 + 48336836091231675x^9 + 2900196984390428225x^8 + 4098328317611888825x^7 - 29327372321687245415x^6 - 87579212713502803421x^5 + 3656876625295283000x^4 + 231433895175806702610x^3 + 190576219504785438330x^2 - 7863433649974415910x - 2276256034653585107	\( 5^{40}\cdot 151^{24} \)	$C_{25}$ (as 25T1)	n/a
25.25.179575427285891034426038718238151945439156258996386904982500709593296051025390625.4	x^25 - 1510x^23 - 3775x^22 + 886370x^21 + 3497311x^20 - 271924575x^19 - 1335514970x^18 + 48545477730x^17 + 271497257835x^16 - 5256678097985x^15 - 31853267558025x^14 + 348130556565355x^13 + 2202080307305665x^12 - 13968017713086990x^11 - 88826082886172992x^10 + 334044432391802925x^9 + 2029959645702275475x^8 - 4669418190098058825x^7 - 25084686408659749065x^6 + 36466896285396543979x^5 + 155067588230737220750x^4 - 141655796051848662890x^3 - 390282190146595604570x^2 + 197854132985078094240x + 160465690548922974793	\( 5^{40}\cdot 151^{24} \)	$C_{25}$ (as 25T1)	n/a