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 matches 1-50 of 240)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.334874047209198762552459264.5	x^12 + 732x^10 + 200934x^8 + 25421872x^6 + 1453813305x^4 + 30405466836x^2 + 51520374361	\( 2^{24}\cdot 3^{18}\cdot 61^{6} \)	$C_6\times C_2$ (as 12T2)	$[42, 27090]$ (GRH)
12.0.365334900454961075024695296.10	x^12 - 2x^11 + 549x^10 - 912x^9 + 127439x^8 - 169318x^7 + 16003958x^6 - 15988294x^5 + 1146467101x^4 - 767614604x^3 + 44414596734x^2 - 14988666216x + 726950311489	\( 2^{12}\cdot 3^{6}\cdot 13^{10}\cdot 31^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 4, 8, 10360]$ (GRH)
12.0.511440175556826827015061504.16	x^12 + 828x^10 + 252333x^8 + 34164936x^6 + 1949372406x^4 + 37536752376x^2 + 107918163081	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 109368]$ (GRH)
12.0.587964759896233890551955456.6	x^12 + 804x^10 + 242406x^8 + 33685456x^6 + 2115867705x^4 + 48604503852x^2 + 90458382169	\( 2^{24}\cdot 3^{18}\cdot 67^{6} \)	$C_6\times C_2$ (as 12T2)	$[14, 80808]$ (GRH)
12.0.606736939537977599814008832.1	x^12 + 858x^10 + 283140x^8 + 44849376x^6 + 3453401952x^4 + 113962264416x^2 + 1074501350208	\( 2^{18}\cdot 3^{6}\cdot 11^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 18, 14274]$ (GRH)
12.0.957442407981875712000000000.1	x^12 + 780x^10 + 212940x^8 + 26364000x^6 + 1542294000x^4 + 40099644000x^2 + 347530248000	\( 2^{18}\cdot 3^{18}\cdot 5^{9}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 26, 24362]$ (GRH)
12.0.988751862409257207447265625.3	x^12 - x^11 + 66x^10 - 222x^9 - 1767x^8 - 8113x^7 + 37220x^6 + 82432x^5 + 428416x^4 - 639536x^3 - 3977856x^2 - 6304000x + 28891136	\( 5^{9}\cdot 7^{10}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 4, 136140]$ (GRH)
12.0.1869778640298827501568000000.1	x^12 + 378x^10 - 4x^9 + 52314x^8 + 36x^7 + 3043978x^6 - 41448x^5 + 63815355x^4 - 247416x^3 + 740590164x^2 + 128427012x + 3754358271	\( 2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{9} \)	$C_{12}$ (as 12T1)	$[6, 266934]$ (GRH)
12.0.1979522439778248324859035648.1	x^12 + 696x^10 + 151380x^8 + 13462728x^6 + 534704436x^4 + 8860816368x^2 + 42827279112	\( 2^{33}\cdot 3^{18}\cdot 29^{6} \)	$C_{12}$ (as 12T1)	$[2, 533234]$ (GRH)
12.0.2055018859092572865671725056.12	x^12 + 812x^10 + 206045x^8 + 18438084x^6 + 623821842x^4 + 8040370408x^2 + 29146342729	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 4, 52, 1872]$ (GRH)
12.0.2055018859092572865671725056.16	x^12 + 604x^10 + 143581x^8 + 16983632x^6 + 1039094758x^4 + 30891844344x^2 + 371530478089	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 4, 52, 936]$ (GRH)
12.0.2055018859092572865671725056.17	x^12 + 1044x^10 + 401157x^8 + 68484312x^6 + 4926919446x^4 + 119621020968x^2 + 433626201009	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 29^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 2, 2, 18, 1638]$ (GRH)
12.0.2918461888950394248000000000.1	x^12 + 1155x^10 + 495495x^8 + 100623600x^6 + 10169272575x^4 + 479408564250x^2 + 7910241310125	\( 2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 4, 86312]$ (GRH)
12.0.2953538285909432612922851328.1	x^12 + 744x^10 + 172980x^8 + 16444632x^6 + 698181876x^4 + 12367793232x^2 + 63900265032	\( 2^{33}\cdot 3^{18}\cdot 31^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 323986]$ (GRH)
12.0.2987012625417735876007428096.10	x^12 + 60x^10 + 2683x^8 + 80840x^6 + 1655491x^4 + 20639500x^2 + 122655625	\( 2^{24}\cdot 3^{6}\cdot 11^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 81528]$ (GRH)
12.0.3133674591916081765366628352.1	x^12 + 924x^10 + 289674x^8 + 38236968x^6 + 2324405160x^4 + 61364296224x^2 + 506255443848	\( 2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 204980]$ (GRH)
12.0.3183115072573672681403731968.1	x^12 + 1131x^10 + 491985x^8 + 102726468x^6 + 10426736502x^4 + 453563037837x^2 + 5637140613117	\( 2^{12}\cdot 3^{6}\cdot 13^{11}\cdot 29^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 162370]$ (GRH)
12.0.6401594233356076787154812928.1	x^12 + 714x^10 + 197064x^8 + 26655048x^6 + 1835265600x^4 + 59903069184x^2 + 718836830208	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 17^{9} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 134660]$ (GRH)
12.0.8538034379472042289149247488.1	x^12 + 1092x^10 + 404586x^8 + 63115416x^6 + 4534344360x^4 + 141471544032x^2 + 1379347554312	\( 2^{33}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 96434]$ (GRH)
12.0.10819730946497133891723300864.16	x^12 - 6x^11 + 111x^10 - 500x^9 + 9519x^8 - 35142x^7 + 504889x^6 - 1393704x^5 + 19106076x^4 - 35929344x^3 + 476053380x^2 - 458315280x + 6075013344	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 6, 24180]$ (GRH)
12.0.14358355998689738428416000000.20	x^12 - 2x^11 + 151x^10 - 214x^9 + 11149x^8 - 15346x^7 + 515448x^6 - 732598x^5 + 15029687x^4 - 18766796x^3 + 248996314x^2 - 193232084x + 1771822921	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 37^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 262104]$ (GRH)
12.0.20830406386325245721904961201.1	x^12 - x^11 + 25x^10 - 665x^9 + 9567x^8 - 36895x^7 - 32397x^6 + 1439117x^5 - 3804588x^4 - 649236x^3 + 100982464x^2 + 76425536x + 14992384	\( 7^{10}\cdot 97^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 12, 26676]$ (GRH)
12.0.21088444099773325470807822336.11	x^12 - 9x^10 - 112x^9 + 2139x^8 + 7056x^7 + 56293x^6 + 2688x^5 + 1618164x^4 + 5742912x^3 + 49780692x^2 + 107430624x + 392457024	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 100104]$ (GRH)
12.0.21088444099773325470807822336.15	x^12 + 111x^10 + 10851x^8 + 594845x^6 + 25800888x^4 + 675452112x^2 + 11307344896	\( 2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 200208]$ (GRH)
12.0.37176212245675331887703543808.1	x^12 + 195x^10 - 52x^9 + 20787x^8 + 25428x^7 + 942422x^6 + 204828x^5 + 4214691x^4 + 12075388x^3 + 427391367x^2 - 807602328x + 3678675897	\( 2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 6, 6, 17862]$ (GRH)
12.0.37176212245675331887703543808.2	x^12 + 195x^10 - 52x^9 + 20787x^8 - 3354x^7 + 943592x^6 - 589134x^5 + 3543930x^4 - 6234410x^3 + 456229527x^2 + 1474874154x + 3926087841	\( 2^{12}\cdot 3^{16}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[3, 6, 6, 30, 390]$ (GRH)
12.0.45006250477353349878303281152.2	x^12 + 247x^10 + 23959x^8 + 1147562x^6 + 27702779x^4 + 296048519x^2 + 816061077	\( 2^{12}\cdot 13^{11}\cdot 19^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 10, 30270]$ (GRH)
12.0.56800822275313340415461609472.1	x^12 - 4x^11 + 475x^10 - 1566x^9 + 77422x^8 - 202300x^7 + 4485909x^6 - 8624434x^5 + 27197377x^4 - 28351612x^3 + 150014294x^2 - 117500690x + 370936189	\( 2^{12}\cdot 3^{6}\cdot 7^{8}\cdot 53^{9} \)	$C_{12}$ (as 12T1)	$[3, 6, 250926]$ (GRH)
12.0.88620023623867115145360460873.1	x^12 - x^11 + 40x^10 + 362x^9 + 3865x^8 + 5787x^7 + 216950x^6 + 605452x^5 + 4161656x^4 + 6762912x^3 + 84181376x^2 + 235215360x + 276287488	\( 7^{10}\cdot 73^{11} \)	$C_{12}$ (as 12T1)	$[1147854]$ (GRH)
12.0.96744152797159210133822373888.2	x^12 + 546x^10 + 95004x^8 + 6722352x^6 + 217120176x^4 + 3125539872x^2 + 15721812288	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 4, 15864]$ (GRH)
12.0.101563848359892128205077741568.1	x^12 + 1092x^10 + 286650x^8 + 29857464x^6 + 1314691560x^4 + 22086818208x^2 + 115955795592	\( 2^{33}\cdot 3^{6}\cdot 7^{6}\cdot 13^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 10, 45370]$ (GRH)
12.0.131961885606929070005069021184.1	x^12 + 354x^10 - 4x^9 + 49098x^8 + 36x^7 + 3301706x^6 + 13800x^5 + 111289299x^4 + 2865640x^3 + 1955645292x^2 + 154582308x + 14516726199	\( 2^{18}\cdot 3^{16}\cdot 61^{9} \)	$C_{12}$ (as 12T1)	$[3, 3, 3, 41574]$ (GRH)
12.0.152019244012074463020096000000.15	x^12 + 228x^10 + 26334x^8 + 1542876x^6 + 57419577x^4 + 588796776x^2 + 2100205584	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 12, 11856]$ (GRH)
12.0.175353438602139317305344000000.1	x^12 + 780x^10 + 216450x^8 + 25623000x^6 + 1174095000x^4 + 11372400000x^2 + 29615625000	\( 2^{33}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 4, 4, 4616]$ (GRH)
12.0.175353438602139317305344000000.2	x^12 + 780x^10 + 216450x^8 + 28431000x^6 + 1890135000x^4 + 60652800000x^2 + 740390625000	\( 2^{33}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 2, 126, 252]$ (GRH)
12.0.218764100914962817683456000000.36	x^12 + 102x^10 - 52x^9 + 8703x^8 + 3198x^7 + 471412x^6 + 83538x^5 + 17475255x^4 + 13489866x^3 + 462875499x^2 + 458844750x + 5314031919	\( 2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 30, 21720]$ (GRH)
12.0.218764100914962817683456000000.37	x^12 + 102x^10 - 52x^9 + 8703x^8 + 2496x^7 + 470242x^6 + 300456x^5 + 18065637x^4 + 14790204x^3 + 438168960x^2 + 279668376x + 5374163484	\( 2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 4, 12, 5928]$ (GRH)
12.0.276135718563307914975107813376.1	x^12 + 861x^10 + 242802x^8 + 27005265x^6 + 1307690244x^4 + 26260555104x^2 + 157563330624	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 41^{9} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 42260]$ (GRH)
12.0.305924618859010011648000000000.1	x^12 + 930x^10 + 306900x^8 + 46872000x^6 + 3487276800x^4 + 119563776000x^2 + 1434765312000	\( 2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 31^{10} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 59060]$ (GRH)
12.0.315992590210501847764992000000.1	x^12 + 312x^10 - 52x^9 + 45123x^8 + 35256x^7 + 2843672x^6 + 794976x^5 + 38233377x^4 + 26701324x^3 + 1641488550x^2 - 2628689544x + 17237397684	\( 2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 6, 6, 28254]$ (GRH)
12.0.315992590210501847764992000000.2	x^12 + 312x^10 - 52x^9 + 45123x^8 - 6162x^7 + 2844842x^6 - 1148862x^5 + 37302525x^4 - 15701114x^3 + 1693748589x^2 + 4707053910x + 17866171479	\( 2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[3, 6, 144534]$ (GRH)
12.0.330966364856493592168450228224.15	x^12 - 2x^11 + 145x^10 - 880x^9 + 13350x^8 - 77392x^7 + 789272x^6 - 3718848x^5 + 22127456x^4 - 62065824x^3 + 227928720x^2 - 351879680x + 1003941856	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 4, 38064]$ (GRH)
12.0.330966364856493592168450228224.22	x^12 - 2x^11 + 121x^10 - 840x^9 + 11938x^8 - 75536x^7 + 810648x^6 - 3407360x^5 + 20369536x^4 - 53662112x^3 + 232061456x^2 - 360419200x + 2117917600	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 2, 102480]$ (GRH)
12.0.330966364856493592168450228224.23	x^12 - 4x^11 - 164x^10 + 760x^9 + 11031x^8 - 57920x^7 - 73396x^6 + 501456x^5 + 8722892x^4 - 27044448x^3 + 36508032x^2 - 129311488x + 2287368448	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 2, 38064]$ (GRH)
12.0.330966364856493592168450228224.27	x^12 - 2x^11 + 73x^10 - 760x^9 + 10554x^8 - 73744x^7 + 842072x^6 - 2403456x^5 + 14402624x^4 - 55312800x^3 + 287379984x^2 - 84951680x + 7114036000	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 40, 7320]$ (GRH)
12.0.330966364856493592168450228224.33	x^12 - 2x^11 + 49x^10 + 344x^9 + 10316x^8 - 55720x^7 + 1515592x^6 - 7745318x^5 + 102108541x^4 - 392352750x^3 + 3740971227x^2 - 7788574854x + 51646472991	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 19^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 12, 7812]$ (GRH)
12.0.367546984815514776264000000000.1	x^12 + 510x^10 + 66555x^8 + 2167500x^6 + 11379375x^4 + 16581375x^2 + 5527125	\( 2^{12}\cdot 3^{18}\cdot 5^{9}\cdot 17^{9} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 4, 20028]$ (GRH)
12.0.367546984815514776264000000000.2	x^12 + 510x^10 + 78795x^8 + 4768500x^6 + 125823375x^4 + 1343091375x^2 + 4029274125	\( 2^{12}\cdot 3^{18}\cdot 5^{9}\cdot 17^{9} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 56940]$ (GRH)
12.0.422882579117748274920892556361.1	x^12 - 1778x^9 + 822833x^6 - 64516000x^3 + 32005984375	\( 3^{18}\cdot 127^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 48, 1680]$ (GRH)
12.0.476278906078322265274202456064.5	x^12 + 364x^10 + 31213x^8 + 979524x^6 + 12073698x^4 + 48294792x^2 + 54331641	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 12, 36, 684]$ (GRH)