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 939)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.1703929099697370095703125.1	x^12 - x^11 + 263x^10 - 81x^9 + 28463x^8 + 5828x^7 + 1619354x^6 + 768444x^5 + 51291336x^4 + 23582808x^3 + 866225088x^2 + 233929177x + 6145345751	\( 5^{9}\cdot 7^{8}\cdot 73^{6} \)	$C_{12}$ (as 12T1)	$[5, 5, 4810]$ (GRH)
12.0.2169681134677448000000000.1	x^12 - 4x^11 + 283x^10 - 926x^9 + 32574x^8 - 84412x^7 + 1935477x^6 - 3748466x^5 + 62575025x^4 - 81302524x^3 + 1065197590x^2 - 709042578x + 7573971901	\( 2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 25012]$ (GRH)
12.0.2401666331349765944953125.1	x^12 - x^11 + 339x^10 - 339x^9 + 44279x^8 - 44279x^7 + 2786135x^6 - 2786135x^5 + 85955767x^4 - 85955767x^3 + 1167160983x^2 - 1167160983x + 5183066071	\( 3^{6}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 4, 1588]$ (GRH)
12.0.3099482676998661139070976.17	x^12 - 2x^11 + 243x^10 - 402x^9 + 25439x^8 - 33658x^7 + 1465592x^6 - 1462780x^5 + 48950518x^4 - 32947364x^3 + 898179909x^2 - 307522146x + 7073009371	\( 2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 30, 2340]$ (GRH)
12.0.3670536736379502144000000.7	x^12 - 6x^11 + 285x^10 - 1370x^9 + 30606x^8 - 114270x^7 + 1536671x^6 - 4215756x^5 + 37645887x^4 - 68396122x^3 + 416049516x^2 - 382535442x + 1914274729	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[20, 5320]$ (GRH)
12.0.3731191473321768182792533.1	x^12 - x^11 + 365x^10 - 365x^9 + 51325x^8 - 51325x^7 + 3475837x^6 - 3475837x^5 + 115343229x^4 - 115343229x^3 + 1681486717x^2 - 1681486717x + 7946060669	\( 13^{11}\cdot 113^{6} \)	$C_{12}$ (as 12T1)	$[2, 51140]$ (GRH)
12.0.4783253053886935470703125.1	x^12 + 318x^10 - x^9 + 35199x^8 - 5601x^7 + 1766048x^6 - 870237x^5 + 42372270x^4 - 39182024x^3 + 490256874x^2 - 445296567x + 2516315671	\( 3^{18}\cdot 5^{9}\cdot 43^{6} \)	$C_{12}$ (as 12T1)	$[2, 52090]$ (GRH)
12.0.5331858433381402593398784.5	x^12 + 183x^10 + 14617x^8 + 651967x^6 + 17056201x^4 + 246520835x^2 + 1526699329	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 43^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 8, 8, 1008]$ (GRH)
12.0.5331858433381402593398784.6	x^12 + 473x^10 + 81356x^8 + 6201546x^6 + 205128060x^4 + 2352135088x^2 + 6321363049	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 43^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 14, 504]$ (GRH)
12.0.5595699693580593283203125.1	x^12 - x^11 + 323x^10 - 101x^9 + 42703x^8 + 8448x^7 + 2950734x^6 + 1390204x^5 + 112725316x^4 + 52702688x^3 + 2278832068x^2 + 640091877x + 19212337691	\( 5^{9}\cdot 7^{8}\cdot 89^{6} \)	$C_{12}$ (as 12T1)	$[2, 77890]$ (GRH)
12.0.5768629464666860572114944.6	x^12 + 372x^10 + 51894x^8 + 3336592x^6 + 96969705x^4 + 1030649436x^2 + 887503681	\( 2^{24}\cdot 3^{18}\cdot 31^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 6, 6552]$ (GRH)
12.0.5946995183757601408203125.1	x^12 - x^11 + 408x^10 - 409x^9 + 61794x^8 - 62203x^7 + 4441807x^6 - 4781629x^5 + 160998290x^4 - 185075146x^3 + 2829532400x^2 - 2683767652x + 19664734321	\( 5^{9}\cdot 7^{10}\cdot 47^{6} \)	$C_{12}$ (as 12T1)	$[2, 93314]$ (GRH)
12.0.6514888485479415604006912.1	x^12 + 403x^10 + 62465x^8 + 4647396x^6 + 168080822x^4 + 2605252741x^2 + 11537547853	\( 2^{12}\cdot 13^{11}\cdot 31^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 16946]$ (GRH)
12.0.6827179527544712000000000.1	x^12 - 4x^11 + 343x^10 - 1126x^9 + 47714x^8 - 124252x^7 + 3418417x^6 - 6656386x^5 + 132905105x^4 - 173414484x^3 + 2704663170x^2 - 1800348698x + 22837898761	\( 2^{12}\cdot 5^{9}\cdot 7^{8}\cdot 23^{6} \)	$C_{12}$ (as 12T1)	$[2, 62770]$ (GRH)
12.0.7284706360423786423828125.1	x^12 - x^11 + 338x^10 - 106x^9 + 46713x^8 + 9178x^7 + 3370404x^6 + 1585644x^5 + 134261761x^4 + 62972433x^3 + 2825933888x^2 + 799850077x + 24768500401	\( 3^{6}\cdot 5^{9}\cdot 7^{8}\cdot 31^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 25012]$ (GRH)
12.0.7659539263855005696000000.16	x^12 - 6x^11 + 321x^10 - 1550x^9 + 38814x^8 - 146022x^7 + 2195273x^6 - 6081186x^5 + 60554802x^4 - 111141586x^3 + 753351309x^2 - 698770170x + 3841091281	\( 2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 45752]$ (GRH)
12.0.7991252743075419172110336.15	x^12 + 506x^10 + 93104x^8 + 7592208x^6 + 268647360x^4 + 3295407616x^2 + 9474296896	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 31992]$ (GRH)
12.0.7991252743075419172110336.16	x^12 - 2x^11 + 265x^10 - 436x^9 + 30354x^8 - 40216x^7 + 1919630x^6 - 1949106x^5 + 70585208x^4 - 49564380x^3 + 1429811640x^2 - 529942832x + 12452899201	\( 2^{18}\cdot 3^{6}\cdot 7^{10}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[10, 17640]$ (GRH)
12.0.8156423581635695080078125.1	x^12 + 348x^10 - x^9 + 42174x^8 - 6651x^7 + 2316848x^6 - 1132947x^5 + 60795645x^4 - 55917689x^3 + 763654464x^2 - 700201812x + 4170430441	\( 3^{18}\cdot 5^{9}\cdot 47^{6} \)	$C_{12}$ (as 12T1)	$[18, 7578]$ (GRH)
12.0.8258765543212396597594677.1	x^12 - x^11 + 417x^10 - 417x^9 + 66977x^8 - 66977x^7 + 5178785x^6 - 5178785x^5 + 196019617x^4 - 196019617x^3 + 3249472929x^2 - 3249472929x + 17208116641	\( 3^{6}\cdot 13^{11}\cdot 43^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 14290]$ (GRH)
12.0.9091907822989955933835264.5	x^12 + 201x^10 + 17560x^8 + 853159x^6 + 24229669x^4 + 379269698x^2 + 2540260801	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 47^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 25544]$ (GRH)
12.0.9091907822989955933835264.6	x^12 + 517x^10 + 97196x^8 + 8098194x^6 + 292780860x^4 + 3669520112x^2 + 10779215329	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 47^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 25956]$ (GRH)
12.0.9378745794895906501953125.1	x^12 - x^11 + 353x^10 - 111x^9 + 50903x^8 + 9938x^7 + 3828104x^6 + 1798584x^5 + 158746986x^4 + 74673288x^3 + 3473412138x^2 + 990002287x + 31603168001	\( 5^{9}\cdot 7^{8}\cdot 97^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 44018]$ (GRH)
12.0.9708038629029565330078125.1	x^12 - x^11 + 443x^10 - 444x^9 + 72854x^8 - 73298x^7 + 5685112x^6 - 6113764x^5 + 223464715x^4 - 256778386x^3 + 4246142315x^2 - 4044668347x + 31633408171	\( 3^{6}\cdot 5^{9}\cdot 7^{10}\cdot 17^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 35906]$ (GRH)
12.0.9919430095046378756575453.1	x^12 - x^11 + 430x^10 - 430x^9 + 71215x^8 - 71215x^7 + 5677387x^6 - 5677387x^5 + 221515009x^4 - 221515009x^3 + 3782835772x^2 - 3782835772x + 20571919369	\( 7^{6}\cdot 13^{11}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 50866]$ (GRH)
12.0.10208309886795316042399744.13	x^12 - 2x^11 + 23x^10 - 70x^9 + 1683x^8 - 1182x^7 + 58064x^6 + 29528x^5 + 1326358x^4 + 312844x^3 + 19852557x^2 - 2851794x + 125095671	\( 2^{18}\cdot 7^{10}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[3, 3, 17784]$ (GRH)
12.0.10437554603200547490103296.6	x^12 - 4x^11 + 202x^10 - 656x^9 + 17604x^8 - 45212x^7 + 847622x^6 - 1633236x^5 + 23739599x^4 - 30808716x^3 + 365351184x^2 - 241593532x + 2404591561	\( 2^{24}\cdot 3^{6}\cdot 7^{8}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 12, 4836]$ (GRH)
12.0.10492184911088211262672896.1	x^12 + 189x^10 + 15972x^8 + 773671x^6 + 22405545x^4 + 361326234x^2 + 2491307569	\( 2^{12}\cdot 3^{18}\cdot 137^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 68328]$ (GRH)
12.0.10907632593203528000000000.1	x^12 + 455x^10 + 76895x^8 + 6151600x^6 + 244910575x^4 + 4548339250x^2 + 29564205125	\( 2^{12}\cdot 5^{9}\cdot 7^{10}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 11258]$ (GRH)
12.0.11339928743479941805637632.1	x^12 + 442x^10 + 75140x^8 + 6131424x^6 + 243213152x^4 + 4134623584x^2 + 20082457408	\( 2^{18}\cdot 13^{11}\cdot 17^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 34858]$ (GRH)
12.0.11711981316148206157955072.1	x^12 + 364x^10 + 44954x^8 + 2337608x^6 + 55979560x^4 + 582187424x^2 + 1892109128	\( 2^{33}\cdot 7^{10}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 4, 3656]$ (GRH)
12.0.11849506903407426861218533.1	x^12 - x^11 + 443x^10 - 443x^9 + 75583x^8 - 75583x^7 + 6207007x^6 - 6207007x^5 + 249420159x^4 - 249420159x^3 + 4384043743x^2 - 4384043743x + 24466501151	\( 13^{11}\cdot 137^{6} \)	$C_{12}$ (as 12T1)	$[100402]$ (GRH)
12.0.11948427342082473984000000.19	x^12 + 420x^10 + 66150x^8 + 4802000x^6 + 157565625x^4 + 1890787500x^2 + 1838265625	\( 2^{24}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 29212]$ (GRH)
12.0.11952055518954678517578125.1	x^12 - x^11 + 368x^10 - 116x^9 + 55273x^8 + 10728x^7 + 4325484x^6 + 2029774x^5 + 186438691x^4 + 87932303x^3 + 4234486768x^2 + 1214690007x + 39941506541	\( 5^{9}\cdot 7^{8}\cdot 101^{6} \)	$C_{12}$ (as 12T1)	$[52, 5044]$ (GRH)
12.0.13494136204675776832000000.1	x^12 + 455x^10 + 79625x^8 + 6688500x^6 + 273113750x^4 + 4779490625x^2 + 23897453125	\( 2^{12}\cdot 5^{6}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 11290]$ (GRH)
12.0.14082882354952696422423117.1	x^12 - x^11 + 456x^10 - 456x^9 + 80081x^8 - 80081x^7 + 6768581x^6 - 6768581x^5 + 279882331x^4 - 279882331x^3 + 5059372956x^2 - 5059372956x + 28956826081	\( 3^{6}\cdot 13^{11}\cdot 47^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 8660]$ (GRH)
12.0.14246703795204608000000000.1	x^12 - 4x^11 + 388x^10 - 1276x^9 + 60959x^8 - 159172x^7 + 4926262x^6 - 9621256x^5 + 215720780x^4 - 282139524x^3 + 4928620860x^2 - 3280867988x + 46545815161	\( 2^{18}\cdot 5^{9}\cdot 7^{8}\cdot 13^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 27130]$ (GRH)
12.0.15088690771598141370990592.1	x^12 - 4x^11 + 409x^10 - 1618x^9 + 64702x^8 - 232812x^7 + 4913521x^6 - 14897420x^5 + 177880768x^4 - 392841486x^3 + 2512428095x^2 - 2287314156x + 6688402169	\( 2^{16}\cdot 11^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 22, 748]$ (GRH)
12.0.16007193286004365741522944.2	x^12 + 144x^10 - 4x^9 + 9417x^8 + 36x^7 + 354874x^6 + 17724x^5 + 8053932x^4 + 638028x^3 + 103405548x^2 + 7102716x + 582677873	\( 2^{24}\cdot 3^{16}\cdot 53^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 252, 252]$ (GRH)
12.0.16201367308849608000000000.1	x^12 + 273x^10 - 4x^9 + 30834x^8 + 36x^7 + 1824563x^6 + 30672x^5 + 59716095x^4 + 2436664x^3 + 1053927204x^2 + 67270842x + 7952847101	\( 2^{12}\cdot 3^{16}\cdot 5^{9}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 2, 2, 14, 364]$ (GRH)
12.0.16656543708527452138703125.1	x^12 - x^11 + 469x^10 - 469x^9 + 84709x^8 - 84709x^7 + 7363045x^6 - 7363045x^5 + 313053157x^4 - 313053157x^3 + 5815475173x^2 - 5815475173x + 34113645541	\( 5^{6}\cdot 13^{11}\cdot 29^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 2, 18, 1332]$ (GRH)
12.0.16675848397406332595994624.16	x^12 + 468x^10 + 80613x^8 + 6169176x^6 + 198955926x^4 + 2165380776x^2 + 3518743761	\( 2^{24}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 12, 12, 228]$ (GRH)
12.0.16676804026947237593481216.5	x^12 + 444x^10 + 73926x^8 + 5673136x^6 + 196786905x^4 + 2496382452x^2 + 2565726409	\( 2^{24}\cdot 3^{18}\cdot 37^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 6, 6, 630]$ (GRH)
12.0.17523242277045191736328125.1	x^12 - 3x^11 + 279x^10 - 831x^9 + 32505x^8 - 91308x^7 + 2005158x^6 - 4813584x^5 + 68420724x^4 - 119458244x^3 + 1226604198x^2 - 1176569685x + 9174406301	\( 3^{16}\cdot 5^{9}\cdot 7^{6}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 28564]$ (GRH)
12.0.18694897744381964174168064.5	x^12 - 6x^11 + 241x^10 - 1150x^9 + 24665x^8 - 91826x^7 + 1372757x^6 - 3801644x^5 + 43884395x^4 - 81537580x^3 + 765535945x^2 - 725385798x + 5718892873	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 53^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 14, 5460]$ (GRH)
12.0.18694897744381964174168064.6	x^12 - 2x^11 + 307x^10 - 506x^9 + 40532x^8 - 53740x^7 + 2941140x^6 - 2980318x^5 + 123571099x^4 - 86207266x^3 + 2848609153x^2 - 1041821864x + 28128047641	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 53^{6} \)	$C_6\times C_2$ (as 12T2)	$[26, 6552]$ (GRH)
12.0.18883102336086538361328125.1	x^12 - x^11 + 398x^10 - 126x^9 + 64553x^8 + 12398x^7 + 5445884x^6 + 2549904x^5 + 252526341x^4 + 119660013x^3 + 6155914968x^2 + 1786052977x + 62174703641	\( 5^{9}\cdot 7^{8}\cdot 109^{6} \)	$C_{12}$ (as 12T1)	$[2, 92410]$ (GRH)
12.0.19366119397482188691050496.10	x^12 - 2x^11 + 333x^10 - 552x^9 + 47339x^8 - 62758x^7 + 3673382x^6 - 3667870x^5 + 163992613x^4 - 110101244x^3 + 3992362134x^2 - 1357569336x + 41405864761	\( 2^{12}\cdot 3^{6}\cdot 13^{10}\cdot 19^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 81468]$ (GRH)
12.0.19610762759203196764498237.1	x^12 - x^11 + 482x^10 - 482x^9 + 89467x^8 - 89467x^7 + 7991335x^6 - 7991335x^5 + 349088637x^4 - 349088637x^3 + 6659388724x^2 - 6659388724x + 40013832041	\( 13^{11}\cdot 149^{6} \)	$C_{12}$ (as 12T1)	$[35, 5110]$ (GRH)
12.0.22102347515370618643283968.1	x^12 + 494x^10 + 93860x^8 + 8560032x^6 + 379494752x^4 + 7210400288x^2 + 39142172992	\( 2^{18}\cdot 13^{11}\cdot 19^{6} \)	$C_{12}$ (as 12T1)	$[2, 122954]$ (GRH)