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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.12111141100130785779768711.1	x^14 + 12x^12 - 60x^11 - 567x^10 + 237x^9 + 1873x^8 + 9867x^7 + 13383x^6 - 49512x^5 + 153774x^4 - 127299x^3 + 116395x^2 - 72588x + 28167	\( -\,3^{7}\cdot 1277^{7} \)	$D_{7}$ (as 14T2)	$[13, 78]$ (GRH)
14.0.28480176617692682623926272.1	x^14 + 43x^12 + 722x^10 + 5993x^8 + 25558x^6 + 51799x^4 + 38148x^2 + 4913	\( -\,2^{14}\cdot 17^{3}\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	$[2, 2, 300]$ (GRH)
14.0.60452572724246936927109375.1	x^14 - 5x^13 + 13x^12 - 19x^11 + 150x^10 - 514x^9 + 2438x^8 - 6347x^7 + 22552x^6 - 42720x^5 + 123031x^4 - 143071x^3 + 363084x^2 - 231593x + 499381	\( -\,3^{7}\cdot 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 226]$ (GRH)
14.0.134239384709553967597109375.1	x^14 - x^13 + 45x^12 + 67x^11 + 585x^10 + 2263x^9 + 4916x^8 + 17291x^7 + 36289x^6 + 71331x^5 + 129077x^4 + 181931x^3 + 270017x^2 + 169588x + 119189	\( -\,5^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2842]$ (GRH)
14.0.199950626296934196778017319.1	x^14 - x^13 + 74x^12 - 75x^11 + 1806x^10 - 1882x^9 + 17670x^8 - 25893x^7 + 68157x^6 - 189003x^5 + 252348x^4 - 306967x^3 + 1166437x^2 - 1133182x + 741761	\( -\,11^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 8, 8, 40]$ (GRH)
14.0.268856242022659049623404544.1	x^14 + 61x^12 + 1402x^10 + 15247x^8 + 80418x^6 + 185798x^4 + 127429x^2 + 18769	\( -\,2^{14}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[3277]$ (GRH)
14.0.316265035547780605989332299.1	x^14 - 5x^13 + 20x^12 - 49x^11 + 288x^10 - 863x^9 + 4381x^8 - 11303x^7 + 44797x^6 - 86598x^5 + 279108x^4 - 343260x^3 + 959807x^2 - 625188x + 1493501	\( -\,19^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[4, 4, 284]$ (GRH)
14.0.383513401375521683097010176.1	x^14 - 24x^12 + 474x^10 + 1144x^8 - 21471x^6 + 13728x^4 + 92356x^2 + 100416	\( -\,2^{14}\cdot 3^{7}\cdot 523^{7} \)	$D_{7}$ (as 14T2)	$[86, 86]$ (GRH)
14.0.452882922503000372480000000.1	x^14 - 2x^13 + 12x^12 - 22x^11 + 261x^10 - 332x^9 + 3687x^8 - 2596x^7 + 35841x^6 - 17536x^5 + 240758x^4 - 110934x^3 + 986314x^2 - 244032x + 1783541	\( -\,2^{14}\cdot 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 406]$ (GRH)
14.0.564302043262742500808327168.1	x^14 - 4x^12 + 122x^10 + 4936x^8 + 46193x^6 + 26604x^4 + 692068x^2 + 106112	\( -\,2^{21}\cdot 829^{7} \)	$D_{7}$ (as 14T2)	$[13, 78]$ (GRH)
14.0.1204677577382769220367486327.1	x^14 - 5x^13 + 27x^12 - 79x^11 + 468x^10 - 1362x^9 + 7314x^8 - 18671x^7 + 80950x^6 - 158128x^5 + 561187x^4 - 714115x^3 + 2179894x^2 - 1446221x + 3780979	\( -\,23^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1806]$ (GRH)
14.0.1622761392560638877063184384.1	x^14 - 2x^13 + 19x^12 - 34x^11 + 402x^10 - 528x^9 + 6227x^8 - 4968x^7 + 67046x^6 - 36022x^5 + 492458x^4 - 218804x^3 + 2200477x^2 - 533070x + 4387351	\( -\,2^{21}\cdot 3^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 602]$ (GRH)
14.0.1692934919397644000811644719.1	x^14 - 4x^13 + 44x^12 - 131x^11 + 223x^10 - 2372x^9 - 1828x^8 + 4867x^7 + 79816x^6 + 233126x^5 + 1093209x^4 + 1284789x^3 - 851090x^2 - 4392150x + 4773375	\( -\,7759^{7} \)	$D_{7}$ (as 14T2)	$[29, 203]$ (GRH)
14.0.1753124609003161170886171875.1	x^14 - x^13 + 103x^12 - 104x^11 + 3546x^10 - 3651x^9 + 50063x^8 - 69132x^7 + 283946x^6 - 695198x^5 + 1099322x^4 - 1801888x^3 + 5495644x^2 - 5241351x + 3832639	\( -\,3^{7}\cdot 5^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 4, 4, 116]$ (GRH)
14.0.1884940749689661095518792759.1	x^14 + 32x^12 + 236x^10 + 1227x^8 + 24852x^6 + 110594x^4 + 6367700x^2 + 6626239	\( -\,7879^{7} \)	$D_{7}$ (as 14T2)	$[13, 91]$ (GRH)
14.0.2812424737865523319657201664.1	x^14 + 84x^12 + 2156x^10 + 19208x^8 + 60368x^6 + 47040x^4 + 12544x^2 + 896	\( -\,2^{21}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[2468]$ (GRH)
14.0.3603461044766854684853927936.1	x^14 + 86x^12 + 2408x^10 + 27176x^8 + 136224x^6 + 288960x^4 + 195392x^2 + 5504	\( -\,2^{21}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[1970]$ (GRH)
14.0.3638057052789377781875859375.1	x^14 + 12x^12 - 36x^10 + 2431x^8 + 35784x^6 + 52722x^4 + 7209736x^2 + 2501295	\( -\,3^{7}\cdot 5^{7}\cdot 577^{7} \)	$D_{7}$ (as 14T2)	$[26, 78]$ (GRH)
14.0.3733376216303663794289149571.1	x^14 - 7x^13 + 49x^11 + 238x^10 - 623x^9 - 497x^8 + 1135x^7 + 15785x^6 + 2002x^5 + 16814x^4 + 4662x^3 + 298305x^2 + 401044x + 766979	\( -\,7^{24}\cdot 11^{7} \)	$C_{14}$ (as 14T1)	$[2059]$ (GRH)
14.0.5227532131604246464597421875.1	x^14 - 6x^13 + 47x^12 - 96x^11 + 817x^10 - 1614x^9 + 15353x^8 - 11976x^7 + 129647x^6 + 14466x^5 + 2094349x^4 - 5253552x^3 + 26472884x^2 - 34197120x + 63264400	\( -\,5^{7}\cdot 1823^{7} \)	$D_{7}$ (as 14T2)	$[29, 58]$ (GRH)
14.0.6827477543251035514764609375.1	x^14 - 5x^13 + x^12 - 15x^11 + 290x^10 - 82x^9 + 1576x^8 - 399x^7 + 22358x^6 + 20590x^5 + 123285x^4 + 99663x^3 + 589214x^2 + 602483x + 1228891	\( -\,3^{7}\cdot 5^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[1766]$ (GRH)
14.0.9479602020119218896677148747.1	x^14 - x^13 + 49x^12 + 122x^11 + 1955x^10 + 2412x^9 + 16259x^8 - 10342x^7 + 95434x^6 + 70x^5 + 15469x^4 - 1212x^3 + 2389x^2 - 49x + 1	\( -\,3^{7}\cdot 113^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 254]$ (GRH)
14.0.34413598978900358351795781632.1	x^14 - 2x^13 - 45x^12 + 30x^11 + 1030x^10 + 632x^9 - 11085x^8 - 20276x^7 + 43102x^6 + 151674x^5 + 206418x^4 + 411952x^3 + 987997x^2 + 1336242x + 1953011	\( -\,2^{21}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[1247]$ (GRH)
14.0.38502899391974811462791218827.1	x^14 - x^13 + 55x^12 - 8x^11 + 2389x^10 - 526x^9 + 27699x^8 + 21346x^7 + 220112x^6 + 184596x^5 + 991629x^4 + 1196220x^3 + 2970241x^2 + 1920273x + 1256641	\( -\,3^{7}\cdot 127^{12} \)	$C_{14}$ (as 14T1)	$[7, 301]$ (GRH)
14.0.71016826473540595520419938304.1	x^14 + 97x^12 + 2854x^10 + 31395x^8 + 102938x^6 + 30646x^4 + 2377x^2 + 1	\( -\,2^{14}\cdot 113^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 406]$ (GRH)
14.0.91022458951991999260243046875.1	x^14 - x^13 + 74x^12 - 82x^11 + 1819x^10 + 937x^9 + 14518x^8 + 14729x^7 + 152364x^6 + 274929x^5 + 790947x^4 + 804688x^3 + 2049631x^2 + 913390x + 867961	\( -\,5^{7}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 116]$ (GRH)
14.0.136055567791244518070906476247.1	x^14 - 5x^13 + 15x^12 - 75x^11 + 512x^10 - 682x^9 + 6620x^8 - 4227x^7 + 79540x^6 + 24230x^5 + 605069x^4 + 323699x^3 + 3152636x^2 + 2157359x + 7742617	\( -\,23^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7899]$ (GRH)
14.0.288446046473761001831902756864.1	x^14 + 109x^12 + 4094x^10 + 64587x^8 + 492142x^6 + 1843230x^4 + 3006113x^2 + 1256641	\( -\,2^{14}\cdot 127^{12} \)	$C_{14}$ (as 14T1)	$[43, 43]$ (GRH)
14.0.1071195028273471735324517808411.1	x^14 - x^13 + 61x^12 - 82x^11 + 908x^10 - 5925x^9 + 1220x^8 - 34756x^7 + 145654x^6 + 6877x^5 + 1495378x^4 + 369519x^3 + 4546573x^2 + 398747x + 3805387	\( -\,3^{7}\cdot 113^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 426]$ (GRH)
14.0.2443365527501925442977500495872.1	x^14 + 142x^12 + 6248x^10 + 106216x^8 + 838368x^6 + 3176256x^4 + 5266496x^2 + 2626432	\( -\,2^{21}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[5212]$ (GRH)
14.0.3569666157501162271525463699383.1	x^14 - 5x^13 - 73x^12 + 489x^11 + 1036x^10 - 13306x^9 + 27880x^8 - 19951x^7 + 48006x^6 - 117192x^5 + 670781x^4 - 1091251x^3 + 2003814x^2 - 1429473x + 1305077	\( -\,7^{7}\cdot 113^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1582]$ (GRH)
14.0.7472114134063096576756423407867.1	x^14 - x^13 + 85x^12 - 350x^11 + 5925x^10 - 19520x^9 + 153467x^8 - 374872x^7 + 2559802x^6 - 4851594x^5 + 17583457x^4 + 2579356x^3 + 6691533x^2 - 1666579x + 1352569	\( -\,3^{7}\cdot 197^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1682]$ (GRH)
14.0.14498762356636996870828289312503.1	x^14 - 5x^13 - 85x^12 + 413x^11 + 2536x^10 - 12422x^9 - 23248x^8 + 150497x^7 + 150754x^6 - 1228000x^5 + 66341x^4 + 5215705x^3 - 2368956x^2 - 14809311x + 22851677	\( -\,7^{7}\cdot 127^{12} \)	$C_{14}$ (as 14T1)	$[8141]$ (GRH)
14.0.17030925399469881272195784585627.1	x^14 - x^13 + 91x^12 + 228x^11 + 6725x^10 + 8698x^9 + 111679x^8 - 102522x^7 + 1215344x^6 - 1305976x^5 + 7192317x^4 - 11528880x^3 + 28130213x^2 - 24476087x + 21743569	\( -\,3^{7}\cdot 211^{12} \)	$C_{14}$ (as 14T1)	$[29, 203]$ (GRH)
14.0.55977648821440226023583557894144.1	x^14 + 169x^12 + 10186x^10 + 284395x^8 + 3790966x^6 + 20272254x^4 + 11329577x^2 + 1352569	\( -\,2^{14}\cdot 197^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1582]$ (GRH)
14.0.75966758316706681853567921242827.1	x^14 - x^13 + 103x^12 - 288x^11 + 8749x^10 - 17168x^9 + 207881x^8 + 164988x^7 + 2712410x^6 + 2203236x^5 + 18493219x^4 + 27913574x^3 + 74729515x^2 + 46299739x + 26863489	\( -\,3^{7}\cdot 239^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1906]$ (GRH)
14.0.100279849256417888141681913458688.1	x^14 - 7x^13 + 35x^12 - 119x^11 + 329x^10 - 721x^9 + 1337x^8 + 2011x^7 - 11522x^6 - 130648x^5 + 357532x^4 + 69076x^3 - 467348x^2 + 127316x + 4139276	\( -\,2^{12}\cdot 3^{12}\cdot 7^{11}\cdot 13^{12} \)	$F_7$ (as 14T4)	$[7, 14, 14]$ (GRH)
14.0.127587874597583234917080811454464.1	x^14 + 181x^12 + 10574x^10 + 250587x^8 + 2642670x^6 + 13082270x^4 + 28708425x^2 + 21743569	\( -\,2^{14}\cdot 211^{12} \)	$C_{14}$ (as 14T1)	$[5923]$ (GRH)
14.0.3328968836295431565149961657333739.1	x^14 - x^13 + 14x^12 + 754x^11 + 840x^10 - 19828x^9 - 8271x^8 + 300557x^7 - 186895x^6 - 3184843x^5 + 2562883x^4 + 17073682x^3 - 11883459x^2 - 10003960x + 148699319	\( -\,379^{13} \)	$C_{14}$ (as 14T1)	$[4497]$ (GRH)
14.0.198376007989432085363129684509608357763.1	x^14 - x^13 + 32x^12 - 766x^11 - 3350x^10 - 49474x^9 + 1057143x^8 - 6931854x^7 + 98559596x^6 - 654977697x^5 + 2734738830x^4 - 9840332223x^3 + 18337865967x^2 - 41024712654x + 132193055349	\( -\,883^{13} \)	$C_{14}$ (as 14T1)	$[3489]$ (GRH)
14.0.872216920681822470521409692289934818668544.1	x^14 - 7x^13 + 91x^12 - 455x^11 + 3185x^10 - 11921x^9 + 57057x^8 - 161157x^7 + 569646x^6 - 1244768x^5 + 3318980x^4 - 3806180x^3 + 7849828x^2 - 8070916x + 10765732	\( -\,2^{12}\cdot 3^{13}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 28, 84]$ (GRH)
14.0.3198128709166682391911835538396427668451328.1	x^14 - 500742x^7 + 80813044224	\( -\,2^{12}\cdot 3^{12}\cdot 7^{14}\cdot 11^{13}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 14, 210]$ (GRH)
14.0.61431129468164088609115434959104000000000000.1	x^14 + 282912400	\( -\,2^{20}\cdot 5^{12}\cdot 7^{14}\cdot 29^{12} \)	$F_7 \times C_2$ (as 14T7)	$[7, 14, 14]$ (GRH)
14.0.74429177231515517484493627075407771193049088.1	x^14 + 91x^12 + 3549x^10 + 76895x^8 - 264x^7 + 999635x^6 + 72072x^5 + 7797153x^4 - 1561560x^3 + 33787663x^2 + 4060056x + 62765941	\( -\,2^{20}\cdot 3^{12}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 14, 42]$ (GRH)