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 41 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.9171686030885637573690636671.1	x^14 - x^13 + 132x^12 - 133x^11 + 5866x^10 - 6000x^9 + 108150x^8 - 144735x^7 + 809745x^6 - 1853951x^5 + 3501044x^4 - 6549159x^3 + 18283513x^2 - 17492952x + 14031649	\( -\,19^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 1846]$ (GRH)
14.0.9734369597099193349790237551.1	x^14 - 5x^13 + 41x^12 - 139x^11 + 954x^10 - 2810x^9 + 16990x^8 - 43043x^7 + 216460x^6 - 427080x^5 + 1779327x^4 - 2350647x^3 + 8361848x^2 - 5698041x + 17394953	\( -\,29^{12}\cdot 31^{7} \)	$C_{14}$ (as 14T1)	$[4, 4, 1356]$ (GRH)
14.0.13133604752587010801920000000.1	x^14 + 145x^12 + 7250x^10 + 155875x^8 + 1413750x^6 + 4893750x^4 + 5890625x^2 + 2265625	\( -\,2^{14}\cdot 5^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 1852]$ (GRH)
14.0.22764194375420436752520546875.1	x^14 - 5x^13 + 48x^12 - 169x^11 + 1260x^10 - 3759x^9 + 24153x^8 - 61247x^7 + 328657x^6 - 650470x^5 + 2903596x^4 - 3877996x^3 + 14758999x^2 - 10152668x + 33177421	\( -\,5^{7}\cdot 7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 5306]$ (GRH)
14.0.32733449455413964710545859375.1	x^14 - 7x^13 + 7x^12 + 7x^11 + 322x^10 - 700x^9 + 966x^8 - 1217x^7 + 27482x^6 - 672x^5 + 104601x^4 + 13965x^3 + 797146x^2 + 807429x + 2290621	\( -\,3^{7}\cdot 5^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[12238]$ (GRH)
14.0.34935649744100307390657103483.1	x^14 - x^13 + 161x^12 - 162x^11 + 8766x^10 - 8929x^9 + 199413x^8 - 261750x^7 + 1855050x^6 - 4073118x^5 + 9051006x^4 - 18171460x^3 + 48954232x^2 - 47391691x + 41183711	\( -\,23^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 8516]$ (GRH)
14.0.35718784670547055607182231339.1	x^14 - 5x^13 + 8x^12 - 45x^11 + 380x^10 - 307x^9 + 3663x^8 - 1563x^7 + 43763x^6 + 25532x^5 + 293844x^4 + 197546x^3 + 1450369x^2 + 1206310x + 3303433	\( -\,19^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7, 3437]$ (GRH)
14.0.48052913294624214844455469056.1	x^14 + 126x^12 + 4851x^10 + 64827x^8 + 305613x^6 + 357210x^4 + 142884x^2 + 15309	\( -\,2^{14}\cdot 3^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[2, 7142]$ (GRH)
14.0.51148327420496097793280000000.1	x^14 - 2x^13 + 46x^11 + 165x^10 - 1044x^9 + 6239x^8 - 16892x^7 + 74769x^6 - 198708x^5 + 622438x^4 - 1134722x^3 + 2734542x^2 - 3553304x + 5334581	\( -\,2^{14}\cdot 5^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[28826]$ (GRH)
14.0.61568510194571181216996409344.1	x^14 + 129x^12 + 5418x^10 + 91719x^8 + 689634x^6 + 2194290x^4 + 2225637x^2 + 94041	\( -\,2^{14}\cdot 3^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2, 18318]$ (GRH)
14.0.84150067079150835865691353219.1	x^14 + 126x^12 - 301x^11 + 4879x^10 - 20776x^9 + 88998x^8 - 354843x^7 + 975541x^6 - 2371978x^5 + 4145911x^4 - 3819046x^3 + 2580193x^2 - 2274769x + 2817187	\( -\,7^{25}\cdot 13^{7} \)	$C_{14}$ (as 14T1)	$[26098]$ (GRH)
14.0.107818525613017436136763734631.1	x^14 - x^13 + 131x^12 + 153x^11 + 5401x^10 + 16023x^9 + 100892x^8 + 382791x^7 + 1195655x^6 + 3751787x^5 + 8385937x^4 + 17768243x^3 + 27352621x^2 + 25865442x + 22606297	\( -\,13^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[74384]$ (GRH)
14.0.171249048453908271645616513339.1	x^14 - 7x^13 + 14x^12 - 35x^11 + 448x^10 - 987x^9 + 3269x^8 - 5165x^7 + 50239x^6 - 15162x^5 + 290430x^4 + 126x^3 + 1882601x^2 + 1399160x + 5746151	\( -\,7^{24}\cdot 19^{7} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 406]$ (GRH)
14.0.245223976167125010433280000000.1	x^14 - 7x^12 - 42x^11 + 308x^10 + 896x^9 + 3871x^8 + 6260x^7 + 57890x^6 + 141946x^5 + 509600x^4 + 789740x^3 + 2839473x^2 + 4042276x + 8465729	\( -\,2^{14}\cdot 5^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[13538]$ (GRH)
14.0.319778293622616136151658322211.1	x^14 - 5x^13 - 30x^12 + 211x^11 + 380x^10 - 4561x^9 + 3573x^8 + 38489x^7 - 84021x^6 - 101414x^5 + 750422x^4 - 1936270x^3 + 3964475x^2 - 5606250x + 6578125	\( -\,11^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[25781]$ (GRH)
14.0.550292317794853063315721009111.1	x^14 + 168x^12 - 392x^11 + 8659x^10 - 36134x^9 + 194649x^8 - 821778x^7 + 2490278x^6 - 6786024x^5 + 12547871x^4 - 13116425x^3 + 11092144x^2 - 10001649x + 11183839	\( -\,7^{25}\cdot 17^{7} \)	$C_{14}$ (as 14T1)	$[35570]$ (GRH)
14.0.652300651772147469026072062247.1	x^14 - 7x^13 + 21x^12 + 7x^11 + 154x^10 - 2058x^9 + 12670x^8 - 44565x^7 + 173194x^6 - 555058x^5 + 1703975x^4 - 3648323x^3 + 8318800x^2 - 12694353x + 19486321	\( -\,7^{24}\cdot 23^{7} \)	$C_{14}$ (as 14T1)	$[19659]$ (GRH)
14.0.660161636887192665823095859375.1	x^14 - x^13 + 248x^12 - 249x^11 + 20946x^10 - 21196x^9 + 747078x^8 - 951747x^7 + 11017281x^6 - 22664583x^5 + 74493972x^4 - 163620583x^3 + 444796489x^2 - 451469716x + 476400689	\( -\,5^{7}\cdot 7^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 5944]$ (GRH)
14.0.878681843101699928584328577024.1	x^14 - 42x^11 + 371x^10 + 854x^9 + 6405x^8 + 10768x^7 + 98329x^6 + 216482x^5 + 949228x^4 + 1471666x^3 + 5724964x^2 + 7397628x + 17724049	\( -\,2^{21}\cdot 3^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[49798]$ (GRH)
14.0.2570974548880469840391308046875.1	x^14 - 5x^13 + 36x^12 - 165x^11 + 1160x^10 - 2707x^9 + 22811x^8 - 27219x^7 + 328903x^6 - 89140x^5 + 3204020x^4 + 602378x^3 + 19889249x^2 + 7744478x + 58736881	\( -\,5^{7}\cdot 7^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 1486]$ (GRH)
14.0.6150772901711899500090300039168.1	x^14 + 252x^12 + 19404x^10 + 518616x^8 + 4889808x^6 + 11430720x^4 + 9144576x^2 + 1959552	\( -\,2^{21}\cdot 3^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[2, 47798]$ (GRH)
14.0.8024901391510087293807453028352.1	x^14 + 113x^12 + 3842x^10 + 49607x^8 + 300354x^6 + 891570x^4 + 1200173x^2 + 569633	\( -\,2^{14}\cdot 113^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 26, 104]$ (GRH)
14.0.9090153788613196226613752102912.1	x^14 - 2x^13 - 81x^12 - 2x^11 + 2330x^10 + 3644x^9 - 10545x^8 + 9188x^7 + 53766x^6 - 12686x^5 + 660458x^4 - 64960x^3 + 1757945x^2 - 76170x + 1550827	\( -\,2^{21}\cdot 113^{12} \)	$C_{14}$ (as 14T1)	$[2, 14, 406]$ (GRH)
14.0.41747190692552429248373387378688.1	x^14 + 213x^12 + 14058x^10 + 358479x^8 + 4244238x^6 + 24119694x^4 + 59988681x^2 + 44875053	\( -\,2^{14}\cdot 3^{7}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[2, 20612]$ (GRH)
14.0.73107511205515163512900457612387.1	x^14 - x^13 + 216x^12 - 224x^11 + 14741x^10 + 3351x^9 + 373778x^8 + 356239x^7 + 5954484x^6 + 8576249x^5 + 52523677x^4 + 58323776x^3 + 226380237x^2 + 112363510x + 215658439	\( -\,13^{7}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[23110]$ (GRH)
14.0.174678077231252895510919809921875.1	x^14 - x^13 + 132x^12 + 180x^11 + 1915x^10 + 2085x^9 + 26433x^8 + 55438x^7 + 760329x^6 + 1125862x^5 + 3273901x^4 + 12466019x^3 + 29806445x^2 + 33909513x + 17221049	\( -\,5^{7}\cdot 127^{13} \)	$C_{14}$ (as 14T1)	$[31370]$ (GRH)
14.0.403372275797631336682377398030279.1	x^14 - x^13 + 174x^12 - 195x^11 + 8592x^10 - 29768x^9 + 139645x^8 - 755470x^7 + 2331639x^6 - 7462084x^5 + 33375503x^4 - 30681299x^3 + 212182491x^2 - 44623278x + 401609231	\( -\,7^{7}\cdot 113^{13} \)	$C_{14}$ (as 14T1)	$[4, 4, 4, 928]$ (GRH)
14.0.530059499186032039461665494643307.1	x^14 - x^13 + 121x^12 - 1302x^11 + 15895x^10 - 88844x^9 + 415211x^8 - 1029384x^7 + 2348246x^6 - 2578842x^5 + 5826655x^4 - 5062204x^3 + 8867677x^2 + 982009x + 117649	\( -\,3^{7}\cdot 281^{12} \)	$C_{14}$ (as 14T1)	$[50723]$ (GRH)
14.0.569108078765853806807890636324864.1	x^14 + 205x^12 + 14494x^10 + 435247x^8 + 5615886x^6 + 31987214x^4 + 69660541x^2 + 26863489	\( -\,2^{14}\cdot 239^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2746]$ (GRH)
14.0.1472006484410430025621015411349799.1	x^14 - x^13 + 106x^12 + 223x^11 + 3759x^10 + 16405x^9 + 45656x^8 + 151316x^7 - 88208x^6 - 1979796x^5 + 6623518x^4 - 7131374x^3 + 191487834x^2 - 886029565x + 1175495059	\( -\,3^{7}\cdot 197^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 4334]$ (GRH)
14.0.2813720754599325443123783814625063.1	x^14 - 5x^13 - 145x^12 + 341x^11 + 8850x^10 + 200x^9 - 234152x^8 - 314915x^7 + 2594626x^6 + 5538516x^5 - 3383529x^4 + 10375639x^3 + 45137186x^2 - 15092353x + 101385859	\( -\,7^{7}\cdot 197^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 6874]$ (GRH)
14.0.6413214172956389772541350262917703.1	x^14 - 5x^13 - 157x^12 + 973x^11 + 7020x^10 - 54802x^9 - 32628x^8 + 542193x^7 + 1063886x^6 - 3813892x^5 - 9544515x^4 + 1156817x^3 + 52095720x^2 + 85068297x + 73732261	\( -\,7^{7}\cdot 211^{12} \)	$C_{14}$ (as 14T1)	$[44303]$ (GRH)
14.0.11027596817823724526645960905146368.1	x^14 + 197x^12 + 13790x^10 + 415079x^8 + 5284722x^6 + 26038278x^4 + 45764873x^2 + 18567053	\( -\,2^{14}\cdot 197^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 5470]$ (GRH)
14.0.44931703384098017538267680344521103.1	x^14 - x^13 + 17x^12 - 71x^11 - 540x^10 - 9712x^9 + 123934x^8 - 900107x^7 + 7843772x^6 - 48211158x^5 + 168859238x^4 - 321562607x^3 + 591306086x^2 - 1637661044x + 2026251923	\( -\,463^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2842]$ (GRH)
14.0.392496006513281583932595840500243827.1	x^14 - x^13 + 20x^12 - 162x^11 - 1238x^10 - 4668x^9 + 92865x^8 - 914451x^7 - 6262919x^6 + 5224933x^5 + 245440053x^4 + 755961898x^3 + 716216243x^2 - 1079662218x + 4124434193	\( -\,547^{13} \)	$C_{14}$ (as 14T1)	$[32259]$ (GRH)
14.0.4420896929577970806479733313662687779.1	x^14 - x^13 + 24x^12 - 760x^11 - 4652x^10 - 14210x^9 + 53254x^8 + 2644631x^7 + 25016954x^6 + 79585767x^5 + 229342015x^4 + 30774107x^3 + 1793249698x^2 + 3458916720x + 18994958023	\( -\,659^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 4334]$ (GRH)
14.0.21030741190818981798961548926499574343.1	x^14 - x^13 + 27x^12 - 963x^11 + 2856x^10 + 100640x^9 - 716739x^8 + 549511x^7 + 9890696x^6 - 41378938x^5 + 412351459x^4 - 4014600069x^3 + 19083041153x^2 - 44249771299x + 41555683709	\( -\,743^{13} \)	$C_{14}$ (as 14T1)	$[66003]$ (GRH)
14.0.474489902930063357496193840307474416087.3	x^14 - 812x^11 + 11571x^10 - 198534x^9 + 5169395x^8 - 38066328x^7 + 215110980x^6 - 2112867848x^5 + 12080530203x^4 - 43947685383x^3 + 263153797984x^2 - 206678117415x + 1787701529889	\( -\,7^{25}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[7, 6769]$ (GRH)
14.0.474489902930063357496193840307474416087.4	x^14 - 812x^11 + 17255x^10 - 221270x^9 + 5175079x^8 - 37003420x^7 + 382419520x^6 - 2313638096x^5 + 10397884315x^4 - 28019912375x^3 + 50915744628x^2 - 433333386675x + 2558606699525	\( -\,7^{25}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[287, 287]$ (GRH)
14.0.13760207184971837367389621368916758066523.5	x^14 - 812x^11 - 22533x^10 - 73486x^9 + 366415x^8 + 7780816x^7 + 302972831x^6 + 1609330814x^5 - 12742935849x^4 - 72797482464x^3 + 323107507394x^2 + 606858815682x + 699223478963	\( -\,7^{25}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[91756]$ (GRH)
14.0.329187156767051876908796215815371233484443.4	x^14 - 7826x^11 + 70735x^10 + 494242x^9 - 4232963x^8 - 54303754x^7 + 285753447x^6 + 4782561910x^5 - 15205020719x^4 - 206213160958x^3 + 375732658658x^2 + 7534219954478x + 20950836200249	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[40187]$ (GRH)