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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.10440732699324736115103484821504.1	x^14 - 2x^13 + 124x^12 - 214x^11 + 7557x^10 - 10668x^9 + 287927x^8 - 310308x^7 + 7248641x^6 - 5536192x^5 + 118383398x^4 - 58021334x^3 + 1144024522x^2 - 277132320x + 4979767381	\( -\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 68966]$ (GRH)
14.0.17721079003151998381007835234304.1	x^14 + 406x^12 + 56840x^10 + 3421768x^8 + 86896992x^6 + 842232384x^4 + 2838635072x^2 + 3056991616	\( -\,2^{21}\cdot 7^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 109544]$ (GRH)
14.0.127310161428861423711034656546331.1	x^14 + 378x^12 - 847x^11 + 43729x^10 - 176134x^9 + 1941534x^8 - 8999703x^7 + 40933963x^6 - 146975164x^5 + 333745951x^4 - 521303860x^3 + 684084919x^2 - 722816269x + 758859649	\( -\,7^{25}\cdot 37^{7} \)	$C_{14}$ (as 14T1)	$[1044572]$ (GRH)
14.0.196959242717829613546212447305728.1	x^14 + 49x^12 - 42x^11 + 1988x^10 + 560x^9 + 59423x^8 + 56436x^7 + 1275554x^6 + 1649242x^5 + 18366768x^4 + 21707980x^3 + 161055601x^2 + 135111620x + 665398601	\( -\,2^{14}\cdot 7^{24}\cdot 13^{7} \)	$C_{14}$ (as 14T1)	$[1217566]$ (GRH)
14.0.219720682645744009348218880000000.1	x^14 + 420x^12 + 53900x^10 + 2401000x^8 + 37730000x^6 + 147000000x^4 + 196000000x^2 + 70000000	\( -\,2^{21}\cdot 5^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[2, 515342]$ (GRH)
14.0.302781248280417347338001059823616.1	x^14 + 609x^12 + 127890x^10 + 11548467x^8 + 439916022x^6 + 6395702166x^4 + 32333827617x^2 + 52231567689	\( -\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 4, 4, 4, 8236]$ (GRH)
14.0.1179170130027156611464857533497344.1	x^14 - 2x^13 + 112x^12 - 146x^11 + 6693x^10 - 9524x^9 + 276271x^8 - 461308x^7 + 7907601x^6 - 13385716x^5 + 147472662x^4 - 207970434x^3 + 1594403790x^2 - 1379805112x + 7521613141	\( -\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 21982]$ (GRH)
14.0.1287998476392981798480681859039232.1	x^14 + 77x^12 - 42x^11 + 3836x^10 + 392x^9 + 135919x^8 + 93620x^7 + 3408482x^6 + 3494218x^5 + 57312920x^4 + 57285116x^3 + 584163825x^2 + 412653556x + 2769616973	\( -\,2^{14}\cdot 7^{24}\cdot 17^{7} \)	$C_{14}$ (as 14T1)	$[1515892]$ (GRH)
14.0.2098425699738568435088694126099051.1	x^14 - x^13 + 358x^12 - 366x^11 + 40159x^10 + 6901x^9 + 1703750x^8 + 1571901x^7 + 39941900x^6 + 54051465x^5 + 499919527x^4 + 560196080x^3 + 2982769075x^2 + 1543186750x + 4370228125	\( -\,3^{7}\cdot 7^{7}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[2, 1046982]$ (GRH)
14.0.2967605119190429807728658374197248.1	x^14 + 602x^12 + 117992x^10 + 9321368x^8 + 327073824x^6 + 4856550720x^4 + 22987673408x^2 + 4532780672	\( -\,2^{21}\cdot 7^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 31764]$ (GRH)
14.0.3754133851142516784723083520000000.1	x^14 + 630x^12 + 121275x^10 + 8103375x^8 + 191008125x^6 + 1116281250x^4 + 2232562500x^2 + 1196015625	\( -\,2^{14}\cdot 3^{7}\cdot 5^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[2, 2, 1454686]$ (GRH)
14.0.7829457398773661133521078601121792.1	x^14 + 112x^12 - 42x^11 + 7091x^10 + 182x^9 + 303989x^8 + 151440x^7 + 9029657x^6 + 7273378x^5 + 178583580x^4 + 148149106x^3 + 2128994980x^2 + 1257735836x + 11696930513	\( -\,2^{21}\cdot 7^{24}\cdot 11^{7} \)	$C_{14}$ (as 14T1)	$[5904502]$ (GRH)
14.0.19640210869081831858492466681823232.1	x^14 + 798x^12 + 194579x^10 + 16468459x^8 + 491701133x^6 + 3639865530x^4 + 9220992676x^2 + 6257102173	\( -\,2^{14}\cdot 7^{25}\cdot 19^{7} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 58, 1682]$ (GRH)
14.0.28341078543880537818112953392562176.1	x^14 - 2x^13 + 39x^12 - 114x^11 + 2254x^10 - 1600x^9 + 65883x^8 - 46196x^7 + 1547230x^6 + 479562x^5 + 31057338x^4 + 34059520x^3 + 395200525x^2 + 349151250x + 2163359375	\( -\,2^{21}\cdot 7^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[7568372]$ (GRH)
14.0.2514094918068134291976760322363658391.1	x^14 - x^13 + 23x^12 - 277x^11 - 5095x^10 + 31737x^9 + 490605x^8 - 1444591x^7 - 15658566x^6 + 26925836x^5 + 243943976x^4 - 414082048x^3 - 2583896960x^2 + 4799748096x + 20455038976	\( -\,631^{13} \)	$C_{14}$ (as 14T1)	$[3108937]$ (GRH)
14.0.56087804311304814754778384359334369663.1	x^14 - x^13 + 432x^12 + 1683x^11 + 40299x^10 + 237027x^9 + 1186487x^8 + 10192584x^7 + 54209527x^6 + 22914955x^5 + 1968955430x^4 - 2618032473x^3 + 23452437113x^2 - 13674940874x + 80838037483	\( -\,7^{7}\cdot 281^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 4, 4, 4, 4068]$ (GRH)
14.0.595490711098343828041968400200063015271.1	x^14 - x^13 + 518x^12 - 1833x^11 + 102790x^10 - 520762x^9 + 8805688x^8 - 50472370x^7 + 317860920x^6 - 1273665671x^5 + 11573214816x^4 + 37382582628x^3 + 232439703661x^2 + 365724334139x + 757415595679	\( -\,7^{7}\cdot 337^{13} \)	$C_{14}$ (as 14T1)	$[2985668]$ (GRH)
14.0.13760207184971837367389621368916758066523.2	x^14 - 2233x^11 - 1218x^10 - 249690x^9 + 5972260x^8 - 9384864x^7 - 13421345x^6 + 139144320x^5 + 959190225x^4 + 11388585418x^3 + 64346564856x^2 + 136319294454x + 97550940167	\( -\,7^{25}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 156044]$ (GRH)
14.0.13760207184971837367389621368916758066523.4	x^14 - 2233x^11 + 15834x^10 + 276080x^9 + 6725390x^8 + 45617783x^7 + 410450166x^6 + 1371017746x^5 + 8530487112x^4 - 10631790456x^3 + 88403705502x^2 - 488778538759x + 525016637623	\( -\,7^{25}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[1383004]$ (GRH)
14.0.13760207184971837367389621368916758066523.6	x^14 - 2233x^11 + 24360x^10 + 125454x^9 + 1069810x^8 - 18378373x^7 - 133193172x^6 + 756770602x^5 + 5834381182x^4 - 26703542026x^3 + 188327791736x^2 - 2109103641127x + 5899794618083	\( -\,7^{25}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[13, 163436]$ (GRH)
14.0.53588606915566584613059849086223224055607.1	x^14 - 7224x^11 + 301x^10 - 68026x^9 + 13842689x^8 + 7961708x^7 + 210375522x^6 + 2524506264x^5 - 3402184037x^4 + 94982321987x^3 + 2062378028046x^2 - 2009656697825x + 657479876713	\( -\,7^{25}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 14, 42742]$ (GRH)
14.0.53588606915566584613059849086223224055607.2	x^14 - 7224x^11 + 25585x^10 + 176386x^9 + 16307879x^8 - 95951318x^7 - 935002320x^6 + 1542753828x^5 + 7724343571x^4 + 49362000457x^3 + 1628162950638x^2 - 164577661339x + 16680217258567	\( -\,7^{25}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7, 172781]$ (GRH)
14.0.329187156767051876908796215815371233484443.2	x^14 - 5719x^11 - 24080x^10 + 1193766x^9 + 24550764x^8 + 307265874x^7 + 2773555771x^6 + 18547361140x^5 + 94817302349x^4 + 366737247170x^3 + 1042967916088x^2 + 2126473677202x + 2771555675837	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2756257]$ (GRH)
14.0.329187156767051876908796215815371233484443.3	x^14 - 1505x^11 + 39130x^10 + 131838x^9 + 6674976x^8 + 4397266x^7 - 85626373x^6 - 2202387502x^5 + 75633303333x^4 + 1283975888426x^3 + 5366060727678x^2 + 406889558152x + 11968080874901	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[3112193]$ (GRH)
14.0.329187156767051876908796215815371233484443.5	x^14 - 5719x^11 + 26488x^10 + 1147412x^9 + 383474x^8 - 156246735x^7 - 336846090x^6 + 13714379322x^5 + 49838686632x^4 - 498852081686x^3 - 2342604234320x^2 + 5856771467617x + 38059805953523	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[1662773]$ (GRH)
14.0.329187156767051876908796215815371233484443.6	x^14 - 1505x^11 + 64414x^10 + 721798x^9 + 13901986x^8 + 93883663x^7 + 1745978192x^6 + 12020663158x^5 + 128672845938x^4 + 540194248076x^3 + 4793924304218x^2 + 6892330333119x + 65986926254491	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 1921402]$ (GRH)