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 37 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.47060080384258527434832347136.1	x^14 + 174x^12 + 10440x^10 + 269352x^8 + 2931552x^6 + 12177216x^4 + 17589312x^2 + 8118144	\( -\,2^{21}\cdot 3^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 6558]$ (GRH)
14.0.282296718315876607143916888979.1	x^14 - x^13 + 219x^12 - 220x^11 + 16306x^10 - 16527x^9 + 511395x^8 - 656208x^7 + 6613602x^6 - 13821758x^5 + 40437938x^4 - 87114552x^3 + 233636092x^2 - 233359527x + 232170751	\( -\,29^{13}\cdot 31^{7} \)	$C_{14}$ (as 14T1)	$[2, 2, 14, 2842]$ (GRH)
14.0.611071689763862013138201214976.1	x^14 - 2x^13 + 75x^12 - 130x^11 + 3042x^10 - 4256x^9 + 81987x^8 - 84712x^7 + 1509222x^6 - 1077430x^5 + 18374426x^4 - 8526420x^3 + 133911229x^2 - 31573230x + 441622847	\( -\,2^{21}\cdot 7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[4, 4, 4, 1964]$ (GRH)
14.0.705070220621502278216740602539.1	x^14 - x^13 + 174x^12 + 196x^11 + 9615x^10 + 27547x^9 + 232859x^8 + 881591x^7 + 3316243x^6 + 11236797x^5 + 27679091x^4 + 65360600x^3 + 105212807x^2 + 114689596x + 104926787	\( -\,17^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[161124]$ (GRH)
14.0.3094745824656233782531059200463.1	x^14 - x^13 + 217x^12 + 239x^11 + 15033x^10 + 42167x^9 + 447988x^8 + 1691539x^7 + 7469613x^6 + 26563459x^5 + 71615373x^4 + 183273867x^3 + 308477505x^2 + 377213368x + 356178109	\( -\,3^{7}\cdot 7^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 904]$ (GRH)
14.0.5270900489883727544021626212511.1	x^14 - 7x^13 + 35x^12 - 77x^11 + 616x^10 - 3514x^9 + 22610x^8 - 87041x^7 + 393736x^6 - 1269674x^5 + 4382567x^4 - 9954511x^3 + 25812486x^2 - 38466645x + 67802507	\( -\,7^{24}\cdot 31^{7} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 5334]$ (GRH)
14.0.23133267811084759683438204281363.1	x^14 + 294x^12 - 665x^11 + 26467x^10 - 107492x^9 + 941430x^8 - 4272939x^7 + 16797641x^6 - 55907334x^5 + 117948719x^4 - 162190658x^3 + 189410389x^2 - 188014449x + 196014583	\( -\,7^{25}\cdot 29^{7} \)	$C_{14}$ (as 14T1)	$[405332]$ (GRH)
14.0.23184414993675232872880143548416.1	x^14 + 301x^12 + 29498x^10 + 1165171x^8 + 20442114x^6 + 151767210x^4 + 359182397x^2 + 35412349	\( -\,2^{14}\cdot 7^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 1964]$ (GRH)
14.0.26290885243157554005466712784279.1	x^14 - 7x^13 + 49x^12 - 161x^11 + 1246x^10 - 5810x^9 + 39270x^8 - 153373x^7 + 774270x^6 - 2507386x^5 + 9634359x^4 - 22503019x^3 + 65267748x^2 - 95761729x + 191861773	\( -\,3^{7}\cdot 7^{24}\cdot 13^{7} \)	$C_{14}$ (as 14T1)	$[109316]$ (GRH)
14.0.31388668949392001335459840000000.1	x^14 + 28x^12 - 42x^11 + 1043x^10 + 686x^9 + 27041x^8 + 33840x^7 + 508025x^6 + 804706x^5 + 6352920x^4 + 8567650x^3 + 48628468x^2 + 47642756x + 178610849	\( -\,2^{21}\cdot 5^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[283234]$ (GRH)
14.0.52075344228034366913450823351907.1	x^14 - 7x^13 + 56x^12 - 203x^11 + 1624x^10 - 7273x^9 + 50645x^8 - 197585x^7 + 1046059x^6 - 3388448x^5 + 13681430x^4 - 32204158x^3 + 98359275x^2 - 143330628x + 304880351	\( -\,7^{24}\cdot 43^{7} \)	$C_{14}$ (as 14T1)	$[297431]$ (GRH)
14.0.57154256495392789026772590782439.1	x^14 + 336x^12 - 756x^11 + 34559x^10 - 139706x^9 + 1381653x^8 - 6345898x^7 + 26899726x^6 - 93323468x^5 + 204461971x^4 - 300869401x^3 + 374349388x^2 - 383621049x + 400484527	\( -\,3^{7}\cdot 7^{25}\cdot 11^{7} \)	$C_{14}$ (as 14T1)	$[2, 190518]$ (GRH)
14.0.69014072539312321109968799399936.1	x^14 - 2x^13 + 63x^12 - 62x^11 + 2514x^10 - 3924x^9 + 80327x^8 - 162296x^7 + 1808214x^6 - 3652314x^5 + 26185174x^4 - 42685580x^3 + 216370161x^2 - 217576562x + 770198807	\( -\,2^{21}\cdot 7^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 8516]$ (GRH)
14.0.97059481264166574360249800987663.1	x^14 - 7x^13 + 63x^12 - 245x^11 + 2044x^10 - 8946x^9 + 64330x^8 - 250281x^7 + 1385356x^6 - 4484578x^5 + 18981767x^4 - 44907863x^3 + 144088714x^2 - 208592853x + 469806631	\( -\,7^{24}\cdot 47^{7} \)	$C_{14}$ (as 14T1)	$[280315]$ (GRH)
14.0.171927042716763378495925978132251.1	x^14 - 7x^13 + 70x^12 - 287x^11 + 2506x^10 - 10829x^9 + 80535x^8 - 312301x^7 + 1803081x^6 - 5829124x^5 + 25808202x^4 - 61248166x^3 + 206001411x^2 - 296315320x + 704858827	\( -\,3^{7}\cdot 7^{24}\cdot 17^{7} \)	$C_{14}$ (as 14T1)	$[513914]$ (GRH)
14.0.261178845247250442478137475921967.1	x^14 + 420x^12 - 938x^11 + 53977x^10 - 216776x^9 + 2635479x^8 - 12306090x^7 + 59795582x^6 - 220994886x^5 + 519273797x^4 - 855223397x^3 + 1175109670x^2 - 1278452721x + 1353299719	\( -\,7^{25}\cdot 41^{7} \)	$C_{14}$ (as 14T1)	$[842506]$ (GRH)
14.0.428173451495434593239433985998848.1	x^14 + 462x^12 + 65219x^10 + 3195731x^8 + 55240493x^6 + 236744970x^4 + 347225956x^2 + 136410197	\( -\,2^{14}\cdot 7^{25}\cdot 11^{7} \)	$C_{14}$ (as 14T1)	$[2, 330404]$ (GRH)
14.0.1027187378113291173607353987629056.1	x^14 + 226x^12 + 15368x^10 + 396856x^8 + 4805664x^6 + 28530240x^4 + 76811072x^2 + 72913024	\( -\,2^{21}\cdot 113^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 16472]$ (GRH)
14.0.1055787449474652775306737176796875.1	x^14 - 5x^13 + 12x^12 + 31x^11 + 722x^10 - 4645x^9 + 23535x^8 - 41683x^7 + 272781x^6 - 1040258x^5 + 7172534x^4 - 22736110x^3 + 85299995x^2 - 143854350x + 314845525	\( -\,5^{7}\cdot 7^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 4, 4, 3164]$ (GRH)
14.0.15720442004808735820984528834936832.1	x^14 + 497x^12 + 76538x^10 + 4554011x^8 + 125807598x^6 + 1668229206x^4 + 9681218561x^2 + 16898278817	\( -\,2^{14}\cdot 7^{7}\cdot 71^{13} \)	$C_{14}$ (as 14T1)	$[2, 336516]$ (GRH)
14.0.28606260651310274757079509174248503.1	x^14 - 5x^13 - 181x^12 + 565x^11 + 12356x^10 - 21350x^9 - 337442x^8 + 673209x^7 + 4463486x^6 - 11390256x^5 - 21789837x^4 + 79245585x^3 + 47158292x^2 - 355150475x + 438678011	\( -\,7^{7}\cdot 239^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 26278]$ (GRH)
14.0.96396085363089927687061485995798171.1	x^14 - x^13 + 18x^12 - 426x^11 - 4914x^10 - 26794x^9 + 63369x^8 + 1847851x^7 + 13603571x^6 + 56179943x^5 + 159906733x^4 + 364486968x^3 + 734418581x^2 + 1080367394x + 979862339	\( -\,491^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 4, 4, 1044]$ (GRH)
14.0.148946719271275003088728003994769267.1	x^14 - x^13 + 151x^12 + 840x^11 + 2926x^10 + 40327x^9 + 7130x^8 + 230853x^7 + 5480474x^6 - 21756177x^5 + 114730846x^4 - 228502327x^3 + 553225015x^2 - 423159590x + 786888991	\( -\,3^{7}\cdot 281^{13} \)	$C_{14}$ (as 14T1)	$[190518]$ (GRH)
14.0.199600727086494002686044072453147223.1	x^14 - 5x^13 - 217x^12 - 287x^11 + 15080x^10 + 103162x^9 + 205552x^8 - 156315x^7 - 490648x^6 + 2570346x^5 + 9043905x^4 + 11488539x^3 + 16150610x^2 + 29680369x + 40539809	\( -\,7^{7}\cdot 281^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 4, 4, 812]$ (GRH)
14.0.554302988656067112295385411481137411.1	x^14 - x^13 + 303x^12 + 420x^11 + 32127x^10 + 89886x^9 + 1369102x^8 + 3680571x^7 + 17975510x^6 + 7832183x^5 + 118057159x^4 - 56932186x^3 + 6537290446x^2 - 32497939521x + 53109997117	\( -\,7^{7}\cdot 197^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 36304]$ (GRH)
14.0.1767034751033661210807027893768732983.1	x^14 - 5x^13 - 265x^12 + 2173x^11 + 16962x^10 - 239968x^9 + 472092x^8 + 4513593x^7 - 24009340x^6 + 6620102x^5 + 267969411x^4 - 995551231x^3 + 1807246866x^2 - 1872983259x + 1015807027	\( -\,7^{7}\cdot 337^{12} \)	$C_{14}$ (as 14T1)	$[7, 21371]$ (GRH)
14.0.84639214494706556897052354063885994667.1	x^14 - x^13 + 30x^12 + 464x^11 - 800x^10 - 104324x^9 - 148079x^8 + 8336957x^7 + 66541559x^6 + 77463303x^5 - 740982278x^4 - 1593603637x^3 + 8180290855x^2 + 39964632396x + 52386024151	\( -\,827^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 4, 28, 196]$ (GRH)
14.0.297672627318406929279256927821316759631.1	x^14 - x^13 + 33x^12 - 1441x^11 + 10483x^10 - 61103x^9 + 1749062x^8 - 12988271x^7 + 107210133x^6 - 265496895x^5 + 869735265x^4 - 2748137801x^3 + 6431287949x^2 - 8581811296x + 5270284469	\( -\,911^{13} \)	$C_{14}$ (as 14T1)	$[161479]$ (GRH)
14.0.474489902930063357496193840307474416087.1	x^14 - 812x^11 + 8729x^10 - 45066x^9 + 4942035x^8 - 2313968x^7 + 215110980x^6 - 1577480520x^5 - 434148589x^4 - 29451595453x^3 + 40865281618x^2 + 463999676273x + 542414506181	\( -\,7^{25}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[4, 28, 3164]$ (GRH)
14.0.474489902930063357496193840307474416087.5	x^14 - 812x^11 - 25375x^10 + 91350x^9 + 5325705x^8 - 4215266x^7 - 437392326x^6 + 329836836x^5 + 19700239139x^4 - 19413083053x^3 - 423674050058x^2 + 251900249993x + 3854284665359	\( -\,7^{25}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[7, 64589]$ (GRH)
14.0.474489902930063357496193840307474416087.6	x^14 - 812x^11 + 8729x^10 + 239134x^9 + 5865685x^8 + 70091666x^7 + 733767454x^6 + 5616786700x^5 + 39308800027x^4 + 200176985575x^3 + 941525394390x^2 + 2923659885741x + 7775628764171	\( -\,7^{25}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[3, 3, 3, 21, 21, 21]$ (GRH)
14.0.646463729067293446729771507117629989287.1	x^14 - x^13 + 35x^12 + 957x^11 - 16886x^10 - 96498x^9 + 3261324x^8 - 26254395x^7 + 106373950x^6 - 206239922x^5 + 54692142x^4 + 683421421x^3 - 65709808x^2 - 3237370650x + 7873416461	\( -\,967^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 45298]$ (GRH)
14.0.13760207184971837367389621368916758066523.1	x^14 - 609x^11 - 18270x^10 + 30856x^9 - 429345x^8 + 24872343x^7 + 342372898x^6 + 947498643x^5 + 14862318170x^4 + 68261720093x^3 + 234668591136x^2 + 7015153824x + 28996645309	\( -\,7^{25}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[307748]$ (GRH)
14.0.53588606915566584613059849086223224055607.3	x^14 - 7224x^11 - 20769x^10 - 413574x^9 + 16012899x^8 + 117159090x^7 + 2010254988x^6 + 6124265196x^5 + 69559163667x^4 + 98387288769x^3 + 886043817568x^2 + 4291822604559x + 22085122836303	\( -\,7^{25}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7, 15491]$ (GRH)
14.0.53588606915566584613059849086223224055607.4	x^14 - 7224x^11 - 50267x^10 - 556850x^9 + 13779479x^8 + 215168302x^7 + 3646509048x^6 + 29686323660x^5 + 262979976931x^4 + 1267459647895x^3 + 7166415442578x^2 + 17279409997031x + 62055692847703	\( -\,7^{25}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7, 134659]$ (GRH)
14.0.53588606915566584613059849086223224055607.5	x^14 - 7224x^11 + 301x^10 + 783202x^9 + 13716269x^8 - 107746304x^7 - 1425878538x^6 + 1870004640x^5 + 104029582531x^4 + 50016502081x^3 - 2822541592794x^2 - 10557595949299x + 79626326570317	\( -\,7^{25}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[7, 7, 16177]$ (GRH)
14.0.329187156767051876908796215815371233484443.1	x^14 - 5719x^11 + 43344x^10 + 780794x^9 + 23613149x^8 + 133073863x^7 + 1161357330x^6 - 1029856751x^5 + 8912217496x^4 - 87810748963x^3 + 610422315916x^2 - 431820674782x + 1580168235629	\( -\,7^{24}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[387499]$ (GRH)