Global number field search results

Further refine search

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 97)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.63163559554724439795112128.1	x^9 - 3x^8 - 357x^7 + 7050x^6 - 67920x^5 + 393639x^4 - 1427271x^3 + 3165981x^2 - 3928704x + 2089711	\( -\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 11^{3}\cdot 13^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 12, 756]$ (GRH)
9.3.167849078585632886671411392.2	x^9 - 3x^8 - 357x^7 - 1320x^6 + 46410x^5 + 450471x^4 - 785715x^3 - 31150623x^2 - 168595476x - 306304831	\( -\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 127^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 6, 10386]$ (GRH)
9.3.1003723006208454853492730368.1	x^9 - 2x^8 - 385x^7 + 7453x^6 - 71581x^5 + 415126x^4 - 1507540x^3 + 3349405x^2 - 4162063x + 2216299	\( -\,2^{9}\cdot 17^{3}\cdot 877^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 83174]$ (GRH)
9.3.1485218459900452713543237312.2	x^9 - 3x^8 - 525x^7 - 9498x^6 - 90516x^5 - 528051x^4 - 1934295x^3 - 4332405x^2 - 5419578x - 2901079	\( -\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 13^{3}\cdot 19^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 12, 5292]$ (GRH)
9.3.1740048058473953724597752000.1	x^9 - x^8 - 413x^7 + 7858x^6 - 75284x^5 + 436979x^4 - 1589503x^3 + 3537221x^2 - 4401470x + 2346343	\( -\,2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 937^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 81342]$ (GRH)
9.3.1976246003762021566578842432.1	x^9 - 4x^8 - 558x^7 + 1489x^6 + 41181x^5 + 425593x^4 + 2005619x^3 + 6956364x^2 + 13241673x + 17915283	\( -\,2^{6}\cdot 11^{3}\cdot 1567^{7} \)	$S_3\times C_3$ (as 9T4)	$[5, 23170]$ (GRH)
9.1.3454181517651148195065000000.1	x^9 - 144x^7 - 771x^6 - 6948x^5 - 92304x^4 - 690915x^3 - 3564324x^2 - 9455616x - 16678913	\( 2^{6}\cdot 3^{16}\cdot 5^{7}\cdot 7^{7}\cdot 11^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 6, 6678]$ (GRH)
9.3.4971849774275392462212163264.1	x^9 - x^8 - 469x^7 - 8674x^6 - 82816x^5 - 481783x^4 - 1758511x^3 - 3926029x^2 - 4898428x - 2616799	\( -\,2^{6}\cdot 37^{3}\cdot 1063^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 104, 936]$ (GRH)
9.3.8210854518959785635944310272.1	x^9 - 2x^8 - 497x^7 - 9085x^6 - 86645x^5 - 504734x^4 - 1845556x^3 - 4127021x^2 - 5155979x - 2757211	\( -\,2^{9}\cdot 19^{3}\cdot 1129^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 17486]$ (GRH)
9.3.14523614533018650773047594176.2	x^9 - 3x^8 - 1677x^7 - 12090x^6 + 194712x^5 - 2410023x^4 + 13118637x^3 - 56776125x^2 + 128903838x - 222062239	\( -\,2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 79^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 18, 18, 774]$ (GRH)
9.3.50648508158554547268925976064.1	x^9 - 3x^8 - 174x^7 + 467x^6 + 77319x^5 - 161625x^4 - 2738803x^3 + 7924692x^2 - 2095714128x + 964112287	\( -\,2^{9}\cdot 3^{9}\cdot 7^{3}\cdot 547^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 13902]$ (GRH)
9.3.62795448979445473796301617187.1	x^9 - 972x^7 - 5833x^6 + 314928x^5 + 3779784x^4 - 22667039x^3 - 612325008x^2 - 3675839940x - 7359239448	\( -\,3^{13}\cdot 19^{6}\cdot 307^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 2457]$ (GRH)
9.3.86151677124164885137506017927.1	x^9 - x^8 - 1342x^7 + 31269x^6 - 353885x^5 + 2987747x^4 - 16016553x^3 + 66301140x^2 - 159070096x + 205759651	\( -\,7^{7}\cdot 17^{3}\cdot 577^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 43134]$ (GRH)
9.3.98578868939483266028443968000.2	x^9 - 3x^8 - 780x^7 - 4407x^6 + 214440x^5 + 2926290x^4 - 8788200x^3 - 421505400x^2 - 3123636000x - 7788259000	\( -\,2^{9}\cdot 3^{15}\cdot 5^{3}\cdot 271^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 15, 2910]$ (GRH)
9.3.165041226467028122193059592704.1	x^9 - x^8 - 959x^7 + 270x^6 + 130894x^5 + 1765845x^4 + 11378151x^3 + 46627247x^2 + 110528996x + 147434209	\( -\,2^{9}\cdot 7^{3}\cdot 2659^{7} \)	$S_3\times C_3$ (as 9T4)	$[19, 27949]$ (GRH)
9.3.169336491889735493022977208000.1	x^9 - 1893x^7 - 18299x^6 + 1220985x^5 + 23870730x^4 - 151440000x^3 - 7973174025x^2 - 79283809125x - 264229593625	\( -\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 631^{7} \)	$S_3\times C_3$ (as 9T4)	$[30, 23310]$ (GRH)
9.1.174565121124349094450651855424.1	x^9 + 108x^7 - 5181x^6 + 3888x^5 + 187164x^4 + 9087609x^3 - 6714576x^2 - 645345360x - 5231495807	\( 2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 9, 54, 54]$ (GRH)
9.3.182948482933696682177369003712.1	x^9 - 6231x^7 - 143313x^6 - 6374313x^5 - 536987580x^4 - 33959764184x^3 - 1281819293415x^2 - 22598935517613x - 162634049131679	\( -\,2^{6}\cdot 3^{12}\cdot 31^{6}\cdot 67^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 6, 4218]$ (GRH)
9.3.287752047109343823899619790336.1	x^9 - x^8 - 765x^7 - 17688x^6 - 209034x^5 - 1507947x^4 - 6871473x^3 - 19300827x^2 - 30508758x - 20768489	\( -\,2^{9}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7}\cdot 23^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 6789]$ (GRH)
9.3.417638200644158140081534197987.1	x^9 - 3x^8 - 2109x^7 - 53679x^6 - 646248x^5 - 6139749x^4 - 35586555x^3 - 167565045x^2 - 437806425x - 650068687	\( -\,3^{15}\cdot 7^{3}\cdot 19^{7}\cdot 37^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 6, 1806]$ (GRH)
9.3.451913018051949106599810353664.1	x^9 - 2757x^7 - 32165x^6 + 2580552x^5 + 60775308x^4 - 461422548x^3 - 29279240748x^2 - 349709062392x - 1398653824392	\( -\,2^{9}\cdot 3^{13}\cdot 919^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 78, 3042]$ (GRH)
9.3.577674903476059682588841474747.2	x^9 - 10972x^6 + 14480427x^3 + 10604499373	\( -\,3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 193^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 36, 252]$ (GRH)
9.1.937789413817123972561566758976.1	x^9 + 270x^7 - 2955x^6 + 24300x^5 + 280530x^4 + 4127133x^3 - 23935500x^2 - 538282800x - 1686858625	\( 2^{6}\cdot 3^{15}\cdot 17^{7}\cdot 59^{7} \)	$S_3^2$ (as 9T8)	$[6, 6, 4212]$ (GRH)
9.1.1202473284949648298688817725504.1	x^9 - 1947x^6 - 35046x^5 - 420552x^4 - 2525259x^3 - 22744854x^2 - 421201	\( 2^{6}\cdot 3^{18}\cdot 11^{7}\cdot 59^{7} \)	$S_3^2$ (as 9T8)	$[3, 6, 6, 6, 180]$ (GRH)
9.3.1324155785067293194662411051027.2	x^9 - 1029x^6 - 6564334x^3 - 40353607	\( -\,3^{9}\cdot 7^{6}\cdot 43^{6}\cdot 67^{6} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 6, 18, 36]$ (GRH)
9.3.1449026992340850243570387026112.2	x^9 - 1095x^7 - 2744x^6 - 190845x^5 + 1609440x^4 - 36547575x^3 + 112348278x^2 - 600693534x - 712835718	\( -\,2^{6}\cdot 3^{13}\cdot 7^{6}\cdot 19^{6}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 9, 180]$ (GRH)
9.1.3096682646352859575292629003264.1	x^9 - 3x^8 - 66x^7 - 27118x^6 + 56028x^5 - 721392x^4 + 292796994x^3 - 307183266x^2 + 12016857987x - 755633606013	\( 2^{10}\cdot 3^{10}\cdot 7^{6}\cdot 331^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 30, 450]$ (GRH)
9.3.4133941313919235994408730715683.1	x^9 - 3x^6 - 35160x^3 - 1	\( -\,3^{19}\cdot 3907^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 6, 6, 126]$ (GRH)
9.3.4511062077990159776441770107072.1	x^9 - 648x^6 - 453744x^3 - 10077696	\( -\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 19^{6}\cdot 31^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 6, 18, 54]$ (GRH)
9.1.5033732571737208972480501000000.1	x^9 - 49380x^6 + 1923844800x^3 - 4459534136000	\( 2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 823^{7} \)	$S_3^2$ (as 9T8)	$[3, 6, 6, 1548]$ (GRH)
9.3.6855544484161445571716295497664.1	x^9 - 3x^8 - 24x^7 + 8215x^6 - 517518x^5 - 30030747x^4 - 102779097x^3 + 6195139356x^2 + 48767020470x + 344091977418	\( -\,2^{6}\cdot 3^{10}\cdot 7^{6}\cdot 19^{7}\cdot 29^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 6, 8262]$ (GRH)
9.1.10881152217470823144247586309184.1	x^9 + 180x^7 - 23997x^6 + 10800x^5 + 1440900x^4 + 192600057x^3 - 86389200x^2 - 23042879280x - 513536239999	\( 2^{6}\cdot 3^{18}\cdot 7^{7}\cdot 127^{7} \)	$S_3^2$ (as 9T8)	$[9, 18, 18, 252]$ (GRH)
9.1.27871608473588242849407388619328.1	x^9 - 120648x^6 + 5496964176x^3 - 65042408797696	\( 2^{6}\cdot 3^{10}\cdot 11^{6}\cdot 457^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 12, 12, 36]$ (GRH)
9.3.31087983635440974402893575697088.1	x^9 - 1536x^6 - 2757264x^3 - 134217728	\( -\,2^{6}\cdot 3^{13}\cdot 13^{6}\cdot 631^{6} \)	$S_3\times C_3$ (as 9T4)	$[231, 1386]$ (GRH)
9.3.42593788591286740440352083000000.1	x^9 - 273x^7 - 16110x^6 - 960687x^5 - 10657920x^4 - 284577381x^3 - 3379898340x^2 - 11833266900x - 157687828390	\( -\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 9, 1197]$ (GRH)
9.3.50761618683380488371588184286667.1	x^9 - 24x^6 - 480489x^3 - 512	\( -\,3^{13}\cdot 19^{6}\cdot 937^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 1404]$ (GRH)
9.3.50804958594472386323223847990347.1	x^9 - 3993x^6 - 43981564x^3 - 2357947691	\( -\,3^{9}\cdot 7^{6}\cdot 11^{6}\cdot 13^{6}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 6, 234]$ (GRH)
9.3.50964287681985502900552332024987.1	x^9 - 192x^6 - 98881x^3 - 262144	\( -\,3^{3}\cdot 19^{6}\cdot 5851^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 18, 18, 378]$ (GRH)
9.3.84412038452001389243232595509312.1	x^9 - 7833x^7 - 120106x^6 - 7120197x^5 - 52919748x^4 - 1042157151x^3 - 5522030010x^2 + 139155156252x - 1032251476536	\( -\,2^{6}\cdot 3^{13}\cdot 7^{7}\cdot 373^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 6, 210]$ (GRH)
9.1.101857357464204117967975089000000.1	x^9 - 3x^8 + 2196x^7 + 26953x^6 + 2850606x^5 + 46441767x^4 + 1882373241x^3 + 27619200930x^2 + 507469495050x + 3977418013950	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 23^{7}\cdot 47^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 1440]$ (GRH)
9.3.165406830862647587062767643940787.1	x^9 - 3x^8 + 4x^7 + 20004x^6 - 806537x^5 + 9998161x^4 - 128056622x^3 - 1175131029x^2 + 37141187197x + 161052287105	\( -\,3^{3}\cdot 17^{6}\cdot 73^{6}\cdot 109^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 9, 9, 3429]$ (GRH)
9.3.173205145504055940264382658420736.1	x^9 - 3x^8 - 1779x^7 - 47993x^6 - 2192826x^5 - 70352358x^4 - 769203028x^3 - 545206164x^2 + 18278886120x - 27749527672	\( -\,2^{13}\cdot 3^{10}\cdot 7^{6}\cdot 19^{7}\cdot 23^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 6, 6, 324]$ (GRH)
9.1.464465622145778726630024995523136.1	x^9 - 3x^8 + 72x^7 + 47771x^6 - 94164x^5 - 1014429x^4 + 778261881x^3 - 752932776x^2 - 34558675410x + 4090575971282	\( 2^{6}\cdot 3^{3}\cdot 13^{7}\cdot 1231^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 954]$ (GRH)
9.3.552393054318753963331980437460672.1	x^9 - 8232x^6 - 195575856x^3 - 20661046784	\( -\,2^{6}\cdot 3^{19}\cdot 7^{6}\cdot 631^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 18, 558]$ (GRH)
9.1.567342263005277517014131111431744.1	x^9 - 16467x^6 - 112947153x^3 - 165378745169	\( 2^{6}\cdot 3^{10}\cdot 11^{7}\cdot 499^{7} \)	$S_3^2$ (as 9T8)	$[3, 30, 2100]$ (GRH)
9.1.868233135163509211623887011678272.1	x^9 + 162x^7 - 17493x^6 + 8748x^5 + 945594x^4 + 102474129x^3 - 51009588x^2 - 11021849496x - 199175758703	\( 2^{6}\cdot 3^{10}\cdot 19^{7}\cdot 307^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 27, 351]$ (GRH)
9.1.1106557871204061644005480204385856.1	x^9 - 3x^8 + 14x^7 - 40879x^6 + 272602x^5 - 504083x^4 + 503397819x^3 - 3368366050x^2 + 1453351806x - 2522949010602	\( 2^{6}\cdot 3^{4}\cdot 7^{6}\cdot 23^{7}\cdot 127^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 6, 6, 36]$ (GRH)
9.1.1145321759696854408690726823436864.1	x^9 - 36x^7 - 45933x^6 + 432x^5 - 578196x^4 + 808315185x^3 - 6614352x^2 + 17292120912x - 3589280635823	\( 2^{6}\cdot 3^{18}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 9, 18, 54]$ (GRH)
9.1.1592032285126866903775647849000000.1	x^9 - 3x^8 - 306x^7 + 21683x^6 - 10614x^5 + 3094293x^4 + 361143471x^3 - 139370508x^2 + 36856055844x + 320063581998	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 1601^{7} \)	$S_3^2$ (as 9T8)	$[6, 84, 840]$ (GRH)
9.3.1650236207144294569861130853086667.1	x^9 - 1029x^6 - 22338904x^3 - 40353607	\( -\,3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 727^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 18, 162]$ (GRH)