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 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.34040472776891254826249629376.1	x^9 - 4x^8 - 585x^7 + 14453x^6 - 172719x^5 + 1243212x^4 - 5630958x^3 + 15712707x^2 - 24689313x + 16722389	\( -\,2^{6}\cdot 13^{7}\cdot 41^{3}\cdot 103^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 48204]$ (GRH)
9.3.82574932050079036833262643392.1	x^9 - 2x^8 - 657x^7 + 15741x^6 - 187083x^5 + 1347288x^4 - 6116310x^3 + 17111595x^2 - 26952291x + 18292829	\( -\,2^{6}\cdot 43^{3}\cdot 1489^{7} \)	$S_3\times C_3$ (as 9T4)	$[5, 557080]$ (GRH)
9.3.213041816736095167667855780544.1	x^9 - 3x^8 - 957x^7 + 27672x^6 - 392592x^5 + 3369291x^4 - 18273543x^3 + 61327815x^2 - 116376726x + 95533631	\( -\,2^{6}\cdot 3^{15}\cdot 17^{3}\cdot 241^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 6, 228438]$ (GRH)
9.3.267412527740852450040686757568.1	x^9 - 1733x^7 - 5755x^6 + 911599x^5 + 7542876x^4 - 118327042x^3 - 1233693595x^2 - 1697154363x - 28351855531	\( -\,2^{6}\cdot 7^{6}\cdot 109^{3}\cdot 223^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 15, 30, 390]$ (GRH)
9.3.1173365778534963459955218936512.1	x^9 - 2x^8 + 1847x^7 + 7383x^6 - 1298809x^5 + 76766070x^4 - 2514365676x^3 + 54052096969x^2 - 1050669706501x + 6529374868801	\( -\,2^{6}\cdot 11^{3}\cdot 13^{6}\cdot 433^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 39102]$ (GRH)
9.3.1503738871438861505094232529088.1	x^9 - 3x^8 - 363x^7 + 938x^6 + 166422x^5 - 344955x^4 - 11546887x^3 + 26836503x^2 - 7301815632x + 3338141159	\( -\,2^{6}\cdot 3^{9}\cdot 17^{3}\cdot 19^{7}\cdot 43^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 18, 16668]$ (GRH)
9.3.2008995096296530754176831359488.1	x^9 - 4x^8 - 2929x^7 + 89835x^6 - 997717x^5 + 8346300x^4 - 39898436x^3 + 136057949x^2 - 264004739x + 338501389	\( -\,2^{9}\cdot 13^{7}\cdot 673^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 78, 8034]$ (GRH)
9.3.5448218194495564195017822122176.1	x^9 - 2x^8 - 4537x^7 + 105119x^6 + 350593x^5 + 10479330x^4 + 34683810x^3 + 270300503x^2 + 453760859x + 1786687487	\( -\,2^{6}\cdot 37^{7}\cdot 367^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 87594]$ (GRH)
9.3.7609973398533735614236179064000.1	x^9 - x^8 - 1133x^7 - 31456x^6 - 442928x^5 - 3804907x^4 - 20712287x^3 - 69811591x^2 - 133016690x - 109584551	\( -\,2^{6}\cdot 5^{3}\cdot 11^{3}\cdot 2557^{7} \)	$S_3\times C_3$ (as 9T4)	$[7, 1322678]$ (GRH)
9.3.9332168603347626532838482899456.1	x^9 - 4971x^7 - 77879x^6 + 8351280x^5 + 263502768x^4 - 2658729408x^3 - 226153616832x^2 - 3605805918720x - 19229559127552	\( -\,2^{9}\cdot 3^{12}\cdot 1657^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 394134]$ (GRH)
9.3.17612583005720393581692774758103.1	x^9 - 105868x^6 - 10923309x^5 + 701065458x^4 - 21202445249x^3 + 1723063587408x^2 - 68444429376636x + 829996847988696	\( -\,3^{13}\cdot 19^{7}\cdot 199^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 18, 1026]$ (GRH)
9.3.19979186107835112727319352074752.1	x^9 - 4x^8 - 1265x^7 - 34315x^6 - 481373x^5 - 4141132x^4 - 22610876x^3 - 76459813x^2 - 146120363x - 120689741	\( -\,2^{9}\cdot 19^{7}\cdot 29^{3}\cdot 151^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 41274]$ (GRH)
9.3.20883971697881478397156686693888.2	x^9 - 3x^8 - 3531x^7 + 5504x^6 + 3608922x^5 - 8520087x^4 - 1188199569x^3 - 589727619x^2 + 126031741812x + 604675550673	\( -\,2^{9}\cdot 3^{9}\cdot 13^{7}\cdot 229^{7} \)	$S_3\times C_3$ (as 9T4)	$[9, 18, 17514]$ (GRH)
9.3.22921419423740655976422475774464.2	x^9 - 3x^8 - 1677x^7 - 53598x^6 - 873462x^5 - 8699295x^4 - 55041225x^3 - 216277977x^2 - 481849122x - 465414193	\( -\,2^{9}\cdot 3^{15}\cdot 11^{3}\cdot 421^{7} \)	$S_3\times C_3$ (as 9T4)	$[2380434]$ (GRH)
9.3.28264732215528487463866635499008.1	x^9 - 6573x^7 - 37247x^6 + 27468567x^5 - 1092209118x^4 - 4817198330x^3 + 1975172308893x^2 - 35660464317639x - 545668039805931	\( -\,2^{9}\cdot 3^{13}\cdot 7^{6}\cdot 313^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 81669]$ (GRH)
9.3.40433066836446159992135460998464.1	x^9 - 2x^8 - 1846x^7 + 1853x^6 + 509545x^5 + 8356431x^4 + 67633779x^3 + 336454694x^2 + 971295101x + 1463451053	\( -\,2^{6}\cdot 19^{3}\cdot 5119^{7} \)	$S_3\times C_3$ (as 9T4)	$[3298369]$ (GRH)
9.3.56441011007883515049554102854848.2	x^9 - 3x^8 - 5325x^7 - 83022x^6 + 9637350x^5 + 323501475x^4 - 2999023125x^3 - 298733761875x^2 - 5200565718750x - 30378244515625	\( -\,2^{6}\cdot 3^{15}\cdot 1801^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 1394946]$ (GRH)
9.3.59147277154624204019933880238272.1	x^9 - 3783x^7 - 51701x^6 + 4846023x^5 + 133517202x^4 - 1180417056x^3 - 87655420125x^2 - 1222267178223x - 5703368086871	\( -\,2^{6}\cdot 3^{12}\cdot 7^{3}\cdot 13^{7}\cdot 97^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 18, 6714]$ (GRH)
9.3.345646515675090906115747805101568.1	x^9 - 8054x^7 - 86135x^6 + 21555397x^5 + 463533973x^4 - 16652946295x^3 - 613128224240x^2 - 6510682901835x - 24496392693493	\( -\,2^{9}\cdot 7^{6}\cdot 13^{3}\cdot 31^{7}\cdot 37^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 21642]$ (GRH)
9.3.549541385991283777839563597275648.2	x^9 - x^8 - 2519x^7 + 3436x^6 + 963642x^5 - 19472713x^4 + 188386031x^3 - 1079663137x^2 + 3548644260x - 5719338877	\( -\,2^{9}\cdot 7^{7}\cdot 11^{3}\cdot 997^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 9, 312291]$ (GRH)
9.3.593788209494622146865757091776000.1	x^9 - 2x^8 - 1905x^7 + 72153x^6 - 1348029x^5 + 15250290x^4 - 109361844x^3 + 487467741x^2 - 1234577043x + 1358906711	\( -\,2^{9}\cdot 5^{3}\cdot 7^{3}\cdot 4297^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 4, 334684]$ (GRH)
9.3.606691308877698193179936850417984.1	x^9 - x^8 - 3934x^7 - 139731x^6 - 2019573x^5 - 19257097x^4 - 113121209x^3 - 421969970x^2 - 911815232x - 999780629	\( -\,2^{6}\cdot 7^{3}\cdot 31^{7}\cdot 373^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 21, 73017]$ (GRH)
9.3.1208245707570684710118650479647296.1	x^9 - x^8 - 2766x^7 + 499x^6 + 1169751x^5 + 23125507x^4 + 223678667x^3 + 1292801328x^2 + 4301447904x + 7077293973	\( -\,2^{6}\cdot 23^{3}\cdot 79^{7}\cdot 97^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 718263]$ (GRH)
9.1.13123898043587859950264152870898688.1	x^9 - 141x^7 - 40230x^6 + 6627x^5 - 1944954x^4 + 586167805x^3 - 88868070x^2 + 51437595240x - 2410089265226	\( 2^{10}\cdot 3^{9}\cdot 7^{7}\cdot 967^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 12, 684]$ (GRH)
9.1.251587267509755082934044273105580608.1	x^9 - 3x^8 + 4x^7 + 4367x^6 - 454490x^5 - 9353495x^4 + 76671981x^3 + 3176369294x^2 + 27294462152x + 77039823246	\( 2^{6}\cdot 3^{3}\cdot 37^{7}\cdot 1063^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 18, 18, 378]$ (GRH)
9.3.6368591954731741019481223481451798528.1	x^9 - 281736x^6 - 38943592506x^3 - 828253479126528	\( -\,2^{13}\cdot 3^{18}\cdot 7^{6}\cdot 13^{7}\cdot 43^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 3, 6, 696]$ (GRH)
9.1.11159851600286913736565911449075667392.1	x^9 - 533988x^6 + 95000870601x^3 - 5639371800543936	\( 2^{6}\cdot 3^{15}\cdot 7^{7}\cdot 13^{6}\cdot 163^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 18, 18, 72]$ (GRH)
9.1.24025177795176030015470943785840136768.1	x^9 - 3x^8 + 96x^7 + 88067x^6 - 173532x^5 - 2562525x^4 + 2594285657x^3 - 2509502424x^2 - 158464296066x + 25539385643706	\( 2^{6}\cdot 3^{9}\cdot 13^{7}\cdot 31^{7}\cdot 73^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 18, 18, 162]$ (GRH)
9.3.51045760796164622552783894927556641472.1	x^9 - 5184x^6 - 71105040x^3 - 5159780352	\( -\,2^{6}\cdot 3^{15}\cdot 163^{6}\cdot 379^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 23751]$ (GRH)
9.1.120426448093662321424207466113182837696.1	x^9 - 3x^8 + 3x^7 + 110888x^6 - 221778x^5 + 222000x^4 + 4172715959x^3 - 4172790033x^2 + 4131662535x + 50499821168978	\( 2^{6}\cdot 3^{9}\cdot 7^{7}\cdot 11^{7}\cdot 13^{7}\cdot 37^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 3, 18, 234]$ (GRH)