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 matches 1-50 of 363)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.38204123342480001000000.1	x^9 - 6x^6 + 100452x^3 - 8	\( 2^{6}\cdot 3^{16}\cdot 5^{6}\cdot 31^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6, 36, 72]$ (GRH)
9.1.287659322055643496809536.1	x^9 - 441x^6 + 55713x^3 - 3176523	\( 2^{6}\cdot 3^{16}\cdot 7^{6}\cdot 31^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 18, 18, 36]$ (GRH)
9.1.326830360514205681000000.1	x^9 - 18x^6 + 143748x^3 - 216	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 7^{6}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 6, 6, 36]$ (GRH)
9.1.404303827364914749420096.1	x^9 - 558x^6 + 252612x^3 - 6434856	\( 2^{6}\cdot 3^{10}\cdot 13^{6}\cdot 53^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6, 18, 324]$ (GRH)
9.3.491067814676959412126912.1	x^9 - 4x^8 - 145x^7 + 2311x^6 - 17059x^5 + 74270x^4 - 199094x^3 + 322247x^2 - 288763x + 110027	\( -\,2^{6}\cdot 23^{3}\cdot 349^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 3458]$ (GRH)
9.1.1060259562738462320460864.1	x^9 - 6x^6 + 121188x^3 - 8	\( 2^{6}\cdot 3^{18}\cdot 11^{6}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[2, 6, 6, 12, 72]$ (GRH)
9.3.7826454121341369636958912.1	x^9 - 2x^8 - 665x^7 + 10091x^6 - 64395x^5 + 340918x^4 - 908794x^3 + 2069539x^2 - 2415705x + 2762623	\( -\,2^{6}\cdot 1987^{7} \)	$S_3\times C_3$ (as 9T4)	$[11438]$ (GRH)
9.1.8971900045847138169000000.1	x^9 - 198x^6 + 114708x^3 - 287496	\( 2^{6}\cdot 3^{16}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 3, 18, 54]$ (GRH)
9.3.10058010512563205689237643.1	x^9 - 3x^8 - 1047x^7 + 6075x^6 + 360612x^5 - 3187947x^4 - 35099561x^3 + 492314319x^2 - 1985287283x + 2899704311	\( -\,7^{7}\cdot 101^{3}\cdot 151^{6} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 618]$ (GRH)
9.3.10145158012317476926656000.2	x^9 - 3x^8 - 285x^7 - 3858x^6 - 28014x^5 - 123375x^4 - 335769x^3 - 550461x^2 - 497958x - 190961	\( -\,2^{9}\cdot 3^{15}\cdot 5^{3}\cdot 73^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 9, 2394]$ (GRH)
9.3.17099207473518045927033408.2	x^9 - 3x^8 - 642x^7 - 8427x^6 - 52905x^5 - 264783x^4 - 655125x^3 - 1294608x^2 - 1360380x - 1323937	\( -\,2^{6}\cdot 3^{15}\cdot 211^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 4758]$ (GRH)
9.3.17266851289011529702381248.1	x^9 - 2686x^6 + 55488x^3 + 2515456	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 234]$ (GRH)
9.3.32999804109981894517713027.1	x^9 - 3x^6 - 44736x^3 - 1	\( -\,3^{13}\cdot 1657^{6} \)	$S_3\times C_3$ (as 9T4)	$[2, 13650]$ (GRH)
9.3.33239511109135135415259243.2	x^9 - 3x^6 - 4974x^3 - 1	\( -\,3^{19}\cdot 7^{6}\cdot 79^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 6, 18]$ (GRH)
9.3.42593788591286740440352083.4	x^9 - 432x^7 - 1729x^6 + 62208x^5 + 497952x^4 - 1988351x^3 - 35852544x^2 - 143659152x - 192209472	\( -\,3^{13}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 9, 378]$ (GRH)
9.3.47390883495218491994011328.1	x^9 - 2x^8 - 265x^7 - 3631x^6 - 26359x^5 - 115802x^4 - 314414x^3 - 514511x^2 - 464833x - 178103	\( -\,2^{6}\cdot 29^{3}\cdot 607^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 2, 2366]$ (GRH)
9.3.49610644771367831365400256.1	x^9 - 3x^8 - 285x^7 + 926x^6 + 21450x^5 - 118125x^4 + 224527x^3 + 441321x^2 - 1109280x + 9262581	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 23^{3}\cdot 31^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 18, 558]$ (GRH)
9.3.51275583698675864210424000.1	x^9 - 1623x^7 - 10311x^6 + 881301x^5 + 11228178x^4 - 123890860x^3 - 3062624775x^2 - 19741368249x - 42966681553	\( -\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3}\cdot 181^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6489]$ (GRH)
9.3.52865041559610605275374912.1	x^9 - 1191x^7 - 9131x^6 + 485928x^5 + 7555704x^4 - 38512176x^3 - 1611394416x^2 - 12800372544x - 34124239808	\( -\,2^{6}\cdot 3^{12}\cdot 397^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 6, 7098]$ (GRH)
9.3.54407477142216048038082723.1	x^9 - 3x^6 - 48624x^3 - 1	\( -\,3^{13}\cdot 1801^{6} \)	$S_3\times C_3$ (as 9T4)	$[2, 26, 546]$ (GRH)
9.3.70656216787339571921316147.1	x^9 - 3x^6 - 3910x^3 - 1	\( -\,3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 43^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 18, 54]$ (GRH)
9.1.79819442672313257636329152.1	x^9 - 3x^8 + 4x^7 + 189x^6 - 959x^5 + 896x^4 + 233408x^3 - 49152x^2 + 4096x + 262144	\( 2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 6, 6, 36]$ (GRH)
9.3.83496688176695495276938419.1	x^9 - 903x^7 - 15050x^6 - 530964x^5 + 1011360x^4 + 5278035x^3 + 1666695996x^2 - 14286781089x - 223609972474	\( -\,3^{12}\cdot 7^{6}\cdot 17^{3}\cdot 43^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 42]$ (GRH)
9.3.85373962053279248646580736.1	x^9 - x^8 - 701x^7 + 4922x^6 + 19570x^5 + 291711x^4 + 875487x^3 + 3767781x^2 + 5364326x + 11322593	\( -\,2^{9}\cdot 31^{7}\cdot 67^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 762]$ (GRH)
9.3.124988540775249857204408000.1	x^9 - 2x^8 + 941x^7 + 16825x^6 - 166443x^5 + 11732922x^4 + 165187300x^3 - 3066921559x^2 - 80668651817x + 602452994221	\( -\,2^{6}\cdot 5^{3}\cdot 7^{6}\cdot 13^{6}\cdot 31^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 21, 21]$ (GRH)
9.1.127616988379106905363496448.1	x^9 - 3x^8 + 57x^7 + 1820x^6 - 2832x^5 - 30882x^4 + 1106665x^3 - 477759x^2 - 43452285x + 291274836	\( 2^{9}\cdot 3^{10}\cdot 7^{6}\cdot 13^{7}\cdot 83^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 6, 24]$ (GRH)
9.3.140292931386008357960279643.1	x^9 - 3x^6 - 6324x^3 - 1	\( -\,3^{19}\cdot 19^{6}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 54]$ (GRH)
9.3.167849078585632886671411392.1	x^9 - 3x^8 - 1155x^7 - 5850x^6 + 40266x^5 - 447417x^4 - 8111571x^3 + 81009675x^2 - 306232344x + 294493899	\( -\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 127^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3411]$ (GRH)
9.3.171707277277450704179928256.1	x^9 - 4x^8 - 305x^7 - 4087x^6 - 29699x^5 - 131134x^4 - 357734x^3 - 587527x^2 - 532163x - 204251	\( -\,2^{6}\cdot 31^{3}\cdot 709^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 4, 5652]$ (GRH)
9.1.228153994086854399553000000.1	x^9 - 7260x^6 - 12034000x^3 - 14172488000	\( 2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 11^{7}\cdot 29^{6} \)	$S_3^2$ (as 9T8)	$[3, 3, 6, 6, 36]$ (GRH)
9.1.268875429019508522531815488.2	x^9 + 42x^7 - 132x^6 - 9324x^5 + 11172x^4 + 244788x^3 - 243936x^2 + 81312x - 85184	\( 2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 59^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 12, 360]$ (GRH)
9.3.293313171198272712471891648.1	x^9 - 192x^6 - 17476x^3 - 262144	\( -\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 1063^{6} \)	$S_3\times C_3$ (as 9T4)	$[45, 315]$ (GRH)
9.1.296127458031276854378155584.1	x^9 - 534x^6 + 18915348x^3 - 5639752	\( 2^{6}\cdot 3^{10}\cdot 11^{6}\cdot 89^{7} \)	$S_3^2$ (as 9T8)	$[3, 6, 1170]$ (GRH)
9.3.335441103555868000315072000.1	x^9 - 2x^8 - 455x^7 + 503x^6 + 26961x^5 + 283750x^4 + 1326746x^3 + 4414921x^2 + 8136717x + 10231171	\( -\,2^{9}\cdot 5^{3}\cdot 7^{7}\cdot 181^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 1098]$ (GRH)
9.3.407490534341705792376105408.1	x^9 - 897x^6 - 9806901x^3 - 26730899	\( -\,2^{6}\cdot 3^{18}\cdot 13^{6}\cdot 23^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 108]$ (GRH)
9.1.454976011147221128650595328.1	x^9 - 3x^8 + 4x^7 - 224x^6 + 15022x^5 + 189154x^4 + 824292x^3 + 4411192x^2 + 28242537x + 47389833	\( 2^{10}\cdot 3^{3}\cdot 7^{7}\cdot 13^{3}\cdot 71^{7} \)	$S_3^2$ (as 9T8)	$[3, 6, 720]$ (GRH)
9.3.470840338912293629780425792.1	x^9 - 4x^8 - 1554x^7 - 6664x^6 + 388461x^5 - 2242508x^4 - 328849540x^3 - 8052829536x^2 - 111471767840x - 648586550912	\( -\,2^{6}\cdot 7^{6}\cdot 673^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 630]$ (GRH)
9.3.667762358812807929515554099.1	x^9 - 4x^8 - 739x^7 - 10594x^6 - 86127x^5 - 600707x^4 - 2369678x^3 - 9081040x^2 - 16299272x - 20250283	\( -\,13^{3}\cdot 31^{7}\cdot 73^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 10374]$ (GRH)
9.3.703188785477141245936092019.1	x^9 - 4x^8 - x^7 - 13713x^6 - 1469000x^5 - 5345113x^4 - 1022085497x^3 - 9331410466x^2 - 101754315320x - 59916774568	\( -\,7^{6}\cdot 1291^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 21, 903]$ (GRH)
9.3.729869605474698767576025792.1	x^9 - 3x^8 - 39x^7 + 128x^6 + 32232x^5 - 67341x^4 - 251707x^3 + 1594959x^2 - 452042910x + 210013607	\( -\,2^{6}\cdot 3^{9}\cdot 11^{3}\cdot 331^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 12, 516]$ (GRH)
9.1.839020922360559596268648000.1	x^9 - 1242x^6 + 558900x^3 - 70957944	\( 2^{6}\cdot 3^{18}\cdot 5^{3}\cdot 23^{7}\cdot 43^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 7560]$ (GRH)
9.3.896908744413904292843521203.1	x^9 - 1296x^7 - 9861x^6 + 614628x^5 + 9834048x^4 - 56864472x^3 - 2331898632x^2 - 18655189056x - 49139005895	\( -\,3^{15}\cdot 7^{4}\cdot 13^{6}\cdot 271^{4} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 6, 774]$ (GRH)
9.1.1107007213595623864316103168.1	x^9 - 407x^6 + 2394381x^3 - 67419143	\( 2^{9}\cdot 3^{9}\cdot 11^{7}\cdot 13^{3}\cdot 37^{6} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 12, 36]$ (GRH)
9.3.1156289358257292074937012736.1	x^9 - 839x^7 - 3987x^6 + 222481x^5 + 1898588x^4 - 16560990x^3 - 247197987x^2 - 790050311x - 63809903	\( -\,2^{9}\cdot 13^{6}\cdot 53^{3}\cdot 61^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 1302]$ (GRH)
9.3.1337608160052568625416156864.1	x^9 - 743x^7 - 3821x^6 + 178729x^5 + 1769618x^4 - 10081940x^3 - 207438269x^2 - 952907617x - 1323920879	\( -\,2^{6}\cdot 7^{7}\cdot 103^{6}\cdot 277^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 1878]$ (GRH)
9.3.1453334803357813012385364987.1	x^9 - 3x^8 - 24x^7 + 16716x^6 - 284739x^5 - 7737933x^4 - 23831493x^3 - 3590248800x^2 - 81561281136x - 472053560768	\( -\,3^{15}\cdot 7^{7}\cdot 103^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 2382]$ (GRH)
9.1.3416092880728681728792000000.1	x^9 - 3x^8 + 4x^7 + 1533x^6 - 7679x^5 + 7168x^4 + 14941696x^3 - 3145728x^2 + 262144x + 134217728	\( 2^{9}\cdot 3^{3}\cdot 5^{6}\cdot 7^{7}\cdot 79^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 702]$ (GRH)
9.3.3692234824910706502401524928.2	x^9 - 648x^6 - 268596x^3 - 10077696	\( -\,2^{6}\cdot 3^{15}\cdot 13^{6}\cdot 97^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 63]$ (GRH)
9.3.5275897551224859345792572503.1	x^9 - 2x^8 + 9x^7 - 39912x^6 + 2204380x^5 - 45861120x^4 + 455207566x^3 - 590515559x^2 - 6369230288x - 6484442771	\( -\,9127^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 2, 21638]$ (GRH)
9.3.5924892413670354888735638016.1	x^9 - 3x^8 - 621x^7 + 15096x^6 - 179874x^5 + 1294947x^4 - 5871825x^3 + 16406091x^2 - 25810002x + 17499609	\( -\,2^{9}\cdot 3^{15}\cdot 7^{3}\cdot 157^{7} \)	$S_3\times C_3$ (as 9T4)	$[2, 21282]$ (GRH)