Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 761 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.1.382...000.1	$x^{9} - 6 x^{6} + 100452 x^{3} - 8$	$9$	[1,4]	$2^{6}\cdot 3^{16}\cdot 5^{6}\cdot 31^{6}$	$4$	$322.941129448$	$343.2654521686006$			?	$C_3^2:C_2$ (as 9T5)	$[6, 36, 72]$	$2$	$4$	$15440.12839205329$
9.3.241...000.6	$x^{9} - 3 x^{7} - x^{6} - 2187 x^{5} - 1458 x^{4} - 531684 x^{3} - 531441 x^{2} - 177147 x - 19683$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 5^{6}\cdot 73^{6}$	$4$	$396.33009597857375$	$421.27315847500523$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 9, 54]$	$2$	$5$	$22954.20800962426$
9.3.255...827.3	$x^{9} + 357 x^{7} - 168 x^{6} + 31752 x^{5} - 29253 x^{4} - 18816 x^{3} + 24696 x^{2} - 7203 x - 343$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 73^{6}$	$3$	$398.8559036454377$	$423.957928025228$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 684]$	$2$	$5$	$19681.577557536104$
9.1.287...536.1	$x^{9} - 441 x^{6} + 55713 x^{3} - 3176523$	$9$	[1,4]	$2^{6}\cdot 3^{16}\cdot 7^{6}\cdot 31^{6}$	$4$	$404.149504138$	$429.58468163804736$			?	$C_3^2:C_2$ (as 9T5)	$[3, 18, 18, 36]$	$2$	$4$	$27173.128436620587$
9.1.326...000.1	$x^{9} - 18 x^{6} + 143748 x^{3} - 216$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 7^{6}\cdot 19^{6}$	$5$	$409.923190356$	$435.7217352042167$			?	$C_3^2:C_2$ (as 9T5)	$[3, 3, 6, 6, 36]$	$2$	$4$	$82016.812930952$
9.1.404...096.1	$x^{9} - 558 x^{6} + 252612 x^{3} - 6434856$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 13^{6}\cdot 53^{6}$	$4$	$419.727610783$	$446.14319752058555$			?	$C_3^2:C_2$ (as 9T5)	$[6, 18, 324]$	$2$	$4$	$23847.883421623676$
9.3.491...912.1	$x^{9} - 4 x^{8} - 145 x^{7} + 2311 x^{6} - 17059 x^{5} + 74270 x^{4} - 199094 x^{3} + 322247 x^{2} - 288763 x + 110027$	$9$	[3,3]	$-\,2^{6}\cdot 23^{3}\cdot 349^{7}$	$3$	$428.893092996$	$1001.3174182250665$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 3458]$	$2$	$5$	$12347.35175999351$
9.3.768...952.4	$x^{9} - 420 x^{6} - 73824 x^{3} - 2744000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 307^{6}$	$3$	$450.79698763493036$	$479.1679277928259$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 126]$	$2$	$5$	$58639.42786250788$
9.1.106...864.1	$x^{9} - 6 x^{6} + 121188 x^{3} - 8$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 11^{6}\cdot 17^{6}$	$4$	$467.186456426$	$496.5888689560723$			?	$C_3^2:C_2$ (as 9T5)	$[2, 6, 6, 12, 72]$	$2$	$4$	$16283.860954495223$
9.3.582...443.5	$x^{9} - 192 x^{7} - 512 x^{6} - 17496 x^{5} - 93312 x^{4} - 655857 x^{3} - 4251528 x^{2} - 11337408 x - 10077696$	$9$	[3,3]	$-\,3^{13}\cdot 17^{6}\cdot 73^{6}$	$3$	$564.5334326623647$	$600.0623839963648$				$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 189]$	$2$	$5$	$2968729.2971688965$
9.3.782...912.1	$x^{9} - 2 x^{8} - 665 x^{7} + 10091 x^{6} - 64395 x^{5} + 340918 x^{4} - 908794 x^{3} + 2069539 x^{2} - 2415705 x + 2762623$	$9$	[3,3]	$-\,2^{6}\cdot 1987^{7}$	$2$	$583.38018187$	$889.5797461174084$			?	$S_3\times C_3$ (as 9T4)	$[11438]$	$2$	$5$	$44925.28174050365$
9.1.897...000.1	$x^{9} - 198 x^{6} + 114708 x^{3} - 287496$	$9$	[1,4]	$2^{6}\cdot 3^{16}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}$	$5$	$592.301338483$	$629.5778649250077$			?	$C_3^2:C_2$ (as 9T5)	$[3, 3, 3, 18, 54]$	$2$	$4$	$112529.3659151661$
9.3.977...688.4	$x^{9} - 6 x^{6} - 50640 x^{3} - 8$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 67^{6}$	$4$	$597.957957991824$	$635.5904841808897$			?	$S_3\times C_3$ (as 9T4)	$[2, 6, 6, 6, 36]$	$2$	$5$	$147776.95962227235$
9.3.100...643.1	$x^{9} - 3 x^{8} - 1047 x^{7} + 6075 x^{6} + 360612 x^{5} - 3187947 x^{4} - 35099561 x^{3} + 492314319 x^{2} - 1985287283 x + 2899704311$	$9$	[3,3]	$-\,7^{7}\cdot 101^{3}\cdot 151^{6}$	$3$	$599.869662016$	$1442.315769118269$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 618]$	$2$	$5$	$113371.29431717664$
9.3.101...000.2	$x^{9} - 3 x^{8} - 285 x^{7} - 3858 x^{6} - 28014 x^{5} - 123375 x^{4} - 335769 x^{3} - 550461 x^{2} - 497958 x - 190961$	$9$	[3,3]	$-\,2^{9}\cdot 3^{15}\cdot 5^{3}\cdot 73^{7}$	$4$	$600.444957138$	$1497.9864098372825$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 2394]$	$2$	$5$	$39394.347223686724$
9.3.103...875.2	$x^{9} - 825 x^{6} - 285000 x^{3} - 20796875$	$9$	[3,3]	$-\,3^{19}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}$	$4$	$601.5387097532936$	$639.3965908065919$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 468]$	$2$	$5$	$54149.587774319036$
9.3.144...907.6	$x^{9} - 273 x^{7} - 30 x^{6} + 81900 x^{5} + 792246 x^{4} + 2377857 x^{3} - 819000 x^{2} - 2702973 x - 729728$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 11^{6}\cdot 13^{6}$	$4$	$624.4410943748522$	$663.7403386168894$				$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 54]$	$2$	$5$	$1825226.415402111$
9.3.144...907.7	$x^{9} - 273 x^{7} - 300 x^{6} + 81900 x^{5} - 2457 x^{4} - 51900 x^{3} + 8190 x^{2} - 30303 x + 2001$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 11^{6}\cdot 13^{6}$	$4$	$624.4410943748522$	$663.7403386168894$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 378]$	$2$	$5$	$27086.715144590977$
9.3.170...408.2	$x^{9} - 3 x^{8} - 642 x^{7} - 8427 x^{6} - 52905 x^{5} - 264783 x^{4} - 655125 x^{3} - 1294608 x^{2} - 1360380 x - 1323937$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 211^{7}$	$3$	$636.303039794$	$1147.2045724752154$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 4758]$	$2$	$5$	$103451.6517600609$
9.3.172...248.1	$x^{9} - 2686 x^{6} + 55488 x^{3} + 2515456$	$9$	[3,3]	$-\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 17^{6}$	$5$	$636.993197206$	$764.9886707207152$				$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 234]$	$2$	$5$	$628031.0268989055$
9.3.245...288.3	$x^{9} - 351 x^{7} - 1305 x^{6} + 41067 x^{5} + 128214 x^{4} + 983672 x^{3} - 2097261 x^{2} - 154907397 x + 233910585$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 19^{6}\cdot 37^{6}$	$5$	$662.3628894849277$	$795.4560717196082$				$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 6, 180]$	$2$	$5$	$1732435.09257056$
9.3.329...027.1	$x^{9} - 3 x^{6} - 44736 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 1657^{6}$	$2$	$684.526319888$	$727.6070320279168$			?	$S_3\times C_3$ (as 9T4)	$[2, 13650]$	$2$	$5$	$95289.25981271428$
9.3.332...243.2	$x^{9} - 3 x^{6} - 4974 x^{3} - 1$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 79^{6}$	$3$	$685.077024929$	$728.1923957294962$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 6, 18]$	$2$	$5$	$290172.0086313884$
9.3.425...083.4	$x^{9} - 432 x^{7} - 1729 x^{6} + 62208 x^{5} + 497952 x^{4} - 1988351 x^{3} - 35852544 x^{2} - 143659152 x - 192209472$	$9$	[3,3]	$-\,3^{13}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}$	$4$	$704.214788848$	$748.5345961686137$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 378]$	$2$	$5$	$945317.1228489663$
9.3.425...083.7	$x^{9} - 3 x^{7} - x^{6} - 5184 x^{5} - 3456 x^{4} - 2986560 x^{3} - 2985984 x^{2} - 995328 x - 110592$	$9$	[3,3]	$-\,3^{13}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}$	$4$	$704.2147888479615$	$748.5345961686137$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 9, 378]$	$2$	$5$	$35616.74085703165$
9.3.473...328.1	$x^{9} - 2 x^{8} - 265 x^{7} - 3631 x^{6} - 26359 x^{5} - 115802 x^{4} - 314414 x^{3} - 514511 x^{2} - 464833 x - 178103$	$9$	[3,3]	$-\,2^{6}\cdot 29^{3}\cdot 607^{7}$	$3$	$712.615030649$	$1783.2390748179473$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 2, 2366]$	$2$	$5$	$19279.69936696387$
9.3.496...256.1	$x^{9} - 3 x^{8} - 285 x^{7} + 926 x^{6} + 21450 x^{5} - 118125 x^{4} + 224527 x^{3} + 441321 x^{2} - 1109280 x + 9262581$	$9$	[3,3]	$-\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 23^{3}\cdot 31^{7}$	$5$	$716.248745977$	$1755.4649007961316$			?	$S_3\times C_3$ (as 9T4)	$[3, 18, 558]$	$2$	$5$	$244134.05098658882$
9.3.512...000.1	$x^{9} - 1623 x^{7} - 10311 x^{6} + 881301 x^{5} + 11228178 x^{4} - 123890860 x^{3} - 3062624775 x^{2} - 19741368249 x - 42966681553$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3}\cdot 181^{6}$	$5$	$718.880552064$	$1300.173795706913$			?	$S_3\times C_3$ (as 9T4)	$[3, 6489]$	$2$	$5$	$68030.42217359117$
9.3.528...912.1	$x^{9} - 1191 x^{7} - 9131 x^{6} + 485928 x^{5} + 7555704 x^{4} - 38512176 x^{3} - 1611394416 x^{2} - 12800372544 x - 34124239808$	$9$	[3,3]	$-\,2^{6}\cdot 3^{12}\cdot 397^{7}$	$3$	$721.323102535$	$1267.2153479503816$			?	$S_3\times C_3$ (as 9T4)	$[2, 6, 7098]$	$2$	$5$	$56192.44263820826$
9.3.544...723.1	$x^{9} - 3 x^{6} - 48624 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 1801^{6}$	$2$	$723.631762078$	$769.1735779760147$			?	$S_3\times C_3$ (as 9T4)	$[2, 26, 546]$	$2$	$5$	$98094.32643489019$
9.3.706...147.1	$x^{9} - 3 x^{6} - 3910 x^{3} - 1$	$9$	[3,3]	$-\,3^{9}\cdot 7^{6}\cdot 13^{6}\cdot 43^{6}$	$4$	$744.951192995$	$894.6394174700885$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 18, 54]$	$2$	$5$	$282508.96324942255$
9.3.794...000.6	$x^{9} + 690 x^{7} - 330 x^{6} + 118800 x^{5} - 111900 x^{4} - 72600 x^{3} + 99000 x^{2} - 30000 x - 1000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 7^{6}\cdot 19^{6}$	$5$	$754.692183335776$	$802.1887890326855$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 9, 126]$	$2$	$5$	$32126.62813594007$
9.1.798...152.1	$x^{9} - 3 x^{8} + 4 x^{7} + 189 x^{6} - 959 x^{5} + 896 x^{4} + 233408 x^{3} - 49152 x^{2} + 4096 x + 262144$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 13^{7}\cdot 19^{7}$	$5$	$755.113225429$	$1728.8332931546176$				$S_3^2$ (as 9T8)	$[3, 3, 6, 6, 36]$	$2$	$4$	$2673943.8398678363$
9.3.834...419.1	$x^{9} - 903 x^{7} - 15050 x^{6} - 530964 x^{5} + 1011360 x^{4} + 5278035 x^{3} + 1666695996 x^{2} - 14286781089 x - 223609972474$	$9$	[3,3]	$-\,3^{12}\cdot 7^{6}\cdot 17^{3}\cdot 43^{7}$	$4$	$758.901606566$	$1499.7143256219335$				$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 42]$	$2$	$5$	$6365194.594055798$
9.3.853...736.1	$x^{9} - x^{8} - 701 x^{7} + 4922 x^{6} + 19570 x^{5} + 291711 x^{4} + 875487 x^{3} + 3767781 x^{2} + 5364326 x + 11322593$	$9$	[3,3]	$-\,2^{9}\cdot 31^{7}\cdot 67^{7}$	$3$	$760.77876477$	$1644.6572630084195$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 762]$	$2$	$5$	$166515.90732729912$
9.3.878...403.1	$x^{9} - 4089 x^{6} - 15595540 x^{3} - 2532139147$	$9$	[3,3]	$-\,3^{3}\cdot 7^{6}\cdot 37^{6}\cdot 47^{6}$	$4$	$763.2008280940915$	$916.5560786791223$			?	$S_3\times C_3$ (as 9T4)	$[2, 12, 420]$	$2$	$5$	$529860.886797058$
9.3.124...000.1	$x^{9} - 2 x^{8} + 941 x^{7} + 16825 x^{6} - 166443 x^{5} + 11732922 x^{4} + 165187300 x^{3} - 3066921559 x^{2} - 80668651817 x + 602452994221$	$9$	[3,3]	$-\,2^{6}\cdot 5^{3}\cdot 7^{6}\cdot 13^{6}\cdot 31^{7}$	$5$	$793.692441039$	$1256.0319082199908$				$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 21, 21]$	$2$	$5$	$935147.1080403534$
9.1.127...448.1	$x^{9} - 3 x^{8} + 57 x^{7} + 1820 x^{6} - 2832 x^{5} - 30882 x^{4} + 1106665 x^{3} - 477759 x^{2} - 43452285 x + 291274836$	$9$	[1,4]	$2^{9}\cdot 3^{10}\cdot 7^{6}\cdot 13^{7}\cdot 83^{3}$	$5$	$795.529884992$	$2880.118281079252$				$S_3^2$ (as 9T8)	$[3, 3, 3, 3, 6, 24]$	$2$	$4$	$3265658.5635054656$
9.3.140...643.1	$x^{9} - 3 x^{6} - 6324 x^{3} - 1$	$9$	[3,3]	$-\,3^{19}\cdot 19^{6}\cdot 37^{6}$	$3$	$803.944741456$	$854.5410603657755$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 6, 6, 54]$	$2$	$5$	$246396.6723873261$
9.3.167...392.1	$x^{9} - 3 x^{8} - 1155 x^{7} - 5850 x^{6} + 40266 x^{5} - 447417 x^{4} - 8111571 x^{3} + 81009675 x^{2} - 306232344 x + 294493899$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 127^{7}$	$4$	$820.124686236$	$1578.0264517537692$			?	$S_3\times C_3$ (as 9T4)	$[3, 3411]$	$2$	$5$	$981650.0146135457$
9.3.171...256.1	$x^{9} - 4 x^{8} - 305 x^{7} - 4087 x^{6} - 29699 x^{5} - 131134 x^{4} - 357734 x^{3} - 587527 x^{2} - 532163 x - 204251$	$9$	[3,3]	$-\,2^{6}\cdot 31^{3}\cdot 709^{7}$	$3$	$822.198201427$	$2098.485825279839$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 4, 5652]$	$2$	$5$	$21709.433536498364$
9.3.204...008.2	$x^{9} - 402 x^{6} - 67416 x^{3} - 2406104$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 1123^{6}$	$3$	$838.3942935313088$	$891.1586974269279$			?	$S_3\times C_3$ (as 9T4)	$[58695]$	$2$	$5$	$130304.28205208834$
9.1.228...000.1	$x^{9} - 7260 x^{6} - 12034000 x^{3} - 14172488000$	$9$	[1,4]	$2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 11^{7}\cdot 29^{6}$	$5$	$848.578469459$	$1164.3066199051143$			?	$S_3^2$ (as 9T8)	$[3, 3, 6, 6, 36]$	$2$	$4$	$903787.2582421625$
9.1.268...488.2	$x^{9} + 42 x^{7} - 132 x^{6} - 9324 x^{5} + 11172 x^{4} + 244788 x^{3} - 243936 x^{2} + 81312 x - 85184$	$9$	[1,4]	$2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 59^{7}$	$4$	$864.205031922$	$1152.1371870526943$			?	$S_3^2$ (as 9T8)	$[3, 3, 12, 360]$	$2$	$4$	$344458.37527059705$
9.3.273...112.1	$x^{9} - 396 x^{6} - 65376 x^{3} - 2299968$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 19^{6}\cdot 43^{6}$	$4$	$865.705398959289$	$1039.6576059055951$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 1386]$	$2$	$5$	$198731.75532269993$
9.3.293...648.1	$x^{9} - 192 x^{6} - 17476 x^{3} - 262144$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 1063^{6}$	$4$	$872.598813996$	$1047.9361627705994$				$S_3\times C_3$ (as 9T4)	$[45, 315]$	$2$	$5$	$3859512.731519649$
9.3.293...648.2	$x^{9} - 294 x^{6} - 10180240 x^{3} - 941192$	$9$	[3,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 1063^{6}$	$4$	$872.5988139960433$	$1047.9361627705994$			?	$S_3\times C_3$ (as 9T4)	$[18, 1638]$	$2$	$5$	$349222.3439747906$
9.1.296...584.1	$x^{9} - 534 x^{6} + 18915348 x^{3} - 5639752$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 11^{6}\cdot 89^{7}$	$4$	$873.525140545$	$1191.4658250010298$			?	$S_3^2$ (as 9T8)	$[3, 6, 1170]$	$2$	$4$	$1159710.2741848961$
9.3.335...000.1	$x^{9} - 2 x^{8} - 455 x^{7} + 503 x^{6} + 26961 x^{5} + 283750 x^{4} + 1326746 x^{3} + 4414921 x^{2} + 8136717 x + 10231171$	$9$	[3,3]	$-\,2^{9}\cdot 5^{3}\cdot 7^{7}\cdot 181^{7}$	$4$	$885.708265514$	$2435.999387333401$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 1098]$	$2$	$5$	$184436.26656721527$
9.3.407...408.1	$x^{9} - 897 x^{6} - 9806901 x^{3} - 26730899$	$9$	[3,3]	$-\,2^{6}\cdot 3^{18}\cdot 13^{6}\cdot 23^{7}$	$4$	$905.064905142$	$1145.0857438716077$			?	$S_3^2$ (as 9T8)	$[3, 3, 3, 6, 108]$	$2$	$5$	$1376479.6330253545$