Number field search results

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

Results (15 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
9.3.273...112.1	$x^{9} - 588 x^{6} - 5620644960 x^{3} - 7529536$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 5419^{6}$	$4$	$11183.220354309362$	$11887.037114730158$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 18, 8743914]$	$2$	$5$	$484679.67802290426$
9.3.282...787.1	$x^{9} - 3 x^{6} - 2970456 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 110017^{6}$	$2$	$11224.017741882904$	$11930.402088763227$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 2, 166563978]$	$2$	$5$	$511165.2947812259$
9.3.300...363.1	$x^{9} - 3 x^{6} - 3001560 x^{3} - 1$	$9$	[3,3]	$-\,3^{13}\cdot 19^{6}\cdot 5851^{6}$	$3$	$11302.233577966117$	$12013.540443997597$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 18, 378, 106974]$	$2$	$5$	$512495.4469834305$
9.3.333...000.1	$x^{9} - 17823 x^{7} - 528749 x^{6} + 106670655 x^{5} + 6352651890 x^{4} - 119663622000 x^{3} - 19226330887725 x^{2} - 575717826396375 x - 5757059141715375$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 5^{3}\cdot 13^{7}\cdot 457^{7}$	$5$	$11430.7810776$	$25747.585461819013$			?	$S_3\times C_3$ (as 9T4)	$[2, 6, 6, 12, 3138180]$	$2$	$5$	$450321.3942190072$
9.3.771...587.1	$x^{9} - 867 x^{6} - 17253267054 x^{3} - 24137569$	$9$	[3,3]	$-\,3^{13}\cdot 7^{6}\cdot 17^{6}\cdot 1093^{6}$	$4$	$12549.311357688637$	$13339.103151595016$			?	$S_3\times C_3$ (as 9T4)	$[2, 6, 6, 63300636]$	$2$	$5$	$563528.7187273789$
9.3.976...563.1	$x^{9} - 867 x^{6} - 17943317556 x^{3} - 24137569$	$9$	[3,3]	$-\,3^{13}\cdot 17^{6}\cdot 73^{6}\cdot 109^{6}$	$4$	$12881.72426134566$	$13692.436484749236$			?	$S_3\times C_3$ (as 9T4)	$[3, 18, 18, 36, 86868]$	$2$	$5$	$570297.8106717326$
9.3.205...000.1	$x^{9} - 150 x^{6} - 716910000 x^{3} - 125000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 13^{6}\cdot 19^{6}\cdot 43^{6}$	$6$	$13995.197462087093$	$14875.986199780153$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 9, 1386, 1386]$	$2$	$5$	$644611.6327244428$
9.3.251...000.1	$x^{9} - 150 x^{6} - 741210000 x^{3} - 125000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 79^{6}\cdot 139^{6}$	$5$	$14309.683193809096$	$15210.264113171352$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 36, 36, 78624]$	$2$	$5$	$651013.4013201951$
9.3.441...243.1	$x^{9} + 6864 x^{7} - 33726 x^{6} + 11725263 x^{5} - 42902244 x^{4} + 5346025509 x^{3} + 2399537448 x^{2} - 479562350652 x - 539917839384$	$9$	[3,3]	$-\,3^{15}\cdot 11^{6}\cdot 19^{6}\cdot 577^{6}$	$4$	$15231.762429328262$	$16190.374470302488$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9, 9, 593271]$	$2$	$5$	$1897151.870448636$
9.3.578...107.1	$x^{9} - 1083 x^{6} - 33697882896 x^{3} - 47045881$	$9$	[3,3]	$-\,3^{13}\cdot 19^{6}\cdot 61^{6}\cdot 157^{6}$	$4$	$15697.501670771184$	$16685.42504369881$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 45, 90, 189630]$	$2$	$5$	$618084.4878505643$
9.3.107...632.1	$x^{9} - 58323 x^{7} - 3130001 x^{6} + 1138523283 x^{5} + 122453454402 x^{4} - 4143242124216 x^{3} - 1202676920502885 x^{2} - 64877600559004083 x - 1167789370823389971$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 19441^{7}$	$3$	$16808.6112106$	$30924.359456035912$			?	$S_3\times C_3$ (as 9T4)	$[3, 9, 18, 54, 329238]$	$2$	$5$	$726341.9525569454$
9.3.144...072.1	$x^{9} - 1302 x^{6} - 706344 x^{3} - 81746504$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 35317^{6}$	$3$	$17375.28150536162$	$18468.796070313445$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 6, 90, 90, 18900]$	$2$	$5$	$1023333.5145732651$
9.3.319...099.1	$x^{9} - 62751 x^{7} - 3493139 x^{6} + 1317771000 x^{5} + 147003504648 x^{4} - 5157643244208 x^{3} - 1552835138570352 x^{2} - 86872327632941760 x - 1621607178023024192$	$9$	[3,3]	$-\,3^{12}\cdot 7^{3}\cdot 13^{7}\cdot 1609^{7}$	$4$	$18977.956159937257$	$45617.01429722084$			?	$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 78, 78, 19266]$	$2$	$5$	$1865917.0192459666$
9.3.362...936.1	$x^{9} - 3 x^{8} - 98565 x^{7} - 6249892 x^{6} + 3254568816 x^{5} + 420957601977 x^{4} - 22123456548437 x^{3} - 7001289980107383 x^{2} - 457568151115573998 x - 9991400752586801679$	$9$	[3,3]	$-\,2^{9}\cdot 3^{12}\cdot 11^{3}\cdot 19^{6}\cdot 577^{7}$	$5$	$19248.910460652063$	$57794.3327376087$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 6, 6832098]$	$2$	$5$	$5182831.720989658$
9.3.547...819.1	$x^{9} - 7845679 x^{6} - 2875595796 x^{5} + 788163444954 x^{4} - 92579497458335 x^{3} + 31921816102083936 x^{2} - 5421440093430248208 x + 277644182655213837504$	$9$	[3,3]	$-\,3^{13}\cdot 163^{7}\cdot 379^{7}$	$3$	$26023.983750998443$	$51054.915380841754$			?	$S_3\times C_3$ (as 9T4)	$[3, 6, 6, 342, 265734]$	$2$	$5$	$4652462.483006366$