Number field search results

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

Results (1-50 of 361017 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
6.0.2185548272.1	$x^{6} + 31 x^{4} - 12 x^{3} + 366 x^{2} - 148 x + 1936$	$6$	[0,3]	$-\,2^{4}\cdot 43\cdot 79^{2}\cdot 509$	$4$	$36.0241216498$	$2629.8844081061816$	✓			$S_4\times C_2$ (as 6T11)	$[102]$	$2$	$2$	$15.653833968455787$
6.0.2267030768.1	$x^{6} - x^{5} + 32 x^{4} - 22 x^{3} + 384 x^{2} - 144 x + 1728$	$6$	[0,3]	$-\,2^{4}\cdot 73\cdot 79^{2}\cdot 311$	$4$	$36.2445658841$	$2678.460005301554$	✓			$S_4\times C_2$ (as 6T11)	$[110]$	$2$	$2$	$15.653833968455787$
6.0.2623637527.2	$x^{6} - x^{5} + 73 x^{4} - 49 x^{3} + 2007 x^{2} - 625 x + 20357$	$6$	[0,3]	$-\,7^{4}\cdot 103^{3}$	$2$	$37.1378968545$	$37.13789685454593$	✓	✓	?	$C_6$ (as 6T1)	$[105]$	$2$	$2$	$2.10181872849$
6.0.2648880112.1	$x^{6} - 3 x^{5} + 35 x^{4} - 65 x^{3} + 318 x^{2} - 286 x + 484$	$6$	[0,3]	$-\,2^{4}\cdot 41\cdot 79^{2}\cdot 647$	$4$	$37.1972114729$	$2895.260264639433$	✓			$S_4\times C_2$ (as 6T11)	$[112]$	$2$	$2$	$15.653833968455787$
6.0.2826224368.1	$x^{6} + 35 x^{4} + 502 x^{2} - 44 x + 2192$	$6$	[0,3]	$-\,2^{4}\cdot 11\cdot 31\cdot 79^{2}\cdot 83$	$5$	$37.6011481328$	$2990.609971226606$	✓			$S_4\times C_2$ (as 6T11)	$[2, 54]$	$2$	$2$	$15.653833968455787$
6.0.2878149488.1	$x^{6} - 2 x^{5} + 37 x^{4} - 34 x^{3} + 468 x^{2} - 120 x + 2144$	$6$	[0,3]	$-\,2^{4}\cdot 19\cdot 37\cdot 41\cdot 79^{2}$	$5$	$37.7154150298$	$3017.9575875084793$	✓			$S_4\times C_2$ (as 6T11)	$[2, 52]$	$2$	$2$	$15.653833968455787$
6.0.2949751232.1	$x^{6} - 3 x^{5} + 41 x^{4} - 77 x^{3} + 356 x^{2} - 318 x + 220$	$6$	[0,3]	$-\,2^{6}\cdot 41\cdot 71^{2}\cdot 223$	$4$	$37.8701970768$	$2278.864629590797$	✓			$S_4\times C_2$ (as 6T11)	$[104]$	$2$	$2$	$24.349563628547063$
6.0.3112538751.2	$x^{6} - x^{5} + 99 x^{4} - 99 x^{3} + 2843 x^{2} - 2843 x + 22051$	$6$	[0,3]	$-\,3^{3}\cdot 7^{5}\cdot 19^{3}$	$3$	$38.2107704489$	$38.21077044890832$	✓	✓	?	$C_6$ (as 6T1)	$[2, 56]$	$2$	$2$	$2.10181872849$
6.0.3116883375.2	$x^{6} - x^{5} - 9 x^{4} - 3 x^{3} + 152 x^{2} + 148 x + 736$	$6$	[0,3]	$-\,3^{3}\cdot 5^{3}\cdot 31^{4}$	$3$	$38.2196546735$	$38.21965467350533$	✓	✓		$C_6$ (as 6T1)	$[3, 42]$	$2$	$2$	$48.7831276503$
6.0.3187940831.1	$x^{6} - 3 x^{5} + 37 x^{4} - 69 x^{3} + 387 x^{2} - 353 x + 1036$	$6$	[0,3]	$-\,31\cdot 37\cdot 53\cdot 229^{2}$	$4$	$38.3635135386$	$3731.104260135329$	✓			$S_4\times C_2$ (as 6T11)	$[2, 52]$	$2$	$2$	$9.421818363378257$
6.0.3202030832.1	$x^{6} - x^{5} + 21 x^{4} - 9 x^{3} + 110 x^{2} + 10 x + 12$	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 11\cdot 13^{5}$	$4$	$38.391721359$	$148.78580024306822$				$S_4\times C_2$ (as 6T11)	$[2, 78]$	$2$	$2$	$25.7091371183$
6.0.3319113584.1	$x^{6} - 3 x^{5} + 33 x^{4} - 61 x^{3} + 296 x^{2} - 266 x + 584$	$6$	[0,3]	$-\,2^{4}\cdot 43\cdot 79^{2}\cdot 773$	$4$	$38.6222009486$	$3240.914068592378$	✓			$S_4\times C_2$ (as 6T11)	$[108]$	$2$	$2$	$15.653833968455787$
6.0.3393090023.1	$x^{6} - 3 x^{5} + 39 x^{4} - 73 x^{3} + 425 x^{2} - 389 x + 1106$	$6$	[0,3]	$-\,89\cdot 229^{2}\cdot 727$	$3$	$38.7643551389$	$3849.2839593877716$	✓			$S_4\times C_2$ (as 6T11)	$[2, 56]$	$2$	$2$	$9.421818363378257$
6.0.3394205296.1	$x^{6} - x^{5} + 27 x^{4} - 53 x^{3} + 266 x^{2} - 492 x + 1096$	$6$	[0,3]	$-\,2^{4}\cdot 19\cdot 79^{2}\cdot 1789$	$4$	$38.7664784208$	$3277.3702872882704$	✓			$S_4\times C_2$ (as 6T11)	$[116]$	$2$	$2$	$15.653833968455787$
6.0.3499230607.1	$x^{6} - 2 x^{5} + 31 x^{4} - 35 x^{3} + 324 x^{2} - 223 x + 1432$	$6$	[0,3]	$-\,53\cdot 229^{2}\cdot 1259$	$3$	$38.9638707518$	$3909.0258377247906$	✓			$S_4\times C_2$ (as 6T11)	$[120]$	$2$	$2$	$9.421818363378257$
6.0.3569979632.1	$x^{6} - 3 x^{5} + 45 x^{4} - 85 x^{3} + 626 x^{2} - 584 x + 2690$	$6$	[0,3]	$-\,2^{4}\cdot 37^{2}\cdot 349\cdot 467$	$4$	$39.094076313$	$3898.151192956886$	✓		✓	$S_4\times C_2$ (as 6T11)	$[108]$	$2$	$2$	$6.649346083071585$
6.0.3630312000.2	$x^{6} + 105 x^{4} + 3150 x^{2} + 23625$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{3}\cdot 7^{5}$	$4$	$39.2034232971$	$39.20342329707507$	✓	✓	?	$C_6$ (as 6T1)	$[2, 2, 26]$	$2$	$2$	$2.10181872849$
6.0.3669298299.1	$x^{6} - 3 x^{5} + 66 x^{4} - 127 x^{3} + 1377 x^{2} - 1314 x + 9063$	$6$	[0,3]	$-\,3^{8}\cdot 559259$	$2$	$39.2732796402$	$3235.69936631413$	✓		?	$A_4\times C_2$ (as 6T6)	$[107]$	$2$	$2$	$3.39714980258477$
6.0.3906734328.1	$x^{6} - 3 x^{5} + 6 x^{4} + 48 x^{2} - 192 x + 512$	$6$	[0,3]	$-\,2^{3}\cdot 3^{8}\cdot 7^{4}\cdot 31$	$4$	$39.68584633447011$	$249.33669969776457$	✓			$A_4\times C_2$ (as 6T6)	$[3, 54]$	$2$	$2$	$50.37675582767471$
6.0.3974415088.5	$x^{6} - x^{5} + 73 x^{4} + 75 x^{3} + 960 x^{2} + 344 x + 3214$	$6$	[0,3]	$-\,2^{4}\cdot 7^{3}\cdot 23^{2}\cdot 37^{2}$	$4$	$39.7996149555$	$122.51815942319539$	✓		?	$S_4\times C_2$ (as 6T11)	$[104]$	$2$	$2$	$6.64934608307$
6.0.4210332239.1	$x^{6} - x^{5} + 27 x^{4} - 27 x^{3} + 364 x^{2} - 252 x + 1744$	$6$	[0,3]	$-\,31^{4}\cdot 47\cdot 97$	$3$	$40.1839595446$	$666.3093772579095$	✓			$A_4\times C_2$ (as 6T6)	$[142]$	$2$	$2$	$48.78312765034341$
6.0.4286177831.1	$x^{6} - x^{5} + 48 x^{4} - 27 x^{3} + 754 x^{2} + 2600$	$6$	[0,3]	$-\,13^{4}\cdot 31\cdot 47\cdot 103$	$4$	$40.3037105284$	$2141.7919887263197$	✓			$A_4\times C_2$ (as 6T6)	$[2, 54]$	$2$	$2$	$5.46019947037753$
6.0.4438983616.1	$x^{6} - 3 x^{5} + 17 x^{4} - 27 x^{3} + 130 x^{2} - 46 x + 440$	$6$	[0,3]	$-\,2^{6}\cdot 71^{2}\cdot 13759$	$3$	$40.5397055842$	$2795.552181591322$	✓			$S_4\times C_2$ (as 6T11)	$[3, 45]$	$2$	$2$	$24.3495636285$
6.0.4450055616.1	$x^{6} - 3 x^{5} + 13 x^{4} + 9 x^{3} + 14 x^{2} + 94 x + 384$	$6$	[0,3]	$-\,2^{6}\cdot 3^{2}\cdot 127^{2}\cdot 479$	$4$	$40.5565408887$	$1208.301286931368$	✓			$S_4\times C_2$ (as 6T11)	$[114]$	$2$	$2$	$40.5157082906$
6.0.4455334919.1	$x^{6} - 3 x^{5} + 59 x^{4} - 113 x^{3} + 872 x^{2} - 816 x + 1528$	$6$	[0,3]	$-\,7\cdot 53\cdot 229^{3}$	$3$	$40.5645559386$	$291.4772718412192$	✓			$S_4\times C_2$ (as 6T11)	$[2, 58]$	$2$	$2$	$9.421818363378257$
6.0.4467667023.1	$x^{6} + 90 x^{4} - 46 x^{3} + 2025 x^{2} - 2070 x + 12241$	$6$	[0,3]	$-\,3^{9}\cdot 61^{3}$	$2$	$40.5832477754$	$40.58324777540605$	✓	✓	?	$C_6$ (as 6T1)	$[104]$	$2$	$2$	$3.39714980258$
6.0.4598788608.8	$x^{6} + 78 x^{4} + 1776 x^{2} + 10952$	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}\cdot 37^{2}$	$3$	$40.7793758587$	$125.19299385464981$	✓		?	$A_4\times C_2$ (as 6T6)	$[2, 52]$	$2$	$2$	$3.39714980258$
6.0.4687333903.1	$x^{6} + 49 x^{4} - 47 x^{3} + 678 x^{2} - 1117 x + 2132$	$6$	[0,3]	$-\,7\cdot 113^{2}\cdot 229^{2}$	$3$	$40.9091995487$	$425.60427629430603$	✓			$S_4\times C_2$ (as 6T11)	$[114]$	$2$	$2$	$9.421818363378257$
6.0.4764886640.1	$x^{6} - 3 x^{5} + 47 x^{4} - 83 x^{3} + 734 x^{2} - 630 x + 4030$	$6$	[0,3]	$-\,2^{4}\cdot 5\cdot 37^{2}\cdot 139\cdot 313$	$5$	$41.0212379187$	$4503.520011455174$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 60]$	$2$	$2$	$6.649346083071585$
6.0.4839622567.1	$x^{6} - 3 x^{5} + 62 x^{4} - 89 x^{3} + 1117 x^{2} - 264 x + 6608$	$6$	[0,3]	$-\,13\cdot 31\cdot 229^{3}$	$3$	$41.1277782116$	$303.78775485526074$	✓			$S_4\times C_2$ (as 6T11)	$[2, 56]$	$2$	$2$	$9.421818363378257$
6.0.4840461623.1	$x^{6} - 3 x^{5} + 39 x^{4} - 73 x^{3} + 452 x^{2} - 416 x + 1544$	$6$	[0,3]	$-\,229^{2}\cdot 241\cdot 383$	$3$	$41.128966528$	$4597.5414081876415$	✓			$S_4\times C_2$ (as 6T11)	$[112]$	$2$	$2$	$9.421818363378257$
6.0.4863286768.1	$x^{6} - x^{5} + 42 x^{4} - 20 x^{3} + 635 x^{2} - 99 x + 3538$	$6$	[0,3]	$-\,2^{4}\cdot 79^{2}\cdot 113\cdot 431$	$4$	$41.1612270678$	$3923.027912212708$	✓			$S_4\times C_2$ (as 6T11)	$[124]$	$2$	$2$	$15.653833968455787$
6.0.4987905687.1	$x^{6} - 3 x^{5} + 27 x^{4} - 41 x^{3} + 273 x^{2} - 159 x + 1233$	$6$	[0,3]	$-\,3^{2}\cdot 107^{2}\cdot 48407$	$3$	$41.3351678506$	$3941.9090552675107$	✓			$S_4\times C_2$ (as 6T11)	$[105]$	$2$	$2$	$10.2770387205$
6.0.5124510064.1	$x^{6} - x^{5} + 27 x^{4} - 29 x^{3} + 260 x^{2} - 186 x + 1304$	$6$	[0,3]	$-\,2^{4}\cdot 19\cdot 37\cdot 73\cdot 79^{2}$	$5$	$41.5217253786$	$4027.0093121322675$	✓			$S_4\times C_2$ (as 6T11)	$[2, 60]$	$2$	$2$	$15.653833968455787$
6.0.5190814448.1	$x^{6} + 41 x^{4} - 2 x^{3} + 656 x^{2} + 4096$	$6$	[0,3]	$-\,2^{4}\cdot 79^{2}\cdot 227\cdot 229$	$4$	$41.6107858139$	$4052.9776707995816$	✓			$S_4\times C_2$ (as 6T11)	$[138]$	$2$	$2$	$15.653833968455787$
6.0.5267762279.1	$x^{6} - x^{5} + 41 x^{4} - 31 x^{3} + 615 x^{2} - 225 x + 3375$	$6$	[0,3]	$-\,13^{4}\cdot 181\cdot 1019$	$3$	$41.7129618285$	$2374.4076398316433$	✓			$A_4\times C_2$ (as 6T6)	$[104]$	$2$	$2$	$5.46019947037753$
6.0.5281871063.1	$x^{6} - 2 x^{5} + 105 x^{4} - 96 x^{3} + 3416 x^{2} - 1240 x + 35503$	$6$	[0,3]	$-\,7^{4}\cdot 97\cdot 22679$	$3$	$41.7315612338$	$5427.458494884186$	✓		?	$A_4\times C_2$ (as 6T6)	$[104]$	$2$	$2$	$2.1018187284902896$
6.0.5397666491.3	$x^{6} - x^{5} + 94 x^{4} - 63 x^{3} + 3239 x^{2} - 1024 x + 40391$	$6$	[0,3]	$-\,7^{4}\cdot 131^{3}$	$2$	$41.8826681887$	$41.88266818867061$	✓	✓	?	$C_6$ (as 6T1)	$[105]$	$2$	$2$	$2.10181872849$
6.0.5444581943.4	$x^{6} - 3 x^{5} + 31 x^{4} - 55 x^{3} + 469 x^{2} - 521 x + 3064$	$6$	[0,3]	$-\,47^{3}\cdot 229^{2}$	$2$	$41.9431222654$	$103.74487939170781$	✓			$D_{6}$ (as 6T3)	$[2, 60]$	$2$	$2$	$9.42181836338$
6.0.5522223168.1	$x^{6} - 17 x^{4} + 31 x^{2} + 2673$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 11^{3}$	$4$	$42.0422217881$	$42.04222178812256$		✓		$S_3$ (as 6T2)	$[6, 18]$	$2$	$2$	$44.4815829276$
6.0.5522223168.10	$x^{6} - 2 x^{5} + 96 x^{4} - 126 x^{3} + 3335 x^{2} - 2248 x + 41581$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 7^{4}\cdot 11^{3}$	$4$	$42.0422217881$	$42.04222178812256$	✓	✓	?	$C_6$ (as 6T1)	$[6, 18]$	$2$	$2$	$2.10181872849$
6.0.5548698352.1	$x^{6} - 2 x^{5} + 45 x^{4} - 62 x^{3} + 720 x^{2} - 512 x + 4096$	$6$	[0,3]	$-\,2^{4}\cdot 79^{2}\cdot 181\cdot 307$	$4$	$42.0757487002$	$4190.366571077046$	✓			$S_4\times C_2$ (as 6T11)	$[110]$	$2$	$2$	$15.653833968455787$
6.0.5609350656.4	$x^{6} + 114 x^{4} + 3744 x^{2} + 36504$	$6$	[0,3]	$-\,2^{9}\cdot 3^{3}\cdot 7^{4}\cdot 13^{2}$	$4$	$42.152056236$	$108.70474136925078$	✓		?	$A_4\times C_2$ (as 6T6)	$[2, 2, 28]$	$2$	$2$	$2.10181872849$
6.0.5655743984.1	$x^{6} - x^{5} + 44 x^{4} - 30 x^{3} + 704 x^{2} - 256 x + 4096$	$6$	[0,3]	$-\,2^{4}\cdot 11\cdot 19\cdot 79^{2}\cdot 271$	$5$	$42.2099615977$	$4230.5938117479445$	✓			$S_4\times C_2$ (as 6T11)	$[2, 74]$	$2$	$2$	$15.653833968455787$
6.0.5795359792.1	$x^{6} + 58 x^{4} + 1106 x^{2} + 6907$	$6$	[0,3]	$-\,2^{4}\cdot 229^{2}\cdot 6907$	$3$	$42.381865336$	$2515.3154871705456$	✓		?	$S_4\times C_2$ (as 6T11)	$[110]$	$2$	$2$	$9.421818363378257$
6.0.5863499975.1	$x^{6} - 3 x^{5} + 36 x^{4} - 67 x^{3} + 452 x^{2} - 362 x + 1743$	$6$	[0,3]	$-\,5^{2}\cdot 53\cdot 67\cdot 257^{2}$	$4$	$42.4645136668$	$2136.1261666858536$	✓		?	$S_4\times C_2$ (as 6T11)	$[2, 52]$	$2$	$2$	$7.8983754831228286$
6.0.5907360375.1	$x^{6} - 3 x^{5} - 27 x^{4} + 3 x^{3} + 522 x^{2} + 1296 x + 2304$	$6$	[0,3]	$-\,3^{9}\cdot 5^{3}\cdot 7^{4}$	$3$	$42.5172902208$	$42.517290220802025$	✓	✓		$C_6$ (as 6T1)	$[222]$	$2$	$2$	$50.3767558277$
6.0.5923358064.7	$x^{6} - x^{5} + 21 x^{4} - 15 x^{3} + 308 x^{2} - 62 x + 1936$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 13^{3}\cdot 79^{2}$	$4$	$42.5364587415$	$111.01351269102334$	✓			$D_{6}$ (as 6T3)	$[132]$	$2$	$2$	$15.6538339685$
6.0.6038177216.1	$x^{6} - x^{5} + 19 x^{4} - 21 x^{3} + 190 x^{2} - 100 x + 1000$	$6$	[0,3]	$-\,2^{6}\cdot 53\cdot 67\cdot 163^{2}$	$4$	$42.672783844$	$2151.860590279956$	✓			$S_4\times C_2$ (as 6T11)	$[108]$	$2$	$2$	$47.70615160309553$
6.0.6043684544.1	$x^{6} - 2 x^{5} + 47 x^{4} - 92 x^{3} + 841 x^{2} - 1082 x + 5023$	$6$	[0,3]	$-\,2^{6}\cdot 79^{2}\cdot 15131$	$3$	$42.6792682445$	$3092.376432454497$	✓			$S_4\times C_2$ (as 6T11)	$[102]$	$2$	$2$	$15.653833968455787$