Number field search results

Results (1-50 of 244008 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
6.2.33856.1	$x^{6} + x^{4} - 1$	$6$	[2,2]	$2^{6}\cdot 23^{2}$	$2$	$5.6877339597$	$13.564659966250536$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.550118007418$
6.2.52441.1	$x^{6} - x^{4} - x^{3} - x^{2} + 1$	$6$	[2,2]	$229^{2}$	$1$	$6.11803317264$	$15.132745950421556$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.794678096272$
6.2.61504.1	$x^{6} + x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 31^{2}$	$2$	$6.28276130478$	$15.748015748023622$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.828712859351$
6.2.66049.1	$x^{6} - x^{5} - x^{4} + x^{3} - x^{2} - x + 1$	$6$	[2,2]	$257^{2}$	$1$	$6.35786117973$	$16.0312195418814$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.873042646654$
6.2.80089.1	$x^{6} + x^{4} - x^{3} - x^{2} - 1$	$6$	[2,2]	$283^{2}$	$1$	$6.56541442735$	$16.822603841260722$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.05997346547$
6.2.87616.1	$x^{6} - x^{4} - 2 x^{3} - x^{2} + 1$	$6$	[2,2]	$2^{6}\cdot 37^{2}$	$2$	$6.66444370329$	$13.655340178276088$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.52572339145$
6.2.109561.1	$x^{6} - x^{5} - 2 x^{3} - x - 1$	$6$	[2,2]	$331^{2}$	$1$	$6.91739641661$	$18.193405398660254$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.29907528031$
6.2.110224.1	$x^{6} + 2 x^{4} + 2 x^{2} - 1$	$6$	[2,2]	$2^{4}\cdot 83^{2}$	$2$	$6.92435557263$	$18.2208671582886$				$S_4$ (as 6T7)	trivial	$2$	$3$	$1.42251197392$
6.2.116281.1	$x^{6} - 2 x^{5} + 6 x^{3} - 7 x^{2} + 2 x - 1$	$6$	[2,2]	$11^{2}\cdot 31^{2}$	$2$	$6.98636802782$	$18.466185312619388$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.24934163649$
6.2.118336.1	$x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 3 x^{2} - 2 x + 1$	$6$	[2,2]	$2^{6}\cdot 43^{2}$	$2$	$7.00679612077$	$14.720951755301632$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.87958769351$
6.2.123904.1	$x^{6} + x^{4} + x^{2} - 1$	$6$	[2,2]	$2^{10}\cdot 11^{2}$	$2$	$7.06069667065$	$14.891141822623867$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.934485574$
6.2.179776.1	$x^{6} - x^{5} + x^{4} - x^{2} - x - 1$	$6$	[2,2]	$2^{6}\cdot 53^{2}$	$2$	$7.51257150844$	$20.591260281974$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.6937531845$
6.2.190969.1	$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 10 x - 1$	$6$	[2,2]	$19^{2}\cdot 23^{2}$	$2$	$7.58857933778$	$20.904544960366874$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$1.66533508512$
6.2.207936.1	$x^{6} - 2 x^{5} + x^{4} + 2 x^{3} - x^{2} - 2 x - 1$	$6$	[2,2]	$2^{6}\cdot 3^{2}\cdot 19^{2}$	$3$	$7.69700226255$	$16.948805249221287$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.72505368184$
6.2.215296.1	$x^{6} - x^{5} - 3 x^{4} + 2 x^{3} - 2 x + 2$	$6$	[2,2]	$2^{8}\cdot 29^{2}$	$2$	$7.74175328126$	$21.540659228538015$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.02535851926$
6.2.222784.1	$x^{6} + 2 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 59^{2}$	$2$	$7.78599283175$	$21.72556098240043$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.0957085279$
6.2.222784.2	$x^{6} + x^{4} - 2 x^{2} - 4$	$6$	[2,2]	$2^{6}\cdot 59^{2}$	$2$	$7.78599283175$	$21.72556098240043$				$S_4$ (as 6T7)	trivial	$2$	$3$	$2.23450043422$
6.2.238144.1	$x^{6} - x^{5} - x^{4} + 4 x^{3} - x^{2} - x + 1$	$6$	[2,2]	$2^{6}\cdot 61^{2}$	$2$	$7.8729943662$	$22.090722034374522$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.27195803566$
6.2.241081.1	$x^{6} + x^{4} + x^{2} - 4$	$6$	[2,2]	$491^{2}$	$1$	$7.88909460402$	$22.15851980616034$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.39619703292$
6.2.316969.1	$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} - x - 1$	$6$	[2,2]	$563^{2}$	$1$	$8.25726326993$	$23.727621035409346$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.44626365158$
6.2.356409.1	$x^{6} - x^{5} + x^{4} + x^{3} - x^{2} - x - 1$	$6$	[2,2]	$3^{2}\cdot 199^{2}$	$2$	$8.42024594795$	$24.43358344574123$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.69889717783$
6.2.369664.1	$x^{6} - x^{4} + 3 x^{2} - 1$	$6$	[2,2]	$2^{10}\cdot 19^{2}$	$2$	$8.47164716851$	$19.570794546160904$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.83607090335$
6.2.379456.1	$x^{6} - 2 x^{5} + 3 x^{4} - 8 x^{3} + 9 x^{2} - 4 x - 1$	$6$	[2,2]	$2^{6}\cdot 7^{2}\cdot 11^{2}$	$3$	$8.50864173023$	$19.699129000227927$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.89943789111$
6.2.399424.1	$x^{6} - x^{5} - x^{4} - x^{2} - x + 1$	$6$	[2,2]	$2^{6}\cdot 79^{2}$	$2$	$8.58168085405$	$25.13961017995307$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.52032874016$
6.2.413449.1	$x^{6} + x^{4} - 5 x^{3} + x^{2} + 1$	$6$	[2,2]	$643^{2}$	$1$	$8.63118299216$	$25.357444666211933$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.39726974883$
6.2.484416.1	$x^{6} + x^{4} + 2 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 3^{2}\cdot 29^{2}$	$3$	$8.86209524339$	$26.38181191654584$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.45513564211$
6.2.485809.1	$x^{6} - 3 x^{5} - x^{4} + 5 x^{3} - x^{2} - 3 x + 1$	$6$	[2,2]	$17^{2}\cdot 41^{2}$	$2$	$8.86633751079$	$26.40075756488817$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$2.80199656282$
6.2.506944.1	$x^{6} - x^{5} + x^{4} - 6 x^{3} - x^{2} - x - 1$	$6$	[2,2]	$2^{6}\cdot 89^{2}$	$2$	$8.92949019117$	$26.68332812825267$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$5.53237560337$
6.2.514089.1	$x^{6} - 2 x^{5} + x^{4} - 4 x^{2} + 3$	$6$	[2,2]	$3^{2}\cdot 239^{2}$	$2$	$8.95034381709$	$26.77685567799177$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.77588950853$
6.2.529984.1	$x^{6} + x^{4} - 2 x^{3} - x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 7^{2}\cdot 13^{2}$	$3$	$8.99588289055$	$21.415210999701447$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$5.16920229548$
6.2.534361.1	$x^{6} - 2 x^{5} + x^{4} - 3 x^{3} - x^{2} - 2 x - 1$	$6$	[2,2]	$17^{2}\cdot 43^{2}$	$2$	$9.00822293742$	$27.03701166919155$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.48930083856$
6.2.547600.1	$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 4$	$6$	[2,2]	$2^{4}\cdot 5^{2}\cdot 37^{2}$	$3$	$9.04504169651$	$21.590988593881082$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$7.63832166666$
6.2.553536.1	$x^{6} - 4 x^{4} + 9 x^{2} - 9$	$6$	[2,2]	$2^{6}\cdot 3^{2}\cdot 31^{2}$	$3$	$9.06130979217$	$27.27636339397171$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.85947053858$
6.2.553536.2	$x^{6} + x^{4} - 6 x^{2} - 9$	$6$	[2,2]	$2^{6}\cdot 3^{2}\cdot 31^{2}$	$3$	$9.06130979217$	$27.27636339397171$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.00547724682$
6.2.561001.1	$x^{6} - 2 x^{5} + x^{4} + 3 x^{3} - x^{2} - 2 x - 1$	$6$	[2,2]	$7^{2}\cdot 107^{2}$	$2$	$9.08156312238$	$27.367864366808018$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.59258175436$
6.2.564001.1	$x^{6} - x^{4} + 6 x^{2} - 1$	$6$	[2,2]	$751^{2}$	$1$	$9.08963921656$	$27.40437921208944$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.77598974271$
6.2.579121.1	$x^{6} - x^{4} - 6 x^{2} - 1$	$6$	[2,2]	$761^{2}$	$1$	$9.12980606272$	$27.586228448267445$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.49348437938$
6.2.620944.1	$x^{6} - 2 x^{5} + 2 x^{3} - 8 x + 8$	$6$	[2,2]	$2^{4}\cdot 197^{2}$	$2$	$9.2365277459$	$22.280235493786417$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$8.34592512065$
6.2.646416.1	$x^{6} - 2 x^{5} + 4 x^{4} - 10 x^{3} + 8 x^{2} - 8 x + 8$	$6$	[2,2]	$2^{4}\cdot 3^{2}\cdot 67^{2}$	$3$	$9.29862391479$	$22.50529408956344$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$8.69427755878$
6.2.648025.1	$x^{6} - x^{5} - 3 x^{4} + 9 x^{3} + 7 x^{2} - 21 x - 19$	$6$	[2,2]	$5^{2}\cdot 7^{2}\cdot 23^{2}$	$3$	$9.30247746845$	$28.372521918222215$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$3.13659811718$
6.2.652864.1	$x^{6} - 2 x^{5} - x^{4} + 2 x^{3} - x^{2} - 2 x + 1$	$6$	[2,2]	$2^{6}\cdot 101^{2}$	$2$	$9.31401901561$	$22.561207949875573$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$5.93287136285$
6.2.692224.1	$x^{6} - x^{4} + 5 x^{2} - 1$	$6$	[2,2]	$2^{12}\cdot 13^{2}$	$2$	$9.40533875088$	$24.255161140409015$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$8.83600851046$
6.2.712336.1	$x^{6} - x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} - x - 1$	$6$	[2,2]	$2^{4}\cdot 211^{2}$	$2$	$9.4503410569$	$29.0516780926679$				$S_4$ (as 6T7)	trivial	$2$	$3$	$4.92278765587$
6.2.732736.1	$x^{6} - 3 x^{4} + 2 x^{2} - 4$	$6$	[2,2]	$2^{6}\cdot 107^{2}$	$2$	$9.49491879705$	$29.257477676655586$				$S_4$ (as 6T7)	trivial	$2$	$3$	$5.34289215164$
6.2.732736.2	$x^{6} - 2 x^{4} + 4 x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 107^{2}$	$2$	$9.49491879705$	$29.257477676655586$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$6.90855315028$
6.2.746496.1	$x^{6} + 3 x^{4} + 3 x^{2} - 1$	$6$	[2,2]	$2^{10}\cdot 3^{6}$	$2$	$9.52440631181$	$16.17607385516733$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$8.84117393639$
6.2.795664.1	$x^{6} - x^{5} - 2 x^{4} + 6 x^{3} - 4 x^{2} - 4 x + 8$	$6$	[2,2]	$2^{4}\cdot 223^{2}$	$2$	$9.62620157035$	$29.866369046136157$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$10.7597682773$
6.2.846400.1	$x^{6} + 4 x^{4} - 5 x^{2} - 25$	$6$	[2,2]	$2^{6}\cdot 5^{2}\cdot 23^{2}$	$3$	$9.72588826219$	$30.331501776206203$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.43651062742$
6.2.846400.2	$x^{6} - 7 x^{4} + 20 x^{2} - 25$	$6$	[2,2]	$2^{6}\cdot 5^{2}\cdot 23^{2}$	$3$	$9.72588826219$	$30.331501776206203$			?	$S_4$ (as 6T7)	trivial	$2$	$3$	$4.10860721723$
6.2.848241.1	$x^{6} - 2 x^{5} + x^{4} - x^{3} - x^{2} - 2 x - 1$	$6$	[2,2]	$3^{2}\cdot 307^{2}$	$2$	$9.72941085875$	$30.347981810987037$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$5.38233678524$