Number field search results

Results (1-50 of 136022 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
6.0.12167.1	$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,23^{3}$	$1$	$4.79583152331$	$4.795831523312719$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.237219601798$
6.0.21296.1	$x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}$	$2$	$5.26481368119$	$5.264813681193971$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.371341380446$
6.0.29791.1	$x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} + 7 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,31^{3}$	$1$	$5.56776436283$	$5.5677643628300215$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.438333916947$
6.0.34992.1	$x^{6} - 3 x^{5} + 5 x^{3} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 3^{7}$	$2$	$5.71910575798$	$5.71910575798162$		✓	✓	$S_3$ (as 6T2)	trivial	$6$	$2$	$1.81542571879$
6.0.109744.2	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 19^{3}$	$2$	$6.9193207684$	$6.919320768399539$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$1.03752929532$
6.0.177147.2	$x^{6} + 3$	$6$	[0,3]	$-\,3^{11}$	$1$	$7.4941485989$	$7.494148598900439$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$6.37401619527$
6.0.205379.1	$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 21 x^{2} - 14 x + 4$	$6$	[0,3]	$-\,59^{3}$	$1$	$7.68114574787$	$7.681145747868608$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$1.87697523076$
6.0.214375.1	$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} + x^{2} - 3 x + 1$	$6$	[0,3]	$-\,5^{4}\cdot 7^{3}$	$2$	$7.73622376445$	$7.736223764452809$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$1.66024903333$
6.0.270000.1	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} - 2 x^{2} + 3 x + 3$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 5^{4}$	$3$	$8.03946768766$	$8.039467687661697$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$9.91336443041$
6.0.273375.1	$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} + 3 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,3^{7}\cdot 5^{3}$	$2$	$8.0561300054$	$8.05613000539548$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$1.28284678343$
6.0.320000.1	$x^{6} + 4 x^{4} - 3 x^{2} + 2$	$6$	[0,3]	$-\,2^{9}\cdot 5^{4}$	$2$	$8.270371084$	$8.270371084000274$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$6.78289627425$
6.0.419904.2	$x^{6} - 2 x^{3} + 9 x^{2} + 6 x + 2$	$6$	[0,3]	$-\,2^{6}\cdot 3^{8}$	$2$	$8.65349742184$	$8.65349742184445$		✓		$S_3$ (as 6T2)	trivial	$4$	$2$	$16.3834035457$
6.0.571787.1	$x^{6} - x^{4} - 4 x^{3} + 21 x^{2} + 2 x + 4$	$6$	[0,3]	$-\,83^{3}$	$1$	$9.11043357914$	$9.1104335791443$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$3.24912325959$
6.0.658503.1	$x^{6} - 2 x^{5} + 4 x^{4} - 9 x^{3} + 30 x^{2} - 9 x + 9$	$6$	[0,3]	$-\,3^{3}\cdot 29^{3}$	$2$	$9.32737905309$	$9.327379053088816$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.62180465573$
6.0.686000.1	$x^{6} - 3 x^{5} + 8 x^{4} - 11 x^{3} + 8 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 5^{3}\cdot 7^{3}$	$3$	$9.39119127122$	$9.391191271220128$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.17170587094$
6.6.810448.1	$x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} - 5 x + 1$	$6$	[6,0]	$2^{4}\cdot 37^{3}$	$2$	$9.65578363947$	$9.65578363946814$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$5$	$6.88569152204$
6.0.937024.1	$x^{6} - 7 x^{4} + 20 x^{2} + 4$	$6$	[0,3]	$-\,2^{6}\cdot 11^{4}$	$2$	$9.8921748865$	$9.892174886497402$		✓		$S_3$ (as 6T2)	trivial	$4$	$2$	$28.1184752065$
6.0.1037232.1	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} - 8 x^{2} + 9 x + 27$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 7^{4}$	$3$	$10.0611120208$	$10.061112020813587$		✓	?	$S_3$ (as 6T2)	$[3]$	$6$	$2$	$8.20718967516$
6.0.1119744.1	$x^{6} - 3 x^{2} + 6$	$6$	[0,3]	$-\,2^{9}\cdot 3^{7}$	$2$	$10.1902879774$	$10.190287977389717$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$9.14201835091$
6.0.1124864.1	$x^{6} + 8 x^{4} + 29 x^{2} + 26$	$6$	[0,3]	$-\,2^{9}\cdot 13^{3}$	$2$	$10.1980390272$	$10.198039027185569$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$7.45211242637$
6.0.1225043.1	$x^{6} - 2 x^{5} - 2 x^{3} + 30 x^{2} - 52 x + 29$	$6$	[0,3]	$-\,107^{3}$	$1$	$10.3440804328$	$10.344080432788601$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$4.73303546266$
6.0.1272112.1	$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 10 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 43^{3}$	$2$	$10.4092848117$	$10.409284811693793$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$3.54174675403$
6.0.1366875.1	$x^{6} - 3 x^{5} + 6 x^{4} + 3 x^{3} - 9 x^{2} - 18 x + 36$	$6$	[0,3]	$-\,3^{7}\cdot 5^{4}$	$2$	$10.5346828782$	$10.534682878229944$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$23.1552144564$
6.0.1560896.1	$x^{6} - 2 x^{5} - x^{4} + 10 x^{3} + 22 x^{2} - 8 x + 16$	$6$	[0,3]	$-\,2^{6}\cdot 29^{3}$	$2$	$10.7703296143$	$10.770329614269007$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$8.84972580022$
6.0.1827904.2	$x^{6} - 2 x^{5} + 2 x^{4} - 6 x^{3} + 25 x^{2} - 20 x + 8$	$6$	[0,3]	$-\,2^{6}\cdot 13^{4}$	$2$	$11.0575496274$	$11.057549627357744$		✓		$S_3$ (as 6T2)	$[3]$	$4$	$2$	$14.336855128$
6.0.2122416.1	$x^{6} - x^{5} + 4 x^{4} - 15 x^{3} + 30 x^{2} - 27 x + 9$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 17^{3}$	$3$	$11.336311$	$11.336311000024526$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$5.5443468539$
6.0.2250423.3	$x^{6} + 6 x^{4} + 9 x^{2} + 7$	$6$	[0,3]	$-\,3^{8}\cdot 7^{3}$	$2$	$11.4475010746$	$11.447501074569505$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$6.07139649505$
6.0.2255067.2	$x^{6} + x^{4} - 11 x^{2} + 12$	$6$	[0,3]	$-\,3^{3}\cdot 17^{4}$	$2$	$11.4514348937$	$11.451434893652847$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$47.3247498433$
6.0.2685619.1	$x^{6} + 3 x^{4} - 12 x^{3} + 37 x^{2} - 18 x + 36$	$6$	[0,3]	$-\,139^{3}$	$1$	$11.7898261226$	$11.789826122551595$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$8.30224307268$
6.0.2834352.1	$x^{6} + 12$	$6$	[0,3]	$-\,2^{4}\cdot 3^{11}$	$2$	$11.8962193695$	$11.896219369500566$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$26.0695560056$
6.0.2834352.2	$x^{6} + 48$	$6$	[0,3]	$-\,2^{4}\cdot 3^{11}$	$2$	$11.8962193695$	$11.896219369500566$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$33.5233142127$
6.0.3359232.4	$x^{6} - 6 x^{4} + 9 x^{2} + 8$	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}$	$2$	$12.2378934159$	$12.237893415933033$		✓		$S_3$ (as 6T2)	$[3]$	$2$	$2$	$14.966213861$
6.0.3511808.1	$x^{6} - 2 x^{5} + 5 x^{4} + 4 x^{3} + 34 x^{2} + 16 x + 16$	$6$	[0,3]	$-\,2^{9}\cdot 19^{3}$	$2$	$12.3288280059$	$12.328828005937952$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$13.6189518389$
6.0.3518667.2	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} - 5 x^{2} + 6 x + 12$	$6$	[0,3]	$-\,3^{3}\cdot 19^{4}$	$2$	$12.3328380342$	$12.332838034173273$		✓		$S_3$ (as 6T2)	$[3]$	$6$	$2$	$20.736073885$
6.0.4804839.1	$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} + 9 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,3^{7}\cdot 13^{3}$	$2$	$12.9901193115$	$12.99011931146003$		✓	✓	$S_3$ (as 6T2)	$[4]$	$2$	$2$	$2.89774139562$
6.0.4812208.1	$x^{6} - x^{5} + 8 x^{4} - 23 x^{3} + 34 x^{2} - 27 x + 9$	$6$	[0,3]	$-\,2^{4}\cdot 67^{3}$	$2$	$12.9934376008$	$12.993437600801144$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$6.35661753635$
6.0.5250987.1	$x^{6} - 3 x^{5} + 6 x^{4} + 7 x^{3} - 15 x^{2} - 24 x + 64$	$6$	[0,3]	$-\,3^{7}\cdot 7^{4}$	$2$	$13.1837863724$	$13.183786372359444$		✓		$S_3$ (as 6T2)	$[3]$	$6$	$2$	$17.8762700749$
6.0.6324912.1	$x^{6} + x^{4} - 29 x^{2} + 75$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 11^{4}$	$3$	$13.5990659908$	$13.599065990841266$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$68.8201495224$
6.0.7880599.1	$x^{6} - 3 x^{4} - 5 x^{3} + 52 x^{2} - 92 x + 56$	$6$	[0,3]	$-\,199^{3}$	$1$	$14.1067359797$	$14.106735979665885$		✓	?	$S_3$ (as 6T2)	$[3]$	$2$	$2$	$5.3599620383$
6.0.8732691.5	$x^{6} - 6 x^{4} + 9 x^{2} + 44$	$6$	[0,3]	$-\,3^{8}\cdot 11^{3}$	$2$	$14.3502020363$	$14.350202036282921$		✓		$S_3$ (as 6T2)	$[3]$	$2$	$2$	$9.68047363147$
6.0.9393931.1	$x^{6} - 2 x^{5} + 4 x^{4} - 18 x^{3} + 70 x^{2} - 128 x + 109$	$6$	[0,3]	$-\,211^{3}$	$1$	$14.5258390463$	$14.52583904633395$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$15.0210026203$
6.0.9528128.1	$x^{6} - 4 x^{4} - 6 x^{3} + 57 x^{2} - 94 x + 62$	$6$	[0,3]	$-\,2^{6}\cdot 53^{3}$	$2$	$14.5602197786$	$14.560219778561036$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$22.0771387497$
6.0.10744731.1	$x^{6} - 3 x^{5} + 9 x^{4} - 3 x^{2} + 27 x + 33$	$6$	[0,3]	$-\,3^{7}\cdot 17^{3}$	$2$	$14.8547697477$	$14.854769747694963$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$13.4648151135$
6.6.12002256.1	$x^{6} - 3 x^{5} - 6 x^{4} + 17 x^{3} - 6 x^{2} - 3 x + 1$	$6$	[6,0]	$2^{4}\cdot 3^{7}\cdot 7^{3}$	$3$	$15.1313315573$	$15.13133155729692$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$5$	$50.7574928582$
6.6.12008989.1	$x^{6} - 2 x^{5} - 14 x^{4} + 14 x^{2} - 2 x - 1$	$6$	[6,0]	$229^{3}$	$1$	$15.1327459504$	$15.132745950421556$		✓		$S_3$ (as 6T2)	trivial	$2$	$5$	$45.1476260287$
6.0.12057136.1	$x^{6} - 3 x^{5} + 14 x^{4} - 23 x^{3} + 44 x^{2} - 33 x + 9$	$6$	[0,3]	$-\,2^{4}\cdot 7^{3}\cdot 13^{3}$	$3$	$15.1428409184$	$15.142840918429636$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$8.62111730461$
6.0.12326391.1	$x^{6} - 2 x^{5} + 4 x^{4} + 15 x^{3} + 42 x^{2} + 27 x + 81$	$6$	[0,3]	$-\,3^{3}\cdot 7^{3}\cdot 11^{3}$	$3$	$15.1986841536$	$15.198684153570664$		✓	?	$S_3$ (as 6T2)	$[2, 2]$	$2$	$2$	$9.14020743573$
6.0.12338352.2	$x^{6} + x^{4} - 17 x^{2} + 27$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 13^{4}$	$3$	$15.2011411853$	$15.201141185311545$		✓	?	$S_3$ (as 6T2)	$[3]$	$6$	$2$	$32.3403639963$
6.6.13122000.1	$x^{6} - 12 x^{4} + 36 x^{2} - 20$	$6$	[6,0]	$2^{4}\cdot 3^{8}\cdot 5^{3}$	$3$	$15.357953167$	$15.357953166968596$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$5$	$49.7510765355$
6.0.13651919.1	$x^{6} - 2 x^{5} + 8 x^{4} + 11 x^{3} + 54 x^{2} + 63 x + 81$	$6$	[0,3]	$-\,239^{3}$	$1$	$15.4596248337$	$15.459624833740307$		✓		$S_3$ (as 6T2)	$[5]$	$2$	$2$	$13.1864653705$