Number field search results

Results (1-50 of 136022 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.0.12167.1	x^6 - 3x^5 + 5x^4 - 5x^3 + 5x^2 - 3x + 1	$6$	[0,3]	$-\,23^{3}$	$1$	$4.79583152331$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.237219601798$
6.0.21296.1	x^6 - x^5 + 2x^4 - 3x^3 + 2x^2 - x + 1	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}$	$2$	$5.26481368119$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.371341380446$
6.0.29791.1	x^6 - 3x^5 + 7x^4 - 9x^3 + 7x^2 - 3x + 1	$6$	[0,3]	$-\,31^{3}$	$1$	$5.56776436283$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$0.438333916947$
6.0.34992.1	x^6 - 3x^5 + 5x^3 - 3x + 1	$6$	[0,3]	$-\,2^{4}\cdot 3^{7}$	$2$	$5.71910575798$		✓	✓	$S_3$ (as 6T2)	trivial	$6$	$2$	$1.81542571879$
6.0.109744.2	x^6 - 3x^5 + 4x^4 - 3x^3 + 4x^2 - 3x + 1	$6$	[0,3]	$-\,2^{4}\cdot 19^{3}$	$2$	$6.9193207684$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$1.03752929532$
6.0.177147.2	x^6 + 3	$6$	[0,3]	$-\,3^{11}$	$1$	$7.4941485989$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$6.37401619527$
6.0.205379.1	x^6 - 3x^5 + 10x^4 - 15x^3 + 21x^2 - 14x + 4	$6$	[0,3]	$-\,59^{3}$	$1$	$7.68114574787$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$1.87697523076$
6.0.214375.1	x^6 - 3x^5 + x^4 + 3x^3 + x^2 - 3x + 1	$6$	[0,3]	$-\,5^{4}\cdot 7^{3}$	$2$	$7.73622376445$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$2$	$1.66024903333$
6.0.270000.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 2x^2 + 3x + 3	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 5^{4}$	$3$	$8.03946768766$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$9.91336443041$
6.0.273375.1	x^6 - 3x^5 + 3x^4 - x^3 + 3x^2 - 3x + 1	$6$	[0,3]	$-\,3^{7}\cdot 5^{3}$	$2$	$8.0561300054$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$1.28284678343$
6.0.320000.1	x^6 + 4x^4 - 3x^2 + 2	$6$	[0,3]	$-\,2^{9}\cdot 5^{4}$	$2$	$8.270371084$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$6.78289627425$
6.0.419904.2	x^6 - 2x^3 + 9x^2 + 6x + 2	$6$	[0,3]	$-\,2^{6}\cdot 3^{8}$	$2$	$8.65349742184$		✓		$S_3$ (as 6T2)	trivial	$4$	$2$	$16.3834035457$
6.0.571787.1	x^6 - x^4 - 4x^3 + 21x^2 + 2x + 4	$6$	[0,3]	$-\,83^{3}$	$1$	$9.11043357914$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$3.24912325959$
6.0.658503.1	x^6 - 2x^5 + 4x^4 - 9x^3 + 30x^2 - 9x + 9	$6$	[0,3]	$-\,3^{3}\cdot 29^{3}$	$2$	$9.32737905309$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.62180465573$
6.0.686000.1	x^6 - 3x^5 + 8x^4 - 11x^3 + 8x^2 - 3x + 1	$6$	[0,3]	$-\,2^{4}\cdot 5^{3}\cdot 7^{3}$	$3$	$9.39119127122$		✓	✓	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$2.17170587094$
6.6.810448.1	x^6 - 3x^5 - 2x^4 + 9x^3 - 5x + 1	$6$	[6,0]	$2^{4}\cdot 37^{3}$	$2$	$9.65578363947$		✓	✓	$S_3$ (as 6T2)	trivial	$2$	$5$	$6.88569152204$
6.0.937024.1	x^6 - 7x^4 + 20x^2 + 4	$6$	[0,3]	$-\,2^{6}\cdot 11^{4}$	$2$	$9.8921748865$		✓		$S_3$ (as 6T2)	trivial	$4$	$2$	$28.1184752065$
6.0.1037232.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 8x^2 + 9x + 27	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 7^{4}$	$3$	$10.0611120208$		✓	?	$S_3$ (as 6T2)	$[3]$	$6$	$2$	$8.20718967516$
6.0.1119744.1	x^6 - 3x^2 + 6	$6$	[0,3]	$-\,2^{9}\cdot 3^{7}$	$2$	$10.1902879774$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$9.14201835091$
6.0.1124864.1	x^6 + 8x^4 + 29x^2 + 26	$6$	[0,3]	$-\,2^{9}\cdot 13^{3}$	$2$	$10.1980390272$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$7.45211242637$
6.0.1225043.1	x^6 - 2x^5 - 2x^3 + 30x^2 - 52x + 29	$6$	[0,3]	$-\,107^{3}$	$1$	$10.3440804328$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$4.73303546266$
6.0.1272112.1	x^6 - 3x^5 + 10x^4 - 15x^3 + 10x^2 - 3x + 1	$6$	[0,3]	$-\,2^{4}\cdot 43^{3}$	$2$	$10.4092848117$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$3.54174675403$
6.0.1366875.1	x^6 - 3x^5 + 6x^4 + 3x^3 - 9x^2 - 18x + 36	$6$	[0,3]	$-\,3^{7}\cdot 5^{4}$	$2$	$10.5346828782$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$23.1552144564$
6.0.1560896.1	x^6 - 2x^5 - x^4 + 10x^3 + 22x^2 - 8x + 16	$6$	[0,3]	$-\,2^{6}\cdot 29^{3}$	$2$	$10.7703296143$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$8.84972580022$
6.0.1827904.2	x^6 - 2x^5 + 2x^4 - 6x^3 + 25x^2 - 20x + 8	$6$	[0,3]	$-\,2^{6}\cdot 13^{4}$	$2$	$11.0575496274$		✓		$S_3$ (as 6T2)	$[3]$	$4$	$2$	$14.336855128$
6.0.2122416.1	x^6 - x^5 + 4x^4 - 15x^3 + 30x^2 - 27x + 9	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 17^{3}$	$3$	$11.336311$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$5.5443468539$
6.0.2250423.3	x^6 + 6x^4 + 9x^2 + 7	$6$	[0,3]	$-\,3^{8}\cdot 7^{3}$	$2$	$11.4475010746$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$6.07139649505$
6.0.2255067.2	x^6 + x^4 - 11x^2 + 12	$6$	[0,3]	$-\,3^{3}\cdot 17^{4}$	$2$	$11.4514348937$		✓		$S_3$ (as 6T2)	trivial	$6$	$2$	$47.3247498433$
6.0.2685619.1	x^6 + 3x^4 - 12x^3 + 37x^2 - 18x + 36	$6$	[0,3]	$-\,139^{3}$	$1$	$11.7898261226$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$8.30224307268$
6.0.2834352.1	x^6 + 12	$6$	[0,3]	$-\,2^{4}\cdot 3^{11}$	$2$	$11.8962193695$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$26.0695560056$
6.0.2834352.2	x^6 + 48	$6$	[0,3]	$-\,2^{4}\cdot 3^{11}$	$2$	$11.8962193695$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$33.5233142127$
6.0.3359232.4	x^6 - 6x^4 + 9x^2 + 8	$6$	[0,3]	$-\,2^{9}\cdot 3^{8}$	$2$	$12.2378934159$		✓		$S_3$ (as 6T2)	$[3]$	$2$	$2$	$14.966213861$
6.0.3511808.1	x^6 - 2x^5 + 5x^4 + 4x^3 + 34x^2 + 16x + 16	$6$	[0,3]	$-\,2^{9}\cdot 19^{3}$	$2$	$12.3288280059$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$13.6189518389$
6.0.3518667.2	x^6 - 3x^5 + 4x^4 - 3x^3 - 5x^2 + 6x + 12	$6$	[0,3]	$-\,3^{3}\cdot 19^{4}$	$2$	$12.3328380342$		✓		$S_3$ (as 6T2)	$[3]$	$6$	$2$	$20.736073885$
6.0.4804839.1	x^6 - 3x^5 + 9x^4 - 13x^3 + 9x^2 - 3x + 1	$6$	[0,3]	$-\,3^{7}\cdot 13^{3}$	$2$	$12.9901193115$		✓	✓	$S_3$ (as 6T2)	$[4]$	$2$	$2$	$2.89774139562$
6.0.4812208.1	x^6 - x^5 + 8x^4 - 23x^3 + 34x^2 - 27x + 9	$6$	[0,3]	$-\,2^{4}\cdot 67^{3}$	$2$	$12.9934376008$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$2$	$6.35661753635$
6.0.5250987.1	x^6 - 3x^5 + 6x^4 + 7x^3 - 15x^2 - 24x + 64	$6$	[0,3]	$-\,3^{7}\cdot 7^{4}$	$2$	$13.1837863724$		✓		$S_3$ (as 6T2)	$[3]$	$6$	$2$	$17.8762700749$
6.0.6324912.1	x^6 + x^4 - 29x^2 + 75	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 11^{4}$	$3$	$13.5990659908$		✓	?	$S_3$ (as 6T2)	trivial	$6$	$2$	$68.8201495224$
6.0.7880599.1	x^6 - 3x^4 - 5x^3 + 52x^2 - 92x + 56	$6$	[0,3]	$-\,199^{3}$	$1$	$14.1067359797$		✓	?	$S_3$ (as 6T2)	$[3]$	$2$	$2$	$5.3599620383$
6.0.8732691.5	x^6 - 6x^4 + 9x^2 + 44	$6$	[0,3]	$-\,3^{8}\cdot 11^{3}$	$2$	$14.3502020363$		✓		$S_3$ (as 6T2)	$[3]$	$2$	$2$	$9.68047363147$
6.0.9393931.1	x^6 - 2x^5 + 4x^4 - 18x^3 + 70x^2 - 128x + 109	$6$	[0,3]	$-\,211^{3}$	$1$	$14.5258390463$		✓		$S_3$ (as 6T2)	trivial	$2$	$2$	$15.0210026203$
6.0.9528128.1	x^6 - 4x^4 - 6x^3 + 57x^2 - 94x + 62	$6$	[0,3]	$-\,2^{6}\cdot 53^{3}$	$2$	$14.5602197786$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$22.0771387497$
6.0.10744731.1	x^6 - 3x^5 + 9x^4 - 3x^2 + 27x + 33	$6$	[0,3]	$-\,3^{7}\cdot 17^{3}$	$2$	$14.8547697477$		✓		$S_3$ (as 6T2)	$[2]$	$2$	$2$	$13.4648151135$
6.6.12002256.1	x^6 - 3x^5 - 6x^4 + 17x^3 - 6x^2 - 3x + 1	$6$	[6,0]	$2^{4}\cdot 3^{7}\cdot 7^{3}$	$3$	$15.1313315573$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$5$	$50.7574928582$
6.6.12008989.1	x^6 - 2x^5 - 14x^4 + 14x^2 - 2x - 1	$6$	[6,0]	$229^{3}$	$1$	$15.1327459504$		✓		$S_3$ (as 6T2)	trivial	$2$	$5$	$45.1476260287$
6.0.12057136.1	x^6 - 3x^5 + 14x^4 - 23x^3 + 44x^2 - 33x + 9	$6$	[0,3]	$-\,2^{4}\cdot 7^{3}\cdot 13^{3}$	$3$	$15.1428409184$		✓	?	$S_3$ (as 6T2)	$[2]$	$2$	$2$	$8.62111730461$
6.0.12326391.1	x^6 - 2x^5 + 4x^4 + 15x^3 + 42x^2 + 27x + 81	$6$	[0,3]	$-\,3^{3}\cdot 7^{3}\cdot 11^{3}$	$3$	$15.1986841536$		✓	?	$S_3$ (as 6T2)	$[2, 2]$	$2$	$2$	$9.14020743573$
6.0.12338352.2	x^6 + x^4 - 17x^2 + 27	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 13^{4}$	$3$	$15.2011411853$		✓	?	$S_3$ (as 6T2)	$[3]$	$6$	$2$	$32.3403639963$
6.6.13122000.1	x^6 - 12x^4 + 36x^2 - 20	$6$	[6,0]	$2^{4}\cdot 3^{8}\cdot 5^{3}$	$3$	$15.357953167$		✓	?	$S_3$ (as 6T2)	trivial	$2$	$5$	$49.7510765355$
6.0.13651919.1	x^6 - 2x^5 + 8x^4 + 11x^3 + 54x^2 + 63x + 81	$6$	[0,3]	$-\,239^{3}$	$1$	$15.4596248337$		✓		$S_3$ (as 6T2)	$[5]$	$2$	$2$	$13.1864653705$