Number field search results

Results (1-50 of 886745 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
6.6.300125.1	x^6 - x^5 - 7x^4 + 2x^3 + 7x^2 - 2x - 1	$6$	[6,0]	$5^{3}\cdot 7^{4}$	$2$	$8.18245631806$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.27756260865$
6.6.371293.1	x^6 - x^5 - 5x^4 + 4x^3 + 6x^2 - 3x - 1	$6$	[6,0]	$13^{5}$	$1$	$8.47785778235$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.77450098008$
6.6.434581.1	x^6 - 2x^5 - 4x^4 + 5x^3 + 4x^2 - 2x - 1	$6$	[6,0]	$7^{4}\cdot 181$	$2$	$8.70318982123$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$4.18794361412$
6.6.453789.1	x^6 - x^5 - 6x^4 + 6x^3 + 8x^2 - 8x + 1	$6$	[6,0]	$3^{3}\cdot 7^{5}$	$2$	$8.7661519443$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$4.39996237517$
6.6.485125.1	x^6 - 2x^5 - 4x^4 + 8x^3 + 2x^2 - 5x + 1	$6$	[6,0]	$5^{3}\cdot 3881$	$2$	$8.86425571331$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$4.52548380861$
6.6.592661.1	x^6 - x^5 - 5x^4 + 4x^3 + 5x^2 - 2x - 1	$6$	[6,0]	$592661$	$1$	$9.16504056635$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$5.23352484306$
6.6.703493.1	x^6 - 2x^5 - 5x^4 + 11x^3 + 2x^2 - 9x + 1	$6$	[6,0]	$7^{4}\cdot 293$	$2$	$9.4306862545$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$5.70730462791$
6.6.722000.1	x^6 - x^5 - 6x^4 + 7x^3 + 4x^2 - 5x + 1	$6$	[6,0]	$2^{4}\cdot 5^{3}\cdot 19^{2}$	$3$	$9.47158947509$			✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$6.412993699$
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	$2$	$5$	$6.88569152204$
6.6.820125.1	x^6 - 9x^4 - 4x^3 + 9x^2 + 3x - 1	$6$	[6,0]	$3^{8}\cdot 5^{3}$	$2$	$9.67490423918$		✓	not computed	$C_6$ (as 6T1)	trivial	$2$	$5$	$6.28127608708$
6.6.905177.1	x^6 - x^5 - 7x^4 + 9x^3 + 7x^2 - 9x - 1	$6$	[6,0]	$7^{4}\cdot 13\cdot 29$	$3$	$9.83532959706$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$6.90930178248$
6.6.966125.1	x^6 - x^5 - 6x^4 + 4x^3 + 8x^2 - 1	$6$	[6,0]	$5^{3}\cdot 59\cdot 131$	$3$	$9.94272787777$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.42490450656$
6.6.980125.1	x^6 - x^5 - 6x^4 + 6x^3 + 7x^2 - 5x - 1	$6$	[6,0]	$5^{3}\cdot 7841$	$2$	$9.96659730416$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.116083735$
6.6.1075648.1	x^6 - 7x^4 + 14x^2 - 7	$6$	[6,0]	$2^{6}\cdot 7^{5}$	$2$	$10.1222803696$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$7.70329572133$
6.6.1081856.1	x^6 - 6x^4 - 2x^3 + 7x^2 + 2x - 1	$6$	[6,0]	$2^{9}\cdot 2113$	$2$	$10.1319936672$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.75742497148$
6.6.1134389.1	x^6 - 2x^5 - 4x^4 + 6x^3 + 4x^2 - 3x - 1	$6$	[6,0]	$1134389$	$1$	$10.2123808154$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$7.81522393133$
6.6.1202933.1	x^6 - 6x^4 - 2x^3 + 6x^2 + x - 1	$6$	[6,0]	$79\cdot 15227$	$2$	$10.3127282342$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$8.74066379511$
6.6.1229312.1	x^6 - 10x^4 + 24x^2 - 8	$6$	[6,0]	$2^{9}\cdot 7^{4}$	$2$	$10.350079528$		✓	not computed	$C_6$ (as 6T1)	trivial	$2$	$5$	$8.7234383498$
6.6.1241125.1	x^6 - 7x^4 - 2x^3 + 11x^2 + 7x + 1	$6$	[6,0]	$5^{3}\cdot 9929$	$2$	$10.3665899557$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$8.83717312888$
6.6.1259712.1	x^6 - 6x^4 + 9x^2 - 3	$6$	[6,0]	$2^{6}\cdot 3^{9}$	$2$	$10.3923048454$		✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$10.1773563373$
6.6.1279733.1	x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11x - 1	$6$	[6,0]	$7^{4}\cdot 13\cdot 41$	$3$	$10.4196523294$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$8.72407995991$
6.6.1292517.1	x^6 - 6x^4 - x^3 + 6x^2 - 1	$6$	[6,0]	$3^{8}\cdot 197$	$2$	$10.4369285573$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$8.26722390741$
6.6.1312625.1	x^6 - x^5 - 7x^4 + 7x^3 + 12x^2 - 12x - 1	$6$	[6,0]	$5^{3}\cdot 10501$	$2$	$10.4638164259$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$9.40484434468$
6.6.1387029.1	x^6 - 3x^5 - 2x^4 + 9x^3 - x^2 - 4x + 1	$6$	[6,0]	$3\cdot 7\cdot 257^{2}$	$3$	$10.5604134987$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$5$	$10.9212586359$
6.6.1397493.1	x^6 - 3x^5 - 3x^4 + 10x^3 + 3x^2 - 6x + 1	$6$	[6,0]	$3^{9}\cdot 71$	$2$	$10.5736502323$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.6270681396$
6.6.1416125.1	x^6 - 2x^5 - 5x^4 + 9x^3 + 6x^2 - 9x + 1	$6$	[6,0]	$5^{3}\cdot 11329$	$2$	$10.5970162011$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$9.38458097367$
6.6.1528713.1	x^6 - 3x^5 - 3x^4 + 7x^3 + 3x^2 - 3x - 1	$6$	[6,0]	$3^{8}\cdot 233$	$2$	$10.7329966333$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$9.67459060125$
6.6.1541581.1	x^6 - x^5 - 6x^4 + 2x^3 + 9x^2 + x - 1	$6$	[6,0]	$1541581$	$1$	$10.7480016599$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$9.99612092275$
6.6.1683101.1	x^6 - 3x^5 - 4x^4 + 13x^3 + 7x^2 - 14x - 7	$6$	[6,0]	$7^{4}\cdot 701$	$2$	$10.906490607$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.3750728693$
6.6.1767625.1	x^6 - 7x^4 - x^3 + 11x^2 + x - 1	$6$	[6,0]	$5^{3}\cdot 79\cdot 179$	$3$	$10.9959229802$			not computed	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$11.518079481$
6.6.1868969.1	x^6 - 6x^4 - x^3 + 8x^2 + x - 2	$6$	[6,0]	$107\cdot 17467$	$2$	$11.0985697646$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$16.3209539925$
6.6.1922000.1	x^6 - x^5 - 8x^4 - x^3 + 12x^2 + 7x + 1	$6$	[6,0]	$2^{4}\cdot 5^{3}\cdot 31^{2}$	$3$	$11.1504457879$			✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$12.1140316048$
6.6.1995125.1	x^6 - 2x^5 - 6x^4 + 6x^3 + 12x^2 + x - 1	$6$	[6,0]	$5^{3}\cdot 11\cdot 1451$	$3$	$11.2200558429$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$10.6947286971$
6.6.1997632.1	x^6 - 8x^4 + 19x^2 - 13	$6$	[6,0]	$2^{6}\cdot 7^{4}\cdot 13$	$3$	$11.2224043978$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.8499143067$
6.6.2115281.1	x^6 - x^5 - 8x^4 + 5x^3 + 16x^2 - 4x - 8	$6$	[6,0]	$7^{4}\cdot 881$	$2$	$11.3299504727$			not computed	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$11.5568148167$
6.6.2235125.1	x^6 - x^5 - 7x^4 + 2x^3 + 12x^2 + 3x - 1	$6$	[6,0]	$5^{3}\cdot 17881$	$2$	$11.4344944851$			not computed	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$12.0760758381$
6.6.2249737.1	x^6 - 2x^5 - 7x^4 + 9x^3 + 14x^2 - 8x - 8	$6$	[6,0]	$7^{4}\cdot 937$	$2$	$11.4469194074$			not computed	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$11.9821781995$
6.6.2286997.1	x^6 - 7x^4 + 13x^2 - x - 5	$6$	[6,0]	$349\cdot 6553$	$2$	$11.4783007335$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.514812154$
6.6.2323397.1	x^6 - 6x^4 + 8x^2 - x - 1	$6$	[6,0]	$2323397$	$1$	$11.5085489883$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$14.7668367318$
6.6.2415125.1	x^6 - x^5 - 8x^4 + 5x^3 + 19x^2 - 4x - 11	$6$	[6,0]	$5^{3}\cdot 139^{2}$	$2$	$11.5830590114$			✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$11.9539682677$
6.6.2460365.1	x^6 - x^5 - 6x^4 + 6x^3 + 7x^2 - 7x + 1	$6$	[6,0]	$5\cdot 263\cdot 1871$	$3$	$11.6189421679$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$14.1458776568$
6.6.2495261.1	x^6 - x^5 - 6x^4 + 6x^3 + 6x^2 - 6x + 1	$6$	[6,0]	$199\cdot 12539$	$2$	$11.6462469957$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.4998566487$
6.6.2501557.1	x^6 - x^5 - 6x^4 + 3x^3 + 9x^2 - 2x - 3	$6$	[6,0]	$769\cdot 3253$	$2$	$11.6511394566$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.344757047$
6.6.2540864.1	x^6 - 8x^4 - 4x^3 + 12x^2 + 10x + 2	$6$	[6,0]	$2^{6}\cdot 29\cdot 37^{2}$	$3$	$11.6814540057$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$5$	$19.7404765035$
6.6.2565429.1	x^6 - 6x^4 - x^3 + 8x^2 + 2x - 1	$6$	[6,0]	$3\cdot 855143$	$2$	$11.7002012871$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$16.8022557829$
6.6.2591125.1	x^6 - x^5 - 7x^4 + 6x^3 + 10x^2 - 9x + 1	$6$	[6,0]	$5^{3}\cdot 19\cdot 1091$	$3$	$11.7196523068$			not computed	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$13.5329996899$
6.6.2623625.1	x^6 - x^5 - 7x^4 + 5x^3 + 13x^2 - 6x - 4	$6$	[6,0]	$5^{3}\cdot 139\cdot 151$	$3$	$11.7440248112$			not computed	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$15.387644903$
6.6.2624293.1	x^6 - x^5 - 9x^4 + 8x^3 + 21x^2 - 14x - 7	$6$	[6,0]	$7^{4}\cdot 1093$	$2$	$11.7445231152$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$13.467860582$
6.6.2661761.1	x^6 - x^5 - 6x^4 + 3x^3 + 9x^2 - x - 1	$6$	[6,0]	$41\cdot 64921$	$2$	$11.7723051137$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$21.0611553343$
6.6.2666432.1	x^6 - 2x^5 - 6x^4 + 4x^3 + 7x^2 - 2x - 1	$6$	[6,0]	$2^{6}\cdot 61\cdot 683$	$3$	$11.7757457102$			✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$13.0212252837$