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Results (1-50 of 886745 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.6.300125.1	$x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1$	$6$	[6,0]	$5^{3}\cdot 7^{4}$	$2$	$8.18245631806$	$8.182456318064498$	✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.27756260865$
6.6.371293.1	$x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 6 x^{2} - 3 x - 1$	$6$	[6,0]	$13^{5}$	$1$	$8.47785778235$	$8.477857782354299$	✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$3.77450098008$
6.6.434581.1	$x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1$	$6$	[6,0]	$7^{4}\cdot 181$	$2$	$8.70318982123$	$49.23092329595919$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$4.18794361412$
6.6.453789.1	$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 8 x^{2} - 8 x + 1$	$6$	[6,0]	$3^{3}\cdot 7^{5}$	$2$	$8.7661519443$	$8.766151944295878$	✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$4.39996237517$
6.6.485125.1	$x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1$	$6$	[6,0]	$5^{3}\cdot 3881$	$2$	$8.86425571331$	$139.30183056945089$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$4.52548380861$
6.6.592661.1	$x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 5 x^{2} - 2 x - 1$	$6$	[6,0]	$592661$	$1$	$9.16504056635$	$769.8447895517642$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$5.23352484306$
6.6.703493.1	$x^{6} - 2 x^{5} - 5 x^{4} + 11 x^{3} + 2 x^{2} - 9 x + 1$	$6$	[6,0]	$7^{4}\cdot 293$	$2$	$9.4306862545$	$62.637224203074084$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$5.70730462791$
6.6.722000.1	$x^{6} - x^{5} - 6 x^{4} + 7 x^{3} + 4 x^{2} - 5 x + 1$	$6$	[6,0]	$2^{4}\cdot 5^{3}\cdot 19^{2}$	$3$	$9.47158947509$	$25.274004971349576$		✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$6.412993699$
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	$2$	$5$	$6.88569152204$
6.6.820125.1	$x^{6} - 9 x^{4} - 4 x^{3} + 9 x^{2} + 3 x - 1$	$6$	[6,0]	$3^{8}\cdot 5^{3}$	$2$	$9.67490423918$	$9.674904239181682$	✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$6.28127608708$
6.6.905177.1	$x^{6} - x^{5} - 7 x^{4} + 9 x^{3} + 7 x^{2} - 9 x - 1$	$6$	[6,0]	$7^{4}\cdot 13\cdot 29$	$3$	$9.83532959706$	$71.05086481765254$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$6.90930178248$
6.6.966125.1	$x^{6} - x^{5} - 6 x^{4} + 4 x^{3} + 8 x^{2} - 1$	$6$	[6,0]	$5^{3}\cdot 59\cdot 131$	$3$	$9.94272787777$	$196.58331567048106$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.42490450656$
6.6.980125.1	$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 7 x^{2} - 5 x - 1$	$6$	[6,0]	$5^{3}\cdot 7841$	$2$	$9.96659730416$	$198.00252523642217$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.116083735$
6.6.1075648.1	$x^{6} - 7 x^{4} + 14 x^{2} - 7$	$6$	[6,0]	$2^{6}\cdot 7^{5}$	$2$	$10.1222803696$	$10.122280369592772$	✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$7.70329572133$
6.6.1081856.1	$x^{6} - 6 x^{4} - 2 x^{3} + 7 x^{2} + 2 x - 1$	$6$	[6,0]	$2^{9}\cdot 2113$	$2$	$10.1319936672$	$130.01538370516005$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$7.75742497148$
6.6.1134389.1	$x^{6} - 2 x^{5} - 4 x^{4} + 6 x^{3} + 4 x^{2} - 3 x - 1$	$6$	[6,0]	$1134389$	$1$	$10.2123808154$	$1065.0769925221368$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$7.81522393133$
6.6.1202933.1	$x^{6} - 6 x^{4} - 2 x^{3} + 6 x^{2} + x - 1$	$6$	[6,0]	$79\cdot 15227$	$2$	$10.3127282342$	$1096.78302320924$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$8.74066379511$
6.6.1229312.1	$x^{6} - 10 x^{4} + 24 x^{2} - 8$	$6$	[6,0]	$2^{9}\cdot 7^{4}$	$2$	$10.350079528$	$10.350079527967589$	✓	?	$C_6$ (as 6T1)	trivial	$2$	$5$	$8.7234383498$
6.6.1241125.1	$x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1$	$6$	[6,0]	$5^{3}\cdot 9929$	$2$	$10.3665899557$	$222.81157959136684$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$8.83717312888$
6.6.1259712.1	$x^{6} - 6 x^{4} + 9 x^{2} - 3$	$6$	[6,0]	$2^{6}\cdot 3^{9}$	$2$	$10.3923048454$	$10.392304845413264$	✓	✓	$C_6$ (as 6T1)	trivial	$2$	$5$	$10.1773563373$
6.6.1279733.1	$x^{6} - 2 x^{5} - 6 x^{4} + 10 x^{3} + 10 x^{2} - 11 x - 1$	$6$	[6,0]	$7^{4}\cdot 13\cdot 41$	$3$	$10.4196523294$	$84.48163257728737$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$8.72407995991$
6.6.1292517.1	$x^{6} - 6 x^{4} - x^{3} + 6 x^{2} - 1$	$6$	[6,0]	$3^{8}\cdot 197$	$2$	$10.4369285573$	$60.72881209336328$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$8.26722390741$
6.6.1312625.1	$x^{6} - x^{5} - 7 x^{4} + 7 x^{3} + 12 x^{2} - 12 x - 1$	$6$	[6,0]	$5^{3}\cdot 10501$	$2$	$10.4638164259$	$229.13969538253298$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$9.40484434468$
6.6.1387029.1	$x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} - x^{2} - 4 x + 1$	$6$	[6,0]	$3\cdot 7\cdot 257^{2}$	$3$	$10.5604134987$	$73.46427703312679$		✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$5$	$10.9212586359$
6.6.1397493.1	$x^{6} - 3 x^{5} - 3 x^{4} + 10 x^{3} + 3 x^{2} - 6 x + 1$	$6$	[6,0]	$3^{9}\cdot 71$	$2$	$10.5736502323$	$43.78355855797927$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.6270681396$
6.6.1416125.1	$x^{6} - 2 x^{5} - 5 x^{4} + 9 x^{3} + 6 x^{2} - 9 x + 1$	$6$	[6,0]	$5^{3}\cdot 11329$	$2$	$10.5970162011$	$238.0021008310641$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$9.38458097367$
6.6.1528713.1	$x^{6} - 3 x^{5} - 3 x^{4} + 7 x^{3} + 3 x^{2} - 3 x - 1$	$6$	[6,0]	$3^{8}\cdot 233$	$2$	$10.7329966333$	$66.04495269844504$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$9.67459060125$
6.6.1541581.1	$x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1$	$6$	[6,0]	$1541581$	$1$	$10.7480016599$	$1241.6042042454592$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$9.99612092275$
6.6.1683101.1	$x^{6} - 3 x^{5} - 4 x^{4} + 13 x^{3} + 7 x^{2} - 14 x - 7$	$6$	[6,0]	$7^{4}\cdot 701$	$2$	$10.906490607$	$96.88525849614126$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.3750728693$
6.6.1767625.1	$x^{6} - 7 x^{4} - x^{3} + 11 x^{2} + x - 1$	$6$	[6,0]	$5^{3}\cdot 79\cdot 179$	$3$	$10.9959229802$	$265.90411805761863$		?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$11.518079481$
6.6.1868969.1	$x^{6} - 6 x^{4} - x^{3} + 8 x^{2} + x - 2$	$6$	[6,0]	$107\cdot 17467$	$2$	$11.0985697646$	$1367.1024102092717$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$16.3209539925$
6.6.1922000.1	$x^{6} - x^{5} - 8 x^{4} - x^{3} + 12 x^{2} + 7 x + 1$	$6$	[6,0]	$2^{4}\cdot 5^{3}\cdot 31^{2}$	$3$	$11.1504457879$	$35.02779466367995$		✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$12.1140316048$
6.6.1995125.1	$x^{6} - 2 x^{5} - 6 x^{4} + 6 x^{3} + 12 x^{2} + x - 1$	$6$	[6,0]	$5^{3}\cdot 11\cdot 1451$	$3$	$11.2200558429$	$282.49778760195625$		✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$10.6947286971$
6.6.1997632.1	$x^{6} - 8 x^{4} + 19 x^{2} - 13$	$6$	[6,0]	$2^{6}\cdot 7^{4}\cdot 13$	$3$	$11.2224043978$	$37.31774244321726$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$10.8499143067$
6.6.2115281.1	$x^{6} - x^{5} - 8 x^{4} + 5 x^{3} + 16 x^{2} - 4 x - 8$	$6$	[6,0]	$7^{4}\cdot 881$	$2$	$11.3299504727$	$108.61420995503914$		?	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$11.5568148167$
6.6.2235125.1	$x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 12 x^{2} + 3 x - 1$	$6$	[6,0]	$5^{3}\cdot 17881$	$2$	$11.4344944851$	$299.0066888883926$		?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$12.0760758381$
6.6.2249737.1	$x^{6} - 2 x^{5} - 7 x^{4} + 9 x^{3} + 14 x^{2} - 8 x - 8$	$6$	[6,0]	$7^{4}\cdot 937$	$2$	$11.4469194074$	$112.01301543929661$		?	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$11.9821781995$
6.6.2286997.1	$x^{6} - 7 x^{4} + 13 x^{2} - x - 5$	$6$	[6,0]	$349\cdot 6553$	$2$	$11.4783007335$	$1512.2820504125546$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.514812154$
6.6.2323397.1	$x^{6} - 6 x^{4} + 8 x^{2} - x - 1$	$6$	[6,0]	$2323397$	$1$	$11.5085489883$	$1524.2693331560536$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$14.7668367318$
6.6.2415125.1	$x^{6} - x^{5} - 8 x^{4} + 5 x^{3} + 19 x^{2} - 4 x - 11$	$6$	[6,0]	$5^{3}\cdot 139^{2}$	$2$	$11.5830590114$	$60.001420981750954$		✓	$S_3\times C_3$ (as 6T5)	trivial	$2$	$5$	$11.9539682677$
6.6.2460365.1	$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 7 x^{2} - 7 x + 1$	$6$	[6,0]	$5\cdot 263\cdot 1871$	$3$	$11.6189421679$	$1568.5550675701506$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$14.1458776568$
6.6.2495261.1	$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 6 x^{2} - 6 x + 1$	$6$	[6,0]	$199\cdot 12539$	$2$	$11.6462469957$	$1579.6395158389778$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.4998566487$
6.6.2501557.1	$x^{6} - x^{5} - 6 x^{4} + 3 x^{3} + 9 x^{2} - 2 x - 3$	$6$	[6,0]	$769\cdot 3253$	$2$	$11.6511394566$	$1581.6311200782563$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$15.344757047$
6.6.2540864.1	$x^{6} - 8 x^{4} - 4 x^{3} + 12 x^{2} + 10 x + 2$	$6$	[6,0]	$2^{6}\cdot 29\cdot 37^{2}$	$3$	$11.6814540057$	$73.5362573575022$		✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$5$	$19.7404765035$
6.6.2565429.1	$x^{6} - 6 x^{4} - x^{3} + 8 x^{2} + 2 x - 1$	$6$	[6,0]	$3\cdot 855143$	$2$	$11.7002012871$	$1601.69566397615$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$16.8022557829$
6.6.2591125.1	$x^{6} - x^{5} - 7 x^{4} + 6 x^{3} + 10 x^{2} - 9 x + 1$	$6$	[6,0]	$5^{3}\cdot 19\cdot 1091$	$3$	$11.7196523068$	$321.93943529800754$		?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$13.5329996899$
6.6.2623625.1	$x^{6} - x^{5} - 7 x^{4} + 5 x^{3} + 13 x^{2} - 6 x - 4$	$6$	[6,0]	$5^{3}\cdot 139\cdot 151$	$3$	$11.7440248112$	$323.95215696148716$		?	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$5$	$15.387644903$
6.6.2624293.1	$x^{6} - x^{5} - 9 x^{4} + 8 x^{3} + 21 x^{2} - 14 x - 7$	$6$	[6,0]	$7^{4}\cdot 1093$	$2$	$11.7445231152$	$120.97866125640319$		✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$5$	$13.467860582$
6.6.2661761.1	$x^{6} - x^{5} - 6 x^{4} + 3 x^{3} + 9 x^{2} - x - 1$	$6$	[6,0]	$41\cdot 64921$	$2$	$11.7723051137$	$1631.4904228955804$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$21.0611553343$
6.6.2666432.1	$x^{6} - 2 x^{5} - 6 x^{4} + 4 x^{3} + 7 x^{2} - 2 x - 1$	$6$	[6,0]	$2^{6}\cdot 61\cdot 683$	$3$	$11.7757457102$	$686.5588373862812$		✓	$S_6$ (as 6T16)	trivial	$2$	$5$	$13.0212252837$

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