Number field search results

Results (1-50 of 2119888 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
6.2.28037.1	$x^{6} - 2 x^{5} + 3 x^{3} - 2 x - 1$	$6$	[2,2]	$23^{2}\cdot 53$	$2$	$5.51173831771$	$34.91418050019218$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.478924705547$
6.2.29077.1	$x^{6} - x^{5} + x^{4} - x^{2} + 2 x - 1$	$6$	[2,2]	$29077$	$1$	$5.54529854883$	$170.51979357247652$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.491602105294$
6.2.29189.1	$x^{6} - 2 x^{5} + x^{4} + x^{3} - 2 x^{2} + x + 1$	$6$	[2,2]	$17^{2}\cdot 101$	$2$	$5.54885278411$	$66.44464230590899$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.49291662671$
6.2.30125.1	$x^{6} - x^{5} + x^{4} - 2 x^{2} + x - 1$	$6$	[2,2]	$5^{3}\cdot 241$	$2$	$5.57811986838$	$34.713109915419565$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.50437245294$
6.2.31133.1	$x^{6} - 2 x^{4} - x^{3} + 2 x + 1$	$6$	[2,2]	$163\cdot 191$	$2$	$5.60880268418$	$176.44545899512406$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.516354684031$
6.2.31213.1	$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$	$6$	[2,2]	$7^{4}\cdot 13$	$2$	$5.6112021989$	$13.193814370085985$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$3$	$0.517040346258$
6.2.31709.1	$x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + 1$	$6$	[2,2]	$37\cdot 857$	$2$	$5.62596584169$	$178.07021087200408$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.522986177098$
6.2.32269.1	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$	$6$	[2,2]	$23^{2}\cdot 61$	$2$	$5.64240494139$	$37.456641600656084$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.529910039105$
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	$2$	$3$	$0.550118007418$
6.2.35125.1	$x^{6} - x^{5} - x^{4} + 2 x^{3} - x^{2} + 1$	$6$	[2,2]	$5^{3}\cdot 281$	$2$	$5.72272296207$	$37.48332962798263$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.563512855802$
6.2.35557.1	$x^{6} - 2 x^{4} - x^{3} + 2 x^{2} - 1$	$6$	[2,2]	$31^{2}\cdot 37$	$2$	$5.73439385986$	$33.8673884437522$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.567960387605$
6.2.37253.1	$x^{6} - x^{4} + x^{2} - x - 1$	$6$	[2,2]	$37253$	$1$	$5.77909999053$	$193.01036241611484$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.590723504629$
6.2.37568.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 2 x - 1$	$6$	[2,2]	$2^{6}\cdot 587$	$2$	$5.78721582791$	$81.49323216626063$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.591962874572$
6.2.39269.1	$x^{6} - x^{5} - 2 x^{4} + 2 x^{3} - 2 x + 1$	$6$	[2,2]	$107\cdot 367$	$2$	$5.83008616837$	$198.16407343411166$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.612802015304$
6.2.40277.1	$x^{6} - x^{5} + 2 x^{3} - 3 x^{2} + 3 x - 1$	$6$	[2,2]	$40277$	$1$	$5.85476569062$	$200.6913052426537$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.623496086403$
6.2.40733.1	$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} + 3 x - 1$	$6$	[2,2]	$7\cdot 11\cdot 23^{2}$	$3$	$5.86576148388$	$42.08325082500163$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.628987885726$
6.2.41069.1	$x^{6} - 2 x^{4} + 2 x^{2} - x - 1$	$6$	[2,2]	$7\cdot 5867$	$2$	$5.8737981937$	$202.6548790431654$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.632541712933$
6.2.44965.1	$x^{6} - 2 x^{4} - 3 x - 1$	$6$	[2,2]	$5\cdot 17\cdot 23^{2}$	$3$	$5.96319621326$	$44.21538193886829$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.690763980612$
6.2.45301.1	$x^{6} - x^{5} + x^{4} + x - 1$	$6$	[2,2]	$89\cdot 509$	$2$	$5.97059983788$	$212.84031572989173$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.678220787578$
6.2.46757.1	$x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + 2 x - 1$	$6$	[2,2]	$46757$	$1$	$6.00216283049$	$216.23366990364843$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.709398649514$
6.2.47081.1	$x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$	$6$	[2,2]	$23^{2}\cdot 89$	$2$	$6.00907484204$	$45.24378410345447$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.694306844279$
6.2.47149.1	$x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - 1$	$6$	[2,2]	$47149$	$1$	$6.01052047616$	$217.13820483738002$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.696683549235$
6.2.47669.1	$x^{6} - x^{5} + x^{4} - x^{2} - 1$	$6$	[2,2]	$73\cdot 653$	$2$	$6.0215182493$	$218.3323155192561$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.700779517527$
6.2.47933.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - 1$	$6$	[2,2]	$47933$	$1$	$6.02706351936$	$218.93606372637652$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.721883438518$
6.2.49664.1	$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 1$	$6$	[2,2]	$2^{9}\cdot 97$	$2$	$6.06280522016$	$27.85677655436824$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.724060154938$
6.2.49781.1	$x^{6} - x - 1$	$6$	[2,2]	$67\cdot 743$	$2$	$6.06518337778$	$223.11656146507815$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.740631472629$
6.2.50173.1	$x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 3 x - 1$	$6$	[2,2]	$131\cdot 383$	$2$	$6.07311742349$	$223.99330347133147$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.726725432084$
6.2.50933.1	$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} + 3 x - 1$	$6$	[2,2]	$31^{2}\cdot 53$	$2$	$6.08835372223$	$40.53393639902249$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.730388860061$
6.2.51125.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{2} + 3 x - 1$	$6$	[2,2]	$5^{3}\cdot 409$	$2$	$6.09217289661$	$45.221676218380054$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.755100154139$
6.2.51757.1	$x^{6} - 2 x^{3} - 2 x^{2} + x + 1$	$6$	[2,2]	$73\cdot 709$	$2$	$6.10466049239$	$227.50164834567684$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.7419673261$
6.2.51869.1	$x^{6} - 2 x^{5} + x^{4} + x^{3} - 2 x^{2} + x - 1$	$6$	[2,2]	$51869$	$1$	$6.10686021517$	$227.74766738651792$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.762567083954$
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	$2$	$3$	$0.794678096272$
6.2.52625.1	$x^{6} - 2 x^{4} - x^{3} + x^{2} + x - 1$	$6$	[2,2]	$5^{3}\cdot 421$	$2$	$6.12160568228$	$45.880278987817846$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.796637527934$
6.2.53429.1	$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} + x^{2} - 2 x - 1$	$6$	[2,2]	$23^{2}\cdot 101$	$2$	$6.13709492811$	$48.19751030914356$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.765009894688$
6.2.55376.1	$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - x + 1$	$6$	[2,2]	$2^{4}\cdot 3461$	$2$	$6.17381479245$	$93.38722346966051$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.825072508548$
6.2.56125.1	$x^{6} - x^{5} + x^{3} - 3 x^{2} + 2 x - 1$	$6$	[2,2]	$5^{3}\cdot 449$	$2$	$6.18765454266$	$47.38143096192854$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.807045361974$
6.2.56144.1	$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 3 x + 1$	$6$	[2,2]	$2^{4}\cdot 11^{2}\cdot 29$	$3$	$6.18800361127$	$28.351889352086026$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.832028349165$
6.2.57152.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} - 1$	$6$	[2,2]	$2^{6}\cdot 19\cdot 47$	$3$	$6.20638299243$	$84.52218643646175$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.795263260959$
6.2.57661.1	$x^{6} - x^{5} + 4 x^{3} - 3 x^{2} + x - 1$	$6$	[2,2]	$23^{2}\cdot 109$	$2$	$6.21556141005$	$50.06995106848019$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.804738209577$
6.2.58589.1	$x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - 4 x^{2} + 4 x - 1$	$6$	[2,2]	$41\cdot 1429$	$2$	$6.23212297231$	$242.05164738129753$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.827820885996$
6.2.58673.1	$x^{6} - x^{3} + x^{2} + x - 1$	$6$	[2,2]	$23\cdot 2551$	$2$	$6.23361126611$	$242.22510191968132$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.857832226065$
6.2.59177.1	$x^{6} - x^{4} - x^{3} + x^{2} - 1$	$6$	[2,2]	$17\cdot 59^{2}$	$2$	$6.24250392532$	$31.670175244226233$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.862058499217$
6.2.61193.1	$x^{6} - x^{5} + x^{4} - x^{3} - x^{2} + x - 1$	$6$	[2,2]	$11\cdot 5563$	$2$	$6.27745523172$	$247.37218922101974$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.828147038467$
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	$2$	$3$	$0.828712859351$
6.2.62437.1	$x^{6} - x^{4} - x^{3} + 2 x^{2} + x - 1$	$6$	[2,2]	$29\cdot 2153$	$2$	$6.29854647102$	$249.8739682319869$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.841411408088$
6.2.63461.1	$x^{6} - x^{3} + 2 x - 1$	$6$	[2,2]	$17\cdot 3733$	$2$	$6.31564657138$	$251.91466809219347$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.857830413975$
6.2.63909.1	$x^{6} + 2 x^{4} - x - 1$	$6$	[2,2]	$3^{5}\cdot 263$	$2$	$6.32305564376$	$121.53466677245456$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.982052555459$
6.2.64829.1	$x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$	$6$	[2,2]	$241\cdot 269$	$2$	$6.3381359996$	$254.61539623518448$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.886369945691$
6.2.65405.1	$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} - 1$	$6$	[2,2]	$5\cdot 103\cdot 127$	$3$	$6.34748707179$	$255.74401263763733$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.890827309199$
6.2.65797.1	$x^{6} - 2 x^{4} - x + 1$	$6$	[2,2]	$19\cdot 3463$	$2$	$6.35381182747$	$256.5092590921427$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.906916792154$