Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

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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
6.0.54691.1	$ x^{6} - x^{5} - 2 x^{3} + 2 x^{2} + 1 $	$6$	[0,3]	$-\,7\cdot 13\cdot 601$	$3$	$6.16102036097$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.665616035351$
6.2.70629.1	$ x^{6} - x^{3} + 2 x^{2} + 2 x - 1 $	$6$	[2,2]	$3\cdot 13\cdot 1811$	$3$	$6.42930224838$			not computed	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.05154203969$
6.2.70837.1	$ x^{6} + 2 x^{4} - x^{3} - 2 x - 1 $	$6$	[2,2]	$13\cdot 5449$	$2$	$6.43245406247$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.941646635002$
6.0.70967.1	$ x^{6} - x^{5} + 3 x^{3} - x^{2} - x + 2 $	$6$	[0,3]	$-\,13\cdot 53\cdot 103$	$3$	$6.43442003203$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.325054343$
6.2.75088.1	$ x^{6} - x^{5} + x^{3} - x - 1 $	$6$	[2,2]	$2^{4}\cdot 13\cdot 19^{2}$	$3$	$6.495238303$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$1.01738805374$
6.0.95667.1	$ x^{6} - x^{5} + x^{4} + x + 1 $	$6$	[0,3]	$-\,3\cdot 11\cdot 13\cdot 223$	$4$	$6.7628075039$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.27737826143$
6.2.100672.1	$ x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + x^{2} - 2 x - 1 $	$6$	[2,2]	$2^{6}\cdot 11^{2}\cdot 13$	$3$	$6.82052988376$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$1.67725537634$
6.2.123344.1	$ x^{6} - x^{5} + 2 x^{4} - x^{3} - x - 1 $	$6$	[2,2]	$2^{4}\cdot 13\cdot 593$	$3$	$7.05536800648$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$1.47208092544$
6.0.176176.1	$ x^{6} - x^{5} + 4 x^{4} - x^{3} + 4 x^{2} - x + 1 $	$6$	[0,3]	$-\,2^{4}\cdot 7\cdot 11^{2}\cdot 13$	$4$	$7.48728660143$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.36797583457$
6.2.190528.1	$ x^{6} - 2 x^{4} + x^{2} - 2 x + 1 $	$6$	[2,2]	$2^{6}\cdot 13\cdot 229$	$3$	$7.58565583702$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.03810363094$
6.2.199004.1	$ x^{6} - x^{5} - 3 x^{4} + x^{3} + 5 x^{2} - 2 $	$6$	[2,2]	$2^{2}\cdot 13\cdot 43\cdot 89$	$4$	$7.64088448935$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.77197636704$
6.2.212381.1	$ x^{6} - 2 x^{5} - 4 x^{4} + 7 x^{3} + 4 x^{2} - 2 x - 1 $	$6$	[2,2]	$13\cdot 17\cdot 31^{2}$	$3$	$7.72418399185$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.58185080315$
6.4.214747.1	$ x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 3 x + 1 $	$6$	[4,1]	$-\,13\cdot 16519$	$2$	$7.7384595636$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$2.24299199866$
6.0.221299.1	$ x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + 4 x^{2} - x + 1 $	$6$	[0,3]	$-\,13\cdot 29\cdot 587$	$3$	$7.77731892705$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$1.86057669779$
6.2.234793.1	$ x^{6} - 2 x^{5} - x^{3} + 3 x^{2} - x + 1 $	$6$	[2,2]	$13\cdot 18061$	$2$	$7.85442126969$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.5203493619$
6.2.246857.1	$ x^{6} - 2 x^{5} - x^{4} + 5 x^{3} - x^{2} - 4 x + 1 $	$6$	[2,2]	$13\cdot 17\cdot 1117$	$3$	$7.92028679582$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.18226443296$
6.0.276848.1	$ x^{6} - x^{5} - x^{4} + 5 x^{3} - 2 x^{2} - 4 x + 4 $	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}\cdot 13$	$3$	$8.07309813547$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$4.06235489076$
6.0.287339.1	$ x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + 10 x^{2} - x + 3 $	$6$	[0,3]	$-\,13\cdot 23\cdot 31^{2}$	$3$	$8.12329882081$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$2.58691560134$
6.2.302965.1	$ x^{6} + x^{4} - 2 x^{3} + 5 x^{2} - 5 x + 1 $	$6$	[2,2]	$5\cdot 13\cdot 59\cdot 79$	$4$	$8.19531045036$			not computed	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.03778159903$
6.2.303381.1	$ x^{6} - 2 x^{5} + x^{4} - x^{3} + 2 x^{2} + x - 1 $	$6$	[2,2]	$3^{2}\cdot 13\cdot 2593$	$3$	$8.19718486945$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.41811388842$
6.2.338897.1	$ x^{6} - x^{5} + 3 x^{3} - 5 x^{2} + 5 x - 2 $	$6$	[2,2]	$13\cdot 131\cdot 199$	$3$	$8.34983616377$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.88843919024$
6.2.353288.1	$ x^{6} - 3 x^{5} + 3 x^{4} + x^{3} - 5 x^{2} + 2 x + 2 $	$6$	[2,2]	$2^{3}\cdot 13\cdot 43\cdot 79$	$4$	$8.40791180875$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.97086116697$
6.2.362297.1	$ x^{6} - x^{5} - 4 x^{4} + 3 x^{3} + 4 x^{2} - 10 x - 1 $	$6$	[2,2]	$13\cdot 29\cdot 31^{2}$	$3$	$8.44327218179$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.54396356086$
6.0.389831.1	$ x^{6} - x^{5} - x^{4} + 3 x^{3} + x^{2} - x + 1 $	$6$	[0,3]	$-\,13\cdot 157\cdot 191$	$3$	$8.54698080596$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.47572815753$
6.0.402688.1	$ x^{6} - 2 x^{5} + 6 x^{4} - 2 x^{3} + 2 x^{2} + 4 x + 2 $	$6$	[0,3]	$-\,2^{8}\cdot 11^{2}\cdot 13$	$3$	$8.59332917198$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$3.43933046822$
6.2.405353.1	$ x^{6} - x^{5} + x^{4} + 3 x^{3} - x^{2} + x + 1 $	$6$	[2,2]	$13\cdot 31181$	$2$	$8.60278162073$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.81544941759$
6.2.407693.1	$ x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 3 x^{2} + 3 x + 1 $	$6$	[2,2]	$11\cdot 13\cdot 2851$	$3$	$8.6110387279$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.6834177089$
6.2.408629.1	$ x^{6} - 2 x^{5} + 4 x^{3} - 2 x^{2} - 3 x + 1 $	$6$	[2,2]	$13\cdot 17\cdot 43^{2}$	$3$	$8.61433051563$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.73210004733$
6.0.427440.1	$ x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 3 x + 1 $	$6$	[0,3]	$-\,2^{4}\cdot 3\cdot 5\cdot 13\cdot 137$	$5$	$8.67918995452$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.2210630831$
6.0.435136.1	$ x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 2 $	$6$	[0,3]	$-\,2^{6}\cdot 13\cdot 523$	$3$	$8.70504129889$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.65427811379$
6.0.435968.1	$ x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 2 $	$6$	[0,3]	$-\,2^{8}\cdot 13\cdot 131$	$3$	$8.70781316447$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.7725558054$
6.2.441168.1	$ x^{6} - x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 3 x + 3 $	$6$	[2,2]	$2^{4}\cdot 3\cdot 7\cdot 13\cdot 101$	$5$	$8.72503813667$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.87962883926$
6.2.462137.1	$ x^{6} - x^{5} - 2 x^{4} + x^{3} - x^{2} + 3 x + 1 $	$6$	[2,2]	$13\cdot 19\cdot 1871$	$3$	$8.79282554937$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$4.39558114741$
6.0.468416.1	$ x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 3 $	$6$	[0,3]	$-\,2^{6}\cdot 13\cdot 563$	$3$	$8.81262493295$				$S_6$ (as 6T16)	trivial	$2$	$2$	$3.67508481297$
6.0.471536.1	$ x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 4 x + 2 $	$6$	[0,3]	$-\,2^{4}\cdot 13\cdot 2267$	$3$	$8.82238100117$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$6.87953114828$
6.2.487513.1	$ x^{6} - x^{5} + x^{4} + 3 x^{3} - 4 x^{2} + 5 x - 1 $	$6$	[2,2]	$13\cdot 37501$	$2$	$8.87151314083$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.20705758596$
6.0.496704.1	$ x^{6} - 2 x^{5} + 2 x^{4} - x^{2} - 2 x + 3 $	$6$	[0,3]	$-\,2^{6}\cdot 3\cdot 13\cdot 199$	$4$	$8.89917218095$			not computed	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.40791191502$
6.0.497783.1	$ x^{6} + 5 x^{4} - x^{3} + 5 x^{2} + 1 $	$6$	[0,3]	$-\,11\cdot 13\cdot 59^{2}$	$3$	$8.90239124335$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$2.15989242101$
6.2.504517.1	$ x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 1 $	$6$	[2,2]	$13\cdot 197^{2}$	$2$	$8.92235093102$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.98596081262$
6.2.508885.1	$ x^{6} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 2 x^{2} - 2 x + 1 $	$6$	[2,2]	$5\cdot 13\cdot 7829$	$3$	$8.93517936468$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.06844177022$
6.2.513344.1	$ x^{6} - x^{4} - 2 x^{3} - 3 x^{2} + 4 x - 1 $	$6$	[2,2]	$2^{6}\cdot 13\cdot 617$	$3$	$8.94818075584$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.81459564002$
6.4.519051.1	$ x^{6} - 2 x^{5} + 4 x^{3} - 4 x^{2} - x + 1 $	$6$	[4,1]	$-\,3\cdot 13\cdot 13309$	$3$	$8.96468440898$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$4.93683311571$
6.2.519285.1	$ x^{6} - x^{5} + x^{4} + 2 x^{3} - 5 x - 1 $	$6$	[2,2]	$3\cdot 5\cdot 13\cdot 2663$	$4$	$8.9653578631$			not computed	$S_6$ (as 6T16)	trivial	$2$	$3$	$4.40071971395$
6.4.533923.1	$ x^{6} - x^{5} - x^{4} - 2 x^{2} + x + 1 $	$6$	[4,1]	$-\,13\cdot 67\cdot 613$	$3$	$9.00699188767$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$3.77375245485$
6.0.537199.1	$ x^{6} - 3 x^{5} + 6 x^{4} - x^{3} - 2 x^{2} + 8 x + 8 $	$6$	[0,3]	$-\,13\cdot 31^{2}\cdot 43$	$3$	$9.01617915226$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$2.5173116516$
6.0.541372.1	$ x^{6} - 2 x^{4} - 3 x^{3} + 2 x^{2} + 4 x + 2 $	$6$	[0,3]	$-\,2^{2}\cdot 13\cdot 29\cdot 359$	$4$	$9.02781460188$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$6.99736741576$
6.0.542984.1	$ x^{6} - 3 x^{5} + 6 x^{4} - 6 x^{3} + 7 x^{2} - 4 x + 2 $	$6$	[0,3]	$-\,2^{3}\cdot 13\cdot 23\cdot 227$	$4$	$9.03228928675$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$4.52057417762$
6.0.548899.1	$ x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} + x + 1 $	$6$	[0,3]	$-\,13\cdot 42223$	$2$	$9.04861422899$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.8637767043$
6.2.560144.1	$ x^{6} - x^{5} + x^{4} + 2 x^{3} - 4 x^{2} + 4 x - 4 $	$6$	[2,2]	$2^{4}\cdot 13\cdot 2693$	$3$	$9.07924944316$			not computed	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.5284997474$
6.2.560625.1	$ x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + 3 x^{2} - 3 x - 2 $	$6$	[2,2]	$3\cdot 5^{4}\cdot 13\cdot 23$	$4$	$9.08054838215$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$6.23920644911$

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