Number field search results

Results (1-50 of 2119888 matches)

  There are too many results (2119888) to download.

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
6.2.28037.1	x^6 - 2x^5 + 3x^3 - 2x - 1	$6$	[2,2]	$23^{2}\cdot 53$	$2$	$5.51173831771$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.478924705547$
6.2.29077.1	x^6 - x^5 + x^4 - x^2 + 2x - 1	$6$	[2,2]	$29077$	$1$	$5.54529854883$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.491602105294$
6.2.29189.1	x^6 - 2x^5 + x^4 + x^3 - 2x^2 + x + 1	$6$	[2,2]	$17^{2}\cdot 101$	$2$	$5.54885278411$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.49291662671$
6.2.30125.1	x^6 - x^5 + x^4 - 2x^2 + x - 1	$6$	[2,2]	$5^{3}\cdot 241$	$2$	$5.57811986838$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.50437245294$
6.2.31133.1	x^6 - 2x^4 - x^3 + 2x + 1	$6$	[2,2]	$163\cdot 191$	$2$	$5.60880268418$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.516354684031$
6.2.31213.1	x^6 - 2x^5 + 2x^4 - 3x^3 + 2x^2 - 2x + 1	$6$	[2,2]	$7^{4}\cdot 13$	$2$	$5.6112021989$			✓	$A_4\times C_2$ (as 6T6)	trivial	$2$	$3$	$0.517040346258$
6.2.31709.1	x^6 - x^5 + 2x^3 - 2x^2 + 1	$6$	[2,2]	$37\cdot 857$	$2$	$5.62596584169$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.522986177098$
6.2.32269.1	x^6 - 3x^5 + 4x^4 - 3x^3 + x^2 - 1	$6$	[2,2]	$23^{2}\cdot 61$	$2$	$5.64240494139$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.529910039105$
6.2.33856.1	x^6 + x^4 - 1	$6$	[2,2]	$2^{6}\cdot 23^{2}$	$2$	$5.6877339597$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.550118007418$
6.2.35125.1	x^6 - x^5 - x^4 + 2x^3 - x^2 + 1	$6$	[2,2]	$5^{3}\cdot 281$	$2$	$5.72272296207$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.563512855802$
6.2.35557.1	x^6 - 2x^4 - x^3 + 2x^2 - 1	$6$	[2,2]	$31^{2}\cdot 37$	$2$	$5.73439385986$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.567960387605$
6.2.37253.1	x^6 - x^4 + x^2 - x - 1	$6$	[2,2]	$37253$	$1$	$5.77909999053$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.590723504629$
6.2.37568.1	x^6 - 2x^5 + 2x^4 - x^2 + 2x - 1	$6$	[2,2]	$2^{6}\cdot 587$	$2$	$5.78721582791$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.591962874572$
6.2.39269.1	x^6 - x^5 - 2x^4 + 2x^3 - 2x + 1	$6$	[2,2]	$107\cdot 367$	$2$	$5.83008616837$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.612802015304$
6.2.40277.1	x^6 - x^5 + 2x^3 - 3x^2 + 3x - 1	$6$	[2,2]	$40277$	$1$	$5.85476569062$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.623496086403$
6.2.40733.1	x^6 - 2x^5 + 3x^4 - 2x^3 - 3x^2 + 3x - 1	$6$	[2,2]	$7\cdot 11\cdot 23^{2}$	$3$	$5.86576148388$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.628987885726$
6.2.41069.1	x^6 - 2x^4 + 2x^2 - x - 1	$6$	[2,2]	$7\cdot 5867$	$2$	$5.8737981937$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.632541712933$
6.2.44965.1	x^6 - 2x^4 - 3x - 1	$6$	[2,2]	$5\cdot 17\cdot 23^{2}$	$3$	$5.96319621326$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.690763980612$
6.2.45301.1	x^6 - x^5 + x^4 + x - 1	$6$	[2,2]	$89\cdot 509$	$2$	$5.97059983788$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.678220787578$
6.2.46757.1	x^6 - x^5 + 2x^3 - 2x^2 + 2x - 1	$6$	[2,2]	$46757$	$1$	$6.00216283049$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.709398649514$
6.2.47081.1	x^6 - x^5 - 3x^4 + 3x^3 + 3x^2 - x - 1	$6$	[2,2]	$23^{2}\cdot 89$	$2$	$6.00907484204$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.694306844279$
6.2.47149.1	x^6 - x^5 + 3x^4 - 2x^3 + x^2 - 1	$6$	[2,2]	$47149$	$1$	$6.01052047616$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.696683549235$
6.2.47669.1	x^6 - x^5 + x^4 - x^2 - 1	$6$	[2,2]	$73\cdot 653$	$2$	$6.0215182493$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.700779517527$
6.2.47933.1	x^6 - 2x^5 + 2x^4 - x^3 - 1	$6$	[2,2]	$47933$	$1$	$6.02706351936$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.721883438518$
6.2.49664.1	x^6 - 2x^5 + 3x^4 - 2x^3 - 1	$6$	[2,2]	$2^{9}\cdot 97$	$2$	$6.06280522016$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.724060154938$
6.2.49781.1	x^6 - x - 1	$6$	[2,2]	$67\cdot 743$	$2$	$6.06518337778$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.740631472629$
6.2.50173.1	x^6 - x^5 + x^4 + 2x^3 - 4x^2 + 3x - 1	$6$	[2,2]	$131\cdot 383$	$2$	$6.07311742349$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.726725432084$
6.2.50933.1	x^6 - 2x^5 - x^4 + 4x^3 - 3x^2 + 3x - 1	$6$	[2,2]	$31^{2}\cdot 53$	$2$	$6.08835372223$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.730388860061$
6.2.51125.1	x^6 - 2x^5 + 2x^4 - 2x^2 + 3x - 1	$6$	[2,2]	$5^{3}\cdot 409$	$2$	$6.09217289661$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.755100154139$
6.2.51757.1	x^6 - 2x^3 - 2x^2 + x + 1	$6$	[2,2]	$73\cdot 709$	$2$	$6.10466049239$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.7419673261$
6.2.51869.1	x^6 - 2x^5 + x^4 + x^3 - 2x^2 + x - 1	$6$	[2,2]	$51869$	$1$	$6.10686021517$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.762567083954$
6.2.52441.1	x^6 - x^4 - x^3 - x^2 + 1	$6$	[2,2]	$229^{2}$	$1$	$6.11803317264$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.794678096272$
6.2.52625.1	x^6 - 2x^4 - x^3 + x^2 + x - 1	$6$	[2,2]	$5^{3}\cdot 421$	$2$	$6.12160568228$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.796637527934$
6.2.53429.1	x^6 - 3x^5 + 2x^4 + x^3 + x^2 - 2x - 1	$6$	[2,2]	$23^{2}\cdot 101$	$2$	$6.13709492811$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.765009894688$
6.2.55376.1	x^6 - x^5 - 2x^4 + 3x^3 - x + 1	$6$	[2,2]	$2^{4}\cdot 3461$	$2$	$6.17381479245$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.825072508548$
6.2.56125.1	x^6 - x^5 + x^3 - 3x^2 + 2x - 1	$6$	[2,2]	$5^{3}\cdot 449$	$2$	$6.18765454266$			✓	$C_3^2:D_4$ (as 6T13)	trivial	$2$	$3$	$0.807045361974$
6.2.56144.1	x^6 - x^5 - 2x^4 + 3x^3 - 3x + 1	$6$	[2,2]	$2^{4}\cdot 11^{2}\cdot 29$	$3$	$6.18800361127$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.832028349165$
6.2.57152.1	x^6 - 2x^5 + 2x^4 - 2x^3 + x^2 - 1	$6$	[2,2]	$2^{6}\cdot 19\cdot 47$	$3$	$6.20638299243$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.795263260959$
6.2.57661.1	x^6 - x^5 + 4x^3 - 3x^2 + x - 1	$6$	[2,2]	$23^{2}\cdot 109$	$2$	$6.21556141005$			not computed	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$0.804738209577$
6.2.58589.1	x^6 - 2x^5 + 2x^4 + x^3 - 4x^2 + 4x - 1	$6$	[2,2]	$41\cdot 1429$	$2$	$6.23212297231$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.827820885996$
6.2.58673.1	x^6 - x^3 + x^2 + x - 1	$6$	[2,2]	$23\cdot 2551$	$2$	$6.23361126611$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.857832226065$
6.2.59177.1	x^6 - x^4 - x^3 + x^2 - 1	$6$	[2,2]	$17\cdot 59^{2}$	$2$	$6.24250392532$			✓	$S_4\times C_2$ (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]	$11\cdot 5563$	$2$	$6.27745523172$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.828147038467$
6.2.61504.1	x^6 + x^2 - 1	$6$	[2,2]	$2^{6}\cdot 31^{2}$	$2$	$6.28276130478$			✓	$S_4$ (as 6T7)	trivial	$2$	$3$	$0.828712859351$
6.2.62437.1	x^6 - x^4 - x^3 + 2x^2 + x - 1	$6$	[2,2]	$29\cdot 2153$	$2$	$6.29854647102$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.841411408088$
6.2.63461.1	x^6 - x^3 + 2x - 1	$6$	[2,2]	$17\cdot 3733$	$2$	$6.31564657138$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.857830413975$
6.2.63909.1	x^6 + 2x^4 - x - 1	$6$	[2,2]	$3^{5}\cdot 263$	$2$	$6.32305564376$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.982052555459$
6.2.64829.1	x^6 - 3x^5 + 4x^4 - 2x^3 - 2x^2 + 2x - 1	$6$	[2,2]	$241\cdot 269$	$2$	$6.3381359996$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.886369945691$
6.2.65405.1	x^6 - x^5 + 2x^4 - 2x^3 - 1	$6$	[2,2]	$5\cdot 103\cdot 127$	$3$	$6.34748707179$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.890827309199$
6.2.65797.1	x^6 - 2x^4 - x + 1	$6$	[2,2]	$19\cdot 3463$	$2$	$6.35381182747$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.906916792154$

  There are too many results (2119888) to download.