Number field search results

Results (1-50 of 320818 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
6.0.14283.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,3^{3}\cdot 23^{2}$	$2$	$4.92572209907$	$8.306623862918075$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$0.803563966653$
6.0.22707.1	$x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 29^{2}$	$2$	$5.32140883904$	$9.327379053088816$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$1.25603528677$
6.0.25947.1	$x^{6} - x^{4} - 2 x^{3} + x^{2} + x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 31^{2}$	$2$	$5.44103089586$	$9.643650760992955$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$1.37763890943$
6.0.30976.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 2$	$6$	[0,3]	$-\,2^{8}\cdot 11^{2}$	$2$	$5.60407866131$	$8.357370775943878$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$1.29138778296$
6.0.33856.2	$x^{6} + x^{4} + 2 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 23^{2}$	$2$	$5.6877339597$	$9.591663046625438$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$1.02428142886$
6.0.52272.1	$x^{6} - x^{5} - 3 x^{3} + 2 x^{2} + x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 11^{2}$	$3$	$6.1147426852$	$9.118924788211691$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$2.0605682102$
6.0.53824.1	$x^{6} - 2 x^{3} + x^{2} + 2 x + 2$	$6$	[0,3]	$-\,2^{6}\cdot 29^{2}$	$2$	$6.14463365137$	$10.770329614269007$			?	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$2.03197727622$
6.0.54675.1	$x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{2} + 3$	$6$	[0,3]	$-\,3^{7}\cdot 5^{2}$	$2$	$6.16071992048$	$8.05613000539548$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$2.3152465159$
6.0.61504.2	$x^{6} - 2 x^{4} + x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 31^{2}$	$2$	$6.28276130478$	$11.135528725660043$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$1.34349356038$
6.2.66125.1	$x^{6} - x^{5} - x^{4} + 4 x^{3} + 3 x^{2} - 1$	$6$	[2,2]	$5^{3}\cdot 23^{2}$	$2$	$6.35907988592$	$10.723805294763608$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$0.897724442255$
6.0.86528.1	$x^{6} + 2 x^{4} - 2 x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,2^{9}\cdot 13^{2}$	$2$	$6.65057881011$	$10.198039027185569$			?	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$1.39505084253$
6.2.91125.1	$x^{6} - x^{3} - 1$	$6$	[2,2]	$3^{6}\cdot 5^{3}$	$2$	$6.7082039325$	$8.05613000539548$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$1.11412400138$
6.0.92416.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 2$	$6$	[0,3]	$-\,2^{8}\cdot 19^{2}$	$2$	$6.7239508136$	$10.983737066662838$			?	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$2.68729827591$
6.0.93987.1	$x^{6} - 2 x^{4} - 2 x^{3} + 4 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 59^{2}$	$2$	$6.74286758598$	$13.30413469565007$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$3.51270071212$
6.2.98000.1	$x^{6} - x^{5} - 2 x^{4} + 5 x^{3} - 2 x^{2} - x + 1$	$6$	[2,2]	$2^{4}\cdot 5^{3}\cdot 7^{2}$	$3$	$6.79001936084$	$9.391191271220128$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$1.26690186417$
6.2.120125.1	$x^{6} + 3 x^{4} - 4 x^{3} + x^{2} - x - 1$	$6$	[2,2]	$5^{3}\cdot 31^{2}$	$2$	$7.02434068195$	$12.449899597988733$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$1.26595089315$
6.0.124848.1	$x^{6} - x^{5} - 4 x^{4} + x^{3} + 4 x^{2} + 3 x + 3$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 17^{2}$	$3$	$7.06963401549$	$11.336311000024526$			✓	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$4.39830187428$
6.0.137200.1	$x^{6} - x^{5} - x^{4} - x^{3} + 2 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 5^{2}\cdot 7^{3}$	$3$	$7.18167396788$	$9.391191271220128$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$2.63273219443$
6.0.139968.1	$x^{6} - 3 x^{5} + 3 x^{3} + 6 x^{2} - 9 x + 3$	$6$	[0,3]	$-\,2^{6}\cdot 3^{7}$	$2$	$7.20562173106$	$10.190287977389717$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$4.93265984551$
6.2.140608.1	$x^{6} - x^{5} + 2 x^{4} + x^{3} - 2 x^{2} - x - 1$	$6$	[2,2]	$2^{6}\cdot 13^{3}$	$2$	$7.21110255093$	$10.198039027185569$				$D_{6}$ (as 6T3)	trivial	$2$	$3$	$1.6667554329$
6.2.153125.1	$x^{6} - x^{5} + 4 x + 1$	$6$	[2,2]	$5^{5}\cdot 7^{2}$	$2$	$7.31432662849$	$10.116354127720633$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$1.56253260729$
6.0.155952.1	$x^{6} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 19^{2}$	$3$	$7.33666165983$	$11.984615124734525$			?	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$4.71280119975$
6.0.160083.1	$x^{6} - x^{4} + x^{2} - 3 x + 3$	$6$	[0,3]	$-\,3^{3}\cdot 7^{2}\cdot 11^{2}$	$3$	$7.36869989008$	$15.198684153570664$			?	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$4.88224679645$
6.0.173056.2	$x^{6} + 2 x^{4} + x^{2} + 4$	$6$	[0,3]	$-\,2^{10}\cdot 13^{2}$	$2$	$7.46502231363$	$14.422205101855956$			?	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$6.00991153366$
6.0.179776.1	$x^{6} - 2 x^{5} - 2 x^{4} + 6 x^{3} - 2 x^{2} - 4 x + 5$	$6$	[0,3]	$-\,2^{6}\cdot 53^{2}$	$2$	$7.51257150844$	$14.560219778561036$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$5.01209370302$
6.0.181447.1	$x^{6} - x^{5} + 2 x^{4} - 5 x^{3} + 6 x^{2} + 8$	$6$	[0,3]	$-\,7^{3}\cdot 23^{2}$	$2$	$7.52416479044$	$12.68857754044952$			?	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$1.2523774505$
6.2.184832.1	$x^{6} + 2 x^{4} - 2 x^{3} - 2 x^{2} - 1$	$6$	[2,2]	$2^{9}\cdot 19^{2}$	$2$	$7.54737960296$	$12.328828005937952$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.74212542888$
6.0.186003.1	$x^{6} - x^{5} + 3 x^{3} - x^{2} - 2 x + 4$	$6$	[0,3]	$-\,3^{3}\cdot 83^{2}$	$2$	$7.55532802917$	$15.7797338380595$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$5.32510096997$
6.0.186624.1	$x^{6} - 2 x^{3} + 2$	$6$	[0,3]	$-\,2^{8}\cdot 3^{6}$	$2$	$7.55952629937$	$9.078514496537409$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$4.6291230071$
6.0.195075.1	$x^{6} - 2 x^{4} + x^{2} + 3$	$6$	[0,3]	$-\,3^{3}\cdot 5^{2}\cdot 17^{2}$	$3$	$7.6155323844$	$15.968719422671311$			?	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$7.25210637396$
6.2.200000.1	$x^{6} - 2 x^{5} - 2 x - 1$	$6$	[2,2]	$2^{6}\cdot 5^{5}$	$2$	$7.64724491332$	$10.81483747120199$				$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.22546474675$
6.2.219501.1	$x^{6} - x^{5} - 3 x^{4} + 3 x^{2} + 4 x + 1$	$6$	[2,2]	$3^{2}\cdot 29^{3}$	$2$	$7.76675162912$	$9.327379053088816$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.0689804453$
6.0.222784.1	$x^{6} - 4 x^{4} + 4 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 59^{2}$	$2$	$7.78599283175$	$15.362291495737216$			✓	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$4.94172689232$
6.0.238144.1	$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} + 3 x^{2} - 6 x + 2$	$6$	[0,3]	$-\,2^{6}\cdot 61^{2}$	$2$	$7.8729943662$	$15.620499351813308$			?	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$5.38720168085$
6.2.242000.1	$x^{6} - x^{5} + 2 x^{4} + 5 x^{3} + 4 x^{2} + x - 1$	$6$	[2,2]	$2^{4}\cdot 5^{3}\cdot 11^{2}$	$3$	$7.89409886204$	$11.772481280020624$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.11794327881$
6.0.247808.1	$x^{6} - 2 x^{4} + 2$	$6$	[0,3]	$-\,2^{11}\cdot 11^{2}$	$2$	$7.92536404743$	$11.819107097120389$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$2.32751866179$
6.2.247808.1	$x^{6} + 2 x^{4} - 2$	$6$	[2,2]	$2^{11}\cdot 11^{2}$	$2$	$7.92536404743$	$11.819107097120389$			✓	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$3.14774163853$
6.0.270848.2	$x^{6} + 2 x^{4} + 8 x^{2} + 8$	$6$	[0,3]	$-\,2^{9}\cdot 23^{2}$	$2$	$8.04367050498$	$13.564659966250536$			?	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$1.36679080169$
6.2.270848.1	$x^{6} - 2 x^{4} + 8 x^{2} - 8$	$6$	[2,2]	$2^{9}\cdot 23^{2}$	$2$	$8.04367050498$	$13.564659966250536$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.10681798995$
6.0.292032.1	$x^{6} + x^{4} - 4 x^{3} + x^{2} - 2 x + 4$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 13^{2}$	$3$	$8.14526228946$	$17.663521732655695$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$5.98857603074$
6.0.309123.1	$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3$	$6$	[0,3]	$-\,3^{3}\cdot 107^{2}$	$2$	$8.22284088511$	$17.916472867168917$	✓		?	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$10.2770387205$
6.0.309123.3	$x^{6} - x^{5} - 2 x^{4} + x^{3} + 7 x^{2} - 6 x + 4$	$6$	[0,3]	$-\,3^{3}\cdot 107^{2}$	$2$	$8.22284088511$	$17.916472867168917$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$7.72794753285$
6.0.313600.1	$x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 2$	$6$	[0,3]	$-\,2^{8}\cdot 5^{2}\cdot 7^{2}$	$3$	$8.24257059962$	$14.907586903169404$			?	$D_{6}$ (as 6T3)	trivial	$4$	$2$	$7.32363122769$
6.0.314928.2	$x^{6} - 3 x^{4} - 2 x^{3} + 9 x^{2} + 12 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 3^{9}$	$2$	$8.24837782199$	$10.392304845413264$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$8.64762228954$
6.0.320787.2	$x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} + x^{2} - 6 x + 3$	$6$	[0,3]	$-\,3^{3}\cdot 109^{2}$	$2$	$8.273757606$	$18.083141320025124$			?	$D_{6}$ (as 6T3)	trivial	$6$	$2$	$9.83270265325$
6.2.325125.1	$x^{6} - 3 x^{5} + 8 x^{4} - 11 x^{3} + 13 x^{2} - 8 x + 1$	$6$	[2,2]	$3^{2}\cdot 5^{3}\cdot 17^{2}$	$3$	$8.29230105386$	$15.968719422671311$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.86544520769$
6.2.328509.1	$x^{6} - 2 x^{5} + 3 x^{4} - 9 x^{3} + 8 x^{2} - 7 x - 5$	$6$	[2,2]	$3^{3}\cdot 23^{3}$	$2$	$8.30662386292$	$8.306623862918075$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$2.58528382694$
6.0.329623.1	$x^{6} - 3 x^{4} - 5 x^{3} + 4 x^{2} + 4 x + 8$	$6$	[0,3]	$-\,7^{3}\cdot 31^{2}$	$2$	$8.31131197962$	$14.730919862656235$			?	$D_{6}$ (as 6T3)	trivial	$2$	$2$	$1.83288262678$
6.2.340736.1	$x^{6} - 2 x^{5} + 6 x^{3} - 2 x^{2} - 8 x - 2$	$6$	[2,2]	$2^{8}\cdot 11^{3}$	$2$	$8.35737077594$	$8.357370775943878$			?	$D_{6}$ (as 6T3)	trivial	$2$	$3$	$3.86541141518$
6.0.344763.1	$x^{6} - 4 x^{4} + 4 x^{2} + 3$	$6$	[0,3]	$-\,3^{3}\cdot 113^{2}$	$2$	$8.37375226983$	$18.411952639521967$				$D_{6}$ (as 6T3)	trivial	$6$	$2$	$9.82929624432$