Number field search results

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Results (1-50 of 33753 matches)

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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
6.0.83248.1	$x^{6} - x^{5} + x^{3} + 2 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 11^{2}\cdot 43$	$3$	$6.60788234144$	$34.52369205633357$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$0.9213154377$
6.2.154456.1	$x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + x + 1$	$6$	[2,2]	$2^{3}\cdot 43\cdot 449$	$3$	$7.3248847734$	$393.00890575151095$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.2390686083$
6.2.166324.1	$x^{6} - x^{5} - x^{3} - 2 x - 1$	$6$	[2,2]	$2^{2}\cdot 43\cdot 967$	$3$	$7.41581954951$	$323.6936118482375$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.36503980182$
6.2.188813.1	$x^{6} - x^{5} + 2 x^{4} - 2 x^{2} + 2 x - 3$	$6$	[2,2]	$43\cdot 4391$	$2$	$7.57423278968$	$434.52617872804854$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.38874159354$
6.2.202057.1	$x^{6} - x^{5} - x^{4} + 3 x^{3} - 3 x^{2} + 3 x - 1$	$6$	[2,2]	$37\cdot 43\cdot 127$	$3$	$7.66029774013$	$449.50750827989515$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.13913010644$
6.0.216376.1	$x^{6} + x^{4} - x^{3} + 3 x^{2} - 3 x + 1$	$6$	[0,3]	$-\,2^{3}\cdot 17\cdot 37\cdot 43$	$4$	$7.7482123508$	$465.1623372544256$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.32581290683$
6.2.235941.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - 4 x - 1$	$6$	[2,2]	$3\cdot 31\cdot 43\cdot 59$	$4$	$7.86080885409$	$485.7375834748635$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.43228798618$
6.2.266944.1	$x^{6} - 2 x^{5} + 2 x^{3} + 3 x^{2} - 4 x + 1$	$6$	[2,2]	$2^{6}\cdot 43\cdot 97$	$3$	$8.02422985558$	$129.1665591397402$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.63629261079$
6.2.270857.1	$x^{6} - 2 x^{5} + x^{3} + x^{2} - 3 x + 1$	$6$	[2,2]	$43\cdot 6299$	$2$	$8.04371505151$	$520.4392375676531$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.38693391723$
6.2.376121.1	$x^{6} - 3 x^{5} + 3 x^{4} + x^{3} - 3 x^{2} + x - 1$	$6$	[2,2]	$43\cdot 8747$	$2$	$8.49613224427$	$613.2870453547832$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.82090550503$
6.0.390784.1	$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 4$	$6$	[0,3]	$-\,2^{7}\cdot 43\cdot 71$	$3$	$8.55045965888$	$234.1581220795389$			?	$S_6$ (as 6T16)	trivial	$2$	$2$	$5.30811259821$
6.0.403555.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} + x + 1$	$6$	[0,3]	$-\,5\cdot 43\cdot 1877$	$3$	$8.59641002756$	$635.2597893775428$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.73344110278$
6.2.432193.1	$x^{6} - 2 x^{5} - x^{4} - 3 x^{3} + 14 x^{2} - 8 x - 8$	$6$	[2,2]	$19\cdot 23^{2}\cdot 43$	$3$	$8.69520091462$	$137.08026845611298$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$2.84706192909$
6.0.437611.1	$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} - x + 2$	$6$	[0,3]	$-\,43\cdot 10177$	$2$	$8.71327400985$	$661.521730557659$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$5.41678871133$
6.4.450124.1	$x^{6} - 2 x^{5} - x^{4} + x^{3} + 2 x^{2} + 2 x - 2$	$6$	[4,1]	$-\,2^{2}\cdot 43\cdot 2617$	$3$	$8.75431215385$	$532.5038510015115$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$5.4523021716$
6.2.469904.1	$x^{6} - x^{5} - x^{4} + 2 x^{3} - x^{2} - x - 1$	$6$	[2,2]	$2^{4}\cdot 43\cdot 683$	$3$	$8.81728455986$	$384.72130855653177$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.33053700312$
6.0.492307.1	$x^{6} - 2 x^{5} + 4 x^{4} - 6 x^{3} + 6 x^{2} - 5 x + 4$	$6$	[0,3]	$-\,43\cdot 107^{2}$	$2$	$8.88599371691$	$67.83067152844649$			✓	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$6.02399190225$
6.2.515828.1	$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - x - 1$	$6$	[2,2]	$2^{2}\cdot 43\cdot 2999$	$3$	$8.95538274859$	$570.0449786311483$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.13009501345$
6.0.537199.1	$x^{6} - 3 x^{5} + 6 x^{4} - x^{3} - 2 x^{2} + 8 x + 8$	$6$	[0,3]	$-\,13\cdot 31^{2}\cdot 43$	$3$	$9.01617915226$	$131.63965967746955$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$2.5173116516$
6.0.597184.1	$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 3 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7\cdot 31\cdot 43$	$4$	$9.17666111429$	$216.85316060937697$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$3.93493003687$
6.0.607375.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{3} + 3 x^{2} + 4 x + 1$	$6$	[0,3]	$-\,5^{3}\cdot 43\cdot 113$	$3$	$9.20257753765$	$233.07782286900954$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$5.49192982348$
6.2.613696.1	$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 2$	$6$	[2,2]	$2^{6}\cdot 43\cdot 223$	$3$	$9.21847075181$	$276.9693123795486$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$6.04608313885$
6.2.613825.1	$x^{6} - x^{4} - 2 x^{3} + 2 x^{2} - 3 x + 2$	$6$	[2,2]	$5^{2}\cdot 43\cdot 571$	$3$	$9.21879368004$	$458.1759455643265$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.65693392888$
6.2.634981.1	$x^{6} - x^{5} - 2 x^{3} + 3 x^{2} + x - 1$	$6$	[2,2]	$43\cdot 14767$	$2$	$9.271004426$	$796.8569507759846$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$3.34097790404$
6.2.659405.1	$x^{6} - x^{5} - x^{4} + 4 x^{3} - 6 x^{2} + x - 1$	$6$	[2,2]	$5\cdot 43\cdot 3067$	$3$	$9.32950723831$	$812.0375607076313$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$4.76175746151$
6.4.662931.1	$x^{6} - x^{5} + 2 x^{4} - 6 x^{3} + 4 x + 1$	$6$	[4,1]	$-\,3^{3}\cdot 43\cdot 571$	$3$	$9.33780330031$	$271.4019159843939$			✓	$S_6$ (as 6T16)	trivial	$2$	$4$	$4.78571911115$
6.2.670585.1	$x^{6} - 3 x^{5} + 3 x^{4} + 5 x^{3} - 4 x^{2} - 3 x + 2$	$6$	[2,2]	$5\cdot 43\cdot 3119$	$3$	$9.35568603725$	$818.892544843339$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$7.28483831059$
6.2.679529.1	$x^{6} - 2 x^{5} + x^{4} + 4 x^{3} - 4 x^{2} - x + 2$	$6$	[2,2]	$43\cdot 15803$	$2$	$9.37636847325$	$824.3354899553943$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.87055047124$
6.2.689204.1	$x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x^{2} + 2 x - 1$	$6$	[2,2]	$2^{2}\cdot 43\cdot 4007$	$3$	$9.39848742952$	$658.9167729204297$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.80654408405$
6.2.690752.1	$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} - 2 x + 1$	$6$	[2,2]	$2^{6}\cdot 43\cdot 251$	$3$	$9.40200241721$	$293.84349575922215$				$S_6$ (as 6T16)	trivial	$2$	$3$	$5.58379306686$
6.0.702491.1	$x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 10 x^{2} - 7 x + 13$	$6$	[0,3]	$-\,17\cdot 31^{2}\cdot 43$	$3$	$9.42844620366$	$150.53571004914414$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$2$	$1.94677700167$
6.2.741277.1	$x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 8 x^{2} - 5 x + 1$	$6$	[2,2]	$43\cdot 17239$	$2$	$9.51327579894$	$860.9744479367549$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$2.99130307833$
6.2.761573.1	$x^{6} - x^{5} - x^{4} + 4 x^{3} + 5 x^{2} - 6 x + 1$	$6$	[2,2]	$43\cdot 89\cdot 199$	$3$	$9.55620057198$	$872.6814997466143$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.96778760709$
6.2.795973.1	$x^{6} - 5 x^{4} - 2 x^{3} + 5 x^{2} + 7 x + 2$	$6$	[2,2]	$43\cdot 107\cdot 173$	$3$	$9.62682453328$	$892.1731894649155$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$9.77620355998$
6.2.796145.1	$x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} - x^{2} + 5 x - 25$	$6$	[2,2]	$5\cdot 7\cdot 23^{2}\cdot 43$	$4$	$9.62717120852$	$186.05106825815324$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$4.43314118282$
6.0.834544.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} - 4 x^{2} + 4 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 43\cdot 1213$	$3$	$9.70304859698$	$512.7035090243354$			?	$S_6$ (as 6T16)	trivial	$2$	$2$	$7.13745940786$
6.2.859828.1	$x^{6} - 2 x^{5} + x^{4} - x^{3} + 2 x - 2$	$6$	[2,2]	$2^{2}\cdot 43\cdot 4999$	$3$	$9.75143650534$	$735.973979325699$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$7.39135025412$
6.2.861161.1	$x^{6} - 2 x^{5} + 3 x^{4} - 5 x^{3} + x^{2} - 2 x - 1$	$6$	[2,2]	$7\cdot 43\cdot 2861$	$3$	$9.75395450432$	$927.9876076758784$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.02918409802$
6.0.867568.1	$x^{6} - x^{5} + x^{4} - 3 x^{3} + 10 x^{2} - 8 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 13\cdot 43\cdot 97$	$4$	$9.76601201229$	$369.6395516944844$			?	$S_6$ (as 6T16)	trivial	$2$	$2$	$9.43257275366$
6.0.874147.1	$x^{6} - x^{5} + 2 x^{4} - 4 x^{3} + 5 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,29\cdot 43\cdot 701$	$3$	$9.77831623831$	$934.9582878396234$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$6.47531517649$
6.0.877888.1	$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 4 x + 3$	$6$	[0,3]	$-\,2^{6}\cdot 11\cdot 29\cdot 43$	$4$	$9.78527838191$	$393.9417970723264$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$5.85929773137$
6.0.887735.1	$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} + 3 x^{2} - 5 x + 2$	$6$	[0,3]	$-\,5\cdot 43\cdot 4129$	$3$	$9.80348654532$	$942.1969008652067$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$6.48459444886$
6.2.902656.1	$x^{6} - 2 x^{3} - x^{2} - 2 x + 1$	$6$	[2,2]	$2^{9}\cdot 41\cdot 43$	$3$	$9.83075890936$	$199.73015838230407$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$5.47561205841$
6.2.915728.1	$x^{6} - x^{5} - 5 x^{4} + 5 x^{3} + 10 x^{2} - 4 x - 8$	$6$	[2,2]	$2^{4}\cdot 11^{3}\cdot 43$	$3$	$9.85434468515$	$34.52369205633357$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$3$	$10.5936361225$
6.2.926392.1	$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} + 3 x^{2} - 4 x - 4$	$6$	[2,2]	$2^{3}\cdot 43\cdot 2693$	$3$	$9.87337879875$	$962.4925973741305$			?	$S_6$ (as 6T16)	trivial	$2$	$3$	$11.0665044669$
6.0.927424.1	$x^{6} + 4 x^{4} - 2 x^{3} + 4 x^{2} - 2 x + 2$	$6$	[0,3]	$-\,2^{6}\cdot 43\cdot 337$	$3$	$9.87521110455$	$270.24075143491297$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$7.65544314809$
6.0.928843.1	$x^{6} - 3 x^{5} + 6 x^{4} - 5 x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,43\cdot 21601$	$2$	$9.8777277527$	$963.765012853237$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$2.17195936894$
6.4.941872.1	$x^{6} - 5 x^{4} - 4 x^{3} + 3 x^{2} + 8 x + 1$	$6$	[4,1]	$-\,2^{4}\cdot 37^{2}\cdot 43$	$3$	$9.90068662243$	$63.31720761977336$			?	$S_4\times C_2$ (as 6T11)	trivial	$2$	$4$	$5.91016637121$
6.0.944624.1	$x^{6} - x^{5} + 3 x^{4} + x^{3} + 2 x^{2} + 2 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 43\cdot 1373$	$3$	$9.90550213481$	$385.70579167221075$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$11.3217307233$
6.0.953396.1	$x^{6} - 2 x^{5} + 2 x^{4} - 6 x^{3} + 8 x^{2} - 4 x + 3$	$6$	[0,3]	$-\,2^{2}\cdot 23\cdot 43\cdot 241$	$4$	$9.92077395297$	$976.4199916019745$				$S_6$ (as 6T16)	trivial	$2$	$2$	$8.51908510819$

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