Number field search results

Results (1-50 of 1168242 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
6.0.14731.1	$x^{6} - x^{5} + x^{3} - x^{2} + 1$	$6$	[0,3]	$-\,14731$	$1$	$4.95114187916$	$121.37133104650373$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.277754459978$
6.0.20627.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - x + 1$	$6$	[0,3]	$-\,20627$	$1$	$5.23688067144$	$143.62102910089456$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.390200557232$
6.0.22291.1	$x^{6} + x^{4} - x^{3} - x + 1$	$6$	[0,3]	$-\,22291$	$1$	$5.30503506276$	$149.30170796075979$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.373661196485$
6.0.25747.1	$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - x + 1$	$6$	[0,3]	$-\,25747$	$1$	$5.43401841081$	$160.45871743224174$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.457055178835$
6.0.27971.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,83\cdot 337$	$2$	$5.50957372539$	$167.24532878379594$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.436494860807$
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	$2$	$3$	$0.49291662671$
6.0.30808.1	$x^{6} - x^{4} - x^{3} + x^{2} + x + 1$	$6$	[0,3]	$-\,2^{3}\cdot 3851$	$2$	$5.59900150547$	$175.52207838331907$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.643679055537$
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	$2$	$3$	$0.516354684031$
6.0.31223.1	$x^{6} - x^{5} + x^{4} - x^{3} + 2 x^{2} - x + 1$	$6$	[0,3]	$-\,31223$	$1$	$5.61150177778$	$176.7003112617519$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.649982527739$
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	$2$	$3$	$0.522986177098$
6.0.32171.1	$x^{6} - x^{5} + 2 x^{4} - x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,53\cdot 607$	$2$	$5.63954535118$	$179.36276090649363$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.536093401482$
6.0.32911.1	$x^{6} - x^{3} - x^{2} + x + 1$	$6$	[0,3]	$-\,32911$	$1$	$5.6609612195$	$181.41389141959334$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.518066133218$
6.0.33791.1	$x^{6} - x^{5} + x^{4} + x^{3} + x + 1$	$6$	[0,3]	$-\,33791$	$1$	$5.68591252578$	$183.8232847057195$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.688322549696$
6.0.35099.1	$x^{6} + x^{4} + x^{2} - x + 1$	$6$	[0,3]	$-\,35099$	$1$	$5.72201673807$	$187.34727113037968$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.585021824316$
6.0.36107.1	$x^{6} - 2 x^{5} + x^{4} - x^{2} + x + 1$	$6$	[0,3]	$-\,36107$	$1$	$5.7490828547$	$190.01842015973082$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.597308900665$
6.0.36235.1	$x^{6} - x^{5} + x^{2} - x + 1$	$6$	[0,3]	$-\,5\cdot 7247$	$2$	$5.75247461617$	$190.35493164086924$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.539332757109$
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	$2$	$3$	$0.590723504629$
6.0.37423.1	$x^{6} - x^{5} + x^{4} + 1$	$6$	[0,3]	$-\,37423$	$1$	$5.78348703835$	$193.45025200293745$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.744187823103$
6.0.37463.1	$x^{6} - x^{4} - x^{3} + 2 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,37463$	$1$	$5.7845168708$	$193.55361014457984$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.73922592406$
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	$2$	$3$	$0.623496086403$
6.0.40543.1	$x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,40543$	$1$	$5.86119243277$	$201.35292399168182$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.786188226735$
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	$2$	$3$	$0.632541712933$
6.0.42316.1	$x^{6} - x^{3} + x + 1$	$6$	[0,3]	$-\,2^{2}\cdot 71\cdot 149$	$3$	$5.90315384063$	$163.27096978237046$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.805822841881$
6.0.43063.1	$x^{6} - x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,43063$	$1$	$5.92039541528$	$207.5162644228158$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.819868329343$
6.0.43531.1	$x^{6} - x + 1$	$6$	[0,3]	$-\,101\cdot 431$	$2$	$5.93107078672$	$208.64083972223654$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.658529208858$
6.0.44423.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + x + 1$	$6$	[0,3]	$-\,31\cdot 1433$	$2$	$5.95115571624$	$210.76764457572705$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.860810474755$
6.0.45203.1	$x^{6} - x^{5} + x^{4} + x^{2} - 2 x + 1$	$6$	[0,3]	$-\,17\cdot 2659$	$2$	$5.96844518752$	$212.60997154413994$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.571509421952$
6.0.45223.1	$x^{6} - x^{5} - x^{4} - x^{3} + 2 x^{2} + x + 1$	$6$	[0,3]	$-\,41\cdot 1103$	$2$	$5.96888522802$	$212.65700082527263$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.871077695404$
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	$2$	$3$	$0.678220787578$
6.0.45508.1	$x^{6} + x^{4} - x^{3} + 3 x^{2} - x + 1$	$6$	[0,3]	$-\,2^{2}\cdot 31\cdot 367$	$3$	$5.97513824991$	$213.32604154204896$			?	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.850739073869$
6.0.45872.1	$x^{6} - x^{5} - x^{3} + x + 1$	$6$	[0,3]	$-\,2^{4}\cdot 47\cdot 61$	$3$	$5.98307728259$	$84.99639580651171$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.72695280893$
6.0.46651.1	$x^{6} - 2 x^{5} + 2 x^{4} - x^{3} + 1$	$6$	[0,3]	$-\,11\cdot 4241$	$2$	$5.99989282786$	$215.98842561581858$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.602239794303$
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	$2$	$3$	$0.709398649514$
6.2.47149.1	$x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - 1$	$6$	[2,2]	$47149$	$1$	$6.01052047616$	$217.13820483738002$			✓	$S_6$ (as 6T16)	trivial	$2$	$3$	$0.696683549235$
6.0.47552.1	$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 743$	$2$	$6.01905249863$	$77.09734106958553$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.700353852026$
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	$2$	$3$	$0.721883438518$
6.0.49615.1	$x^{6} - 2 x^{5} + 3 x^{4} - x^{3} + 1$	$6$	[0,3]	$-\,5\cdot 9923$	$2$	$6.06180785233$	$222.74424796164772$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.927845321337$
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	$2$	$3$	$0.726725432084$
6.0.50587.1	$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,50587$	$1$	$6.0814408565$	$224.9155397032406$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.83864298503$
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	$2$	$3$	$0.762567083954$
6.0.52271.1	$x^{6} - x^{5} + x^{4} - x^{3} + 1$	$6$	[0,3]	$-\,167\cdot 313$	$2$	$6.11472318849$	$228.62851965579446$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.70441289436$
6.0.52891.1	$x^{6} - x^{5} + 2 x^{4} - x^{3} + x^{2} - 2 x + 1$	$6$	[0,3]	$-\,227\cdot 233$	$2$	$6.12675193156$	$229.9804339503689$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.773536140546$
6.0.54691.1	$x^{6} - x^{5} - 2 x^{3} + 2 x^{2} + 1$	$6$	[0,3]	$-\,7\cdot 13\cdot 601$	$3$	$6.16102036097$	$233.86106986841568$			✓	$S_6$ (as 6T16)	trivial	$2$	$2$	$0.665616035351$
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	$2$	$3$	$0.825072508548$