Number field search results

Results (1-50 of 14805 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
8.0.60886809.1	$x^{8} + 7 x^{6} + 18 x^{4} + 16 x^{2} + 1$	$8$	[0,4]	$3^{6}\cdot 17^{4}$	$2$	$9.39864837017$	$15.070935874553902$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$10.543427475$
8.0.71639296.2	$x^{8} - x^{6} - 3 x^{4} + 4 x^{2} + 4$	$8$	[0,4]	$2^{8}\cdot 23^{4}$	$2$	$9.59166304663$	$16.175158798180128$				$S_4$ (as 8T14)	trivial	$4$	$3$	$11.2478320219$
8.0.96059601.1	$x^{8} - x^{7} - 2 x^{6} - 5 x^{5} + 11 x^{4} + x^{3} + 4 x^{2} - x + 1$	$8$	[0,4]	$3^{8}\cdot 11^{4}$	$2$	$9.94987437107$	$17.819817582388065$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$11.2924984888$
8.0.116640000.2	$x^{8} - 2 x^{6} + 6 x^{4} - 12 x^{3} + 16 x^{2} - 12 x + 4$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 5^{4}$	$3$	$10.1942654691$	$14.963135389464592$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$17.8405677725$
8.0.136048896.1	$x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{5} + 5 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{12}$	$2$	$10.3923048454$	$16.82379477331321$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$28.1796625828$
8.0.332150625.1	$x^{8} - x^{7} + x^{6} - 8 x^{5} + 5 x^{4} - 2 x^{3} + 16 x^{2} - 4 x + 1$	$8$	[0,4]	$3^{12}\cdot 5^{4}$	$2$	$11.6189500386$	$21.91302343598798$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$19.6566266931$
8.0.333135504.3	$x^{8} + 4 x^{6} + 12 x^{4} + 28 x^{2} + 16$	$8$	[0,4]	$2^{4}\cdot 3^{6}\cdot 13^{4}$	$3$	$11.6232509648$	$20.005826881210375$				$S_4$ (as 8T14)	trivial	$6$	$3$	$39.4714772754$
8.0.429981696.1	$x^{8} - 2 x^{6} + 15 x^{4} + 10 x^{2} + 1$	$8$	[0,4]	$2^{16}\cdot 3^{8}$	$2$	$12.0$	$17.3069948436889$			?	$S_4$ (as 8T14)	trivial	$4$	$3$	$28.6493846676$
8.0.429981696.3	$x^{8} - 6 x^{6} - 8 x^{5} + 9 x^{4} + 24 x^{3} + 22 x^{2} + 12 x + 3$	$8$	[0,4]	$2^{16}\cdot 3^{8}$	$2$	$12.0$	$16.17607385516733$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$62.096926078$
8.0.448084224.10	$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} - 5 x^{4} + 2 x^{3} + 28 x^{2} - 28 x + 7$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 7^{4}$	$3$	$12.062017569$	$18.725839469079336$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$44.1851178135$
8.0.453519616.1	$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 27 x^{4} - 22 x^{3} + 16 x^{2} - 8 x + 3$	$8$	[0,4]	$2^{8}\cdot 11^{6}$	$2$	$12.0802107091$	$13.559578056516557$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$22.8048359505$
8.0.479785216.2	$x^{8} + 4 x^{6} - 4 x^{5} + 11 x^{4} - 8 x^{3} + 18 x^{2} - 14 x + 3$	$8$	[0,4]	$2^{8}\cdot 37^{4}$	$2$	$12.1655250606$	$13.655340178276088$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$22.1357761962$
8.0.479785216.3	$x^{8} + 3 x^{6} + 13 x^{4} + 20 x^{2} + 4$	$8$	[0,4]	$2^{8}\cdot 37^{4}$	$2$	$12.1655250606$	$22.20740493717357$				$S_4$ (as 8T14)	trivial	$4$	$3$	$31.2810018817$
8.0.752734096.1	$x^{8} - 3 x^{7} + 5 x^{6} - 2 x^{4} + 5 x^{2} - 3 x + 1$	$8$	[0,4]	$2^{4}\cdot 19^{6}$	$2$	$12.8700489453$	$14.446141500988903$				$S_4$ (as 8T14)	trivial	$2$	$3$	$25.6417981886$
8.0.835210000.1	$x^{8} - 3 x^{7} + 11 x^{6} - 18 x^{5} + 34 x^{4} - 18 x^{3} + 11 x^{2} - 3 x + 1$	$8$	[0,4]	$2^{4}\cdot 5^{4}\cdot 17^{4}$	$3$	$13.0384048104$	$23.46772264658785$				$S_4$ (as 8T14)	trivial	$2$	$3$	$16.4638220565$
8.0.875213056.2	$x^{8} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 8 x^{3} + 10 x^{2} - 6 x + 13$	$8$	[0,4]	$2^{8}\cdot 43^{4}$	$2$	$13.1148770486$	$14.720951755301632$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$14.9686265205$
8.0.959512576.3	$x^{8} + 2 x^{6} - 8 x^{5} + 13 x^{4} - 8 x^{3} + 6 x^{2} - 4 x + 3$	$8$	[0,4]	$2^{16}\cdot 11^{4}$	$2$	$13.2664991614$	$14.891141822623867$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$34.2515579012$
8.0.959512576.4	$x^{8} - 4 x^{5} + 5 x^{4} - 12 x^{3} + 8 x^{2} + 8 x + 4$	$8$	[0,4]	$2^{16}\cdot 11^{4}$	$2$	$13.2664991614$	$19.784349772994805$			?	$S_4$ (as 8T14)	$[2]$	$4$	$3$	$51.9671971775$
8.0.1049760000.2	$x^{8} - 8 x^{5} + 21 x^{4} - 4 x^{2} + 6 x + 9$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 5^{4}$	$3$	$13.416407865$	$21.719425659017812$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$17.0690103888$
8.0.1049760000.4	$x^{8} - 2 x^{7} + 4 x^{6} + 8 x^{5} - 7 x^{4} - 4 x^{3} + 16 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 5^{4}$	$3$	$13.416407865$	$18.08540037460562$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$51.5026598813$
8.0.1146228736.6	$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 17 x^{4} - 22 x^{3} + 42 x^{2} - 32 x + 26$	$8$	[0,4]	$2^{12}\cdot 23^{4}$	$2$	$13.5646599663$	$13.564659966250536$			?	$S_4$ (as 8T14)	$[3]$	$2$	$3$	$26.0130014194$
8.0.1222830961.1	$x^{8} - 3 x^{7} + 7 x^{6} - 13 x^{5} + 16 x^{4} - 18 x^{3} + 13 x^{2} - 3 x + 2$	$8$	[0,4]	$11^{4}\cdot 17^{4}$	$2$	$13.6747943312$	$20.39324096205559$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$51.509600867$
8.0.1275989841.1	$x^{8} - x^{7} - 8 x^{6} - 3 x^{5} + 21 x^{4} + 33 x^{3} + 30 x^{2} + 15 x + 3$	$8$	[0,4]	$3^{12}\cdot 7^{4}$	$2$	$13.7477270849$	$27.423380759717027$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$57.4692346888$
8.0.1366263369.2	$x^{8} - x^{7} - 2 x^{6} + 11 x^{5} + x^{4} - 19 x^{3} + 46 x^{2} - 7 x + 1$	$8$	[0,4]	$3^{6}\cdot 37^{4}$	$2$	$13.8657001136$	$25.31096813546976$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$52.912962287$
8.0.1640250000.1	$x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 6 x^{4} + 5 x^{3} + 5 x^{2} - 30 x + 20$	$8$	[0,4]	$2^{4}\cdot 3^{8}\cdot 5^{6}$	$3$	$14.186124135$	$22.965496550279074$				$S_4$ (as 8T14)	$[4]$	$2$	$3$	$9.4319549508$
8.0.1871773696.6	$x^{8} - 4 x^{5} - x^{4} - 4 x^{3} + 8 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{16}\cdot 13^{4}$	$2$	$14.4222051019$	$22.11509925471549$			?	$S_4$ (as 8T14)	trivial	$4$	$3$	$60.9604008$
8.0.2176782336.3	$x^{8} - 2 x^{7} + 4 x^{6} + 8 x^{5} - 10 x^{4} + 8 x^{3} + 16 x^{2} - 8 x + 4$	$8$	[0,4]	$2^{12}\cdot 3^{12}$	$2$	$14.6969384567$	$21.196653174008656$			?	$S_4$ (as 8T14)	$[2]$	$6$	$3$	$76.2961725516$
8.0.2176782336.5	$x^{8} + 9 x^{4} + 48 x^{2} - 108 x + 81$	$8$	[0,4]	$2^{12}\cdot 3^{12}$	$2$	$14.6969384567$	$21.196653174008656$				$S_4$ (as 8T14)	$[4]$	$6$	$3$	$47.0270960244$
8.0.2621440000.14	$x^{8} + 4 x^{6} - 8 x^{5} + 24 x^{2} + 16 x + 12$	$8$	[0,4]	$2^{22}\cdot 5^{4}$	$2$	$15.0424123723$	$19.670368273611786$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$50.9500558475$
8.0.2621440000.15	$x^{8} + 4 x^{6} + 24 x^{2} + 4$	$8$	[0,4]	$2^{22}\cdot 5^{4}$	$2$	$15.0424123723$	$19.670368273611786$			?	$S_4$ (as 8T14)	$[2]$	$2$	$3$	$36.9367874458$
8.0.2702336256.3	$x^{8} - 4 x^{7} + 10 x^{6} - 10 x^{5} + 21 x^{4} - 26 x^{3} - 8 x^{2} + 16 x + 7$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 19^{4}$	$3$	$15.0996688705$	$16.948805249221287$			?	$S_4$ (as 8T14)	$[2]$	$2$	$3$	$23.6999270915$
8.0.2702336256.4	$x^{8} - 2 x^{7} - 4 x^{6} + 16 x^{5} - 11 x^{4} - 10 x^{3} + 38 x^{2} - 76 x + 76$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 19^{4}$	$3$	$15.0996688705$	$24.665676068346546$				$S_4$ (as 8T14)	$[2]$	$6$	$3$	$66.6012242841$
8.0.2732361984.9	$x^{8} - 8 x^{6} + 6 x^{4} + 52 x^{2} + 25$	$8$	[0,4]	$2^{8}\cdot 3^{6}\cdot 11^{4}$	$3$	$15.1205392298$	$25.31071378065398$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$87.2113448362$
8.0.2750058481.1	$x^{8} + 4 x^{6} - 14 x^{5} + 35 x^{4} - 28 x^{3} + 111 x^{2} - 217 x + 183$	$8$	[0,4]	$229^{4}$	$1$	$15.1327459504$	$15.132745950421556$			?	$S_4$ (as 8T14)	$[3]$	$2$	$3$	$19.7429526233$
8.0.2897022976.2	$x^{8} + 4 x^{6} + x^{4} + 4 x^{2} - 12 x + 9$	$8$	[0,4]	$2^{12}\cdot 29^{4}$	$2$	$15.2315462117$	$26.697893241960433$				$S_4$ (as 8T14)	trivial	$2$	$3$	$47.7084518017$
8.0.2998219536.1	$x^{8} - 3 x^{7} + 11 x^{6} - 20 x^{5} + 36 x^{4} - 40 x^{3} + 48 x^{2} - 36 x + 12$	$8$	[0,4]	$2^{4}\cdot 3^{8}\cdot 13^{4}$	$3$	$15.2970585408$	$24.76395538367976$				$S_4$ (as 8T14)	trivial	$2$	$3$	$110.248889815$
8.0.3049800625.1	$x^{8} - 2 x^{7} + 6 x^{6} - 11 x^{5} + 23 x^{4} - 22 x^{3} + 24 x^{2} - 16 x + 16$	$8$	[0,4]	$5^{4}\cdot 47^{4}$	$2$	$15.3297097168$	$29.121712326588785$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$22.7158477533$
8.0.3102044416.2	$x^{8} + 5 x^{6} - 8 x^{4} - 19 x^{2} + 25$	$8$	[0,4]	$2^{8}\cdot 59^{4}$	$2$	$15.3622914957$	$30.310842188004106$				$S_4$ (as 8T14)	trivial	$4$	$3$	$81.7319765262$
8.0.3264065424.1	$x^{8} - x^{7} - 2 x^{6} - 13 x^{5} + 16 x^{4} + 11 x^{3} + 31 x^{2} - 10 x + 4$	$8$	[0,4]	$2^{4}\cdot 3^{6}\cdot 23^{4}$	$3$	$15.4603690591$	$29.264840547661525$				$S_4$ (as 8T14)	trivial	$6$	$3$	$146.739959242$
8.0.3317760000.18	$x^{8} + 4 x^{6} - 8 x^{5} + 14 x^{4} - 16 x^{3} + 24 x^{2} + 8 x + 4$	$8$	[0,4]	$2^{16}\cdot 3^{4}\cdot 5^{4}$	$3$	$15.4919333848$	$22.739048476302873$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$111.243918169$
8.0.3782742016.4	$x^{8} + 6 x^{6} - 16 x^{5} + 41 x^{4} - 48 x^{3} + 36 x^{2} - 8 x + 8$	$8$	[0,4]	$2^{12}\cdot 31^{4}$	$2$	$15.748015748$	$15.748015748023622$			?	$S_4$ (as 8T14)	$[3]$	$2$	$3$	$39.5209586903$
8.0.4032758016.2	$x^{8} - 2 x^{7} - 2 x^{6} + 12 x^{5} - 3 x^{4} - 12 x^{3} + 12 x^{2} - 12 x + 15$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 7^{4}$	$3$	$15.8745078664$	$21.398934305093306$			?	$S_4$ (as 8T14)	$[2]$	$2$	$3$	$36.6539049589$
8.0.4032758016.3	$x^{8} - 4 x^{7} - 2 x^{6} + 18 x^{5} + 3 x^{4} - 30 x^{3} - 12 x^{2} + 24 x + 21$	$8$	[0,4]	$2^{8}\cdot 3^{8}\cdot 7^{4}$	$3$	$15.8745078664$	$29.59659971198356$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$236.229814956$
8.0.4362470401.1	$x^{8} + 14 x^{6} - 6 x^{5} + 82 x^{4} - 42 x^{3} + 240 x^{2} - 99 x + 208$	$8$	[0,4]	$257^{4}$	$1$	$16.0312195419$	$16.0312195418814$			?	$S_4$ (as 8T14)	$[3]$	$2$	$3$	$38.2492235483$
8.0.4569760000.12	$x^{8} - 4 x^{7} + 6 x^{6} - 2 x^{5} - 11 x^{4} + 18 x^{3} + 6 x^{2} - 8 x + 3$	$8$	[0,4]	$2^{8}\cdot 5^{4}\cdot 13^{4}$	$3$	$16.1245154966$	$23.667552036665935$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$54.5041475238$
8.0.4640470641.1	$x^{8} - 3 x^{7} + 7 x^{6} - 19 x^{5} + 30 x^{4} - 31 x^{3} + 35 x^{2} - 18 x + 5$	$8$	[0,4]	$3^{8}\cdot 29^{4}$	$2$	$16.1554944214$	$23.300254887372947$			?	$S_4$ (as 8T14)	trivial	$2$	$3$	$44.4493116871$
8.0.4857532416.13	$x^{8} + 6 x^{6} - 13 x^{4} + 18 x^{2} + 1$	$8$	[0,4]	$2^{12}\cdot 3^{4}\cdot 11^{4}$	$3$	$16.2480768093$	$24.230780918292734$			?	$S_4$ (as 8T14)	$[2]$	$4$	$3$	$53.2704622783$
8.0.5082121521.1	$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 11 x^{4} + 38 x^{3} + 49 x^{2} - 41 x + 7$	$8$	[0,4]	$3^{4}\cdot 89^{4}$	$2$	$16.3401346384$	$34.52661206259704$				$S_4$ (as 8T14)	$[2]$	$6$	$3$	$191.633322593$
8.0.5314410000.3	$x^{8} - x^{7} - 8 x^{6} + 3 x^{5} + 6 x^{4} - 15 x^{3} + 120 x^{2} - 39 x + 129$	$8$	[0,4]	$2^{4}\cdot 3^{12}\cdot 5^{4}$	$3$	$16.4316767252$	$26.60075518545295$				$S_4$ (as 8T14)	$[4]$	$6$	$3$	$68.6668112391$
8.0.5752160649.1	$x^{8} - 3 x^{7} + 6 x^{6} - 9 x^{5} + 3 x^{4} + 27 x^{3} + 18 x^{2} - 27 x + 9$	$8$	[0,4]	$3^{6}\cdot 53^{4}$	$2$	$16.595061868$	$32.163121211649134$			?	$S_4$ (as 8T14)	trivial	$6$	$3$	$114.883606025$