Number field search results

Results (1-50 of 262561 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	Narrow class group	Unit group torsion	Unit group rank	Regulator
8.0.1342413.1	$x^{8} - x^{7} + x^{6} + x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 16573$	$2$	$5.83425985742$	$222.97757734803739$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$0.970727427757$
8.0.1797309.1	$x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 10 x^{4} - 9 x^{3} + 7 x^{2} - 4 x + 1$	$8$	[0,4]	$3^{4}\cdot 22189$	$2$	$6.05100962346$	$258.005813887982$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.20014144807$
8.0.2118069.1	$x^{8} - x^{7} - x^{3} + 2 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 79\cdot 331$	$3$	$6.17650095624$	$280.083915996617$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.33864883478$
8.0.2217213.1	$x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - x + 1$	$8$	[0,4]	$3^{4}\cdot 31\cdot 883$	$3$	$6.21192104402$	$286.5641289484781$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.37910404568$
8.0.2314413.1	$x^{8} - x^{6} - x^{5} - x^{3} + 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 28573$	$2$	$6.24532592023$	$292.77807294946115$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.42029894182$
8.0.2712933.1	$x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + x^{4} - 2 x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 33493$	$2$	$6.37059334437$	$316.9842267369151$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.57666375612$
8.0.2824713.1	$x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} - 4 x^{4} + x^{2} + 1$	$8$	[0,4]	$3^{4}\cdot 43\cdot 811$	$3$	$6.40282734558$	$323.4486048818266$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.7400253268$
8.0.2844928.1	$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 11113$	$2$	$6.40853720479$	$210.83642948978243$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$4$	$3$	$1.11974748455$
8.0.3057993.1	$x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + x^{3} + 2 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 19\cdot 1987$	$3$	$6.46665305207$	$336.5397450524975$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.83028307754$
8.0.3167829.1	$x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 37\cdot 151$	$4$	$6.49524019945$	$342.53029063135426$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.77871765724$
8.0.3198933.1	$x^{8} - x^{7} - x^{6} + 4 x^{4} - x^{3} - 3 x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 73\cdot 541$	$3$	$6.50317802496$	$344.20778608276714$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.04684730841$
8.0.3243888.1	$x^{8} - x^{7} + 2 x^{5} - 3 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$	$8$	[0,4]	$2^{4}\cdot 3^{4}\cdot 2503$	$3$	$6.51453214511$	$245.0958995985041$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.90341831177$
8.0.3339873.1	$x^{8} - x^{7} - x^{5} + 3 x^{4} - x^{3} + 2 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 41233$	$2$	$6.53832108405$	$351.7086862731712$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.79480563528$
8.0.3379725.1	$x^{8} - x^{7} - x^{6} + x^{5} + 2 x^{3} + x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 5^{2}\cdot 1669$	$3$	$6.54802261285$	$158.22452401571636$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.12614827503$
8.0.3567321.1	$x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 9 x^{4} - 9 x^{3} + 6 x^{2} - 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 44041$	$2$	$6.59238820691$	$363.4872762559922$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.02666468748$
8.0.3684933.1	$x^{8} - x^{7} + x^{6} - 2 x^{5} - x^{3} + x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 67\cdot 97$	$4$	$6.61917250375$	$369.43064301706215$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$1.90964552544$
8.0.3707289.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{3} + 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 37\cdot 1237$	$3$	$6.62417893574$	$370.54959182274104$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.12456448497$
8.0.3747141.1	$x^{8} - x^{7} - x^{6} + x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 46261$	$2$	$6.63303829144$	$372.53590430990675$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.27220445923$
8.0.3853089.1	$x^{8} - x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{3} + 4 x^{2} - 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 47569$	$2$	$6.65619643317$	$377.76580046372646$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.17718433097$
8.0.3925989.1	$x^{8} - 3 x^{6} - x^{5} + 4 x^{4} - 2 x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 19\cdot 2551$	$3$	$6.67180946002$	$381.3226979868888$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.0361720282$
8.0.4132053.1	$x^{8} - 3 x^{7} + 2 x^{6} + 4 x^{5} - 6 x^{4} + x^{3} + 3 x^{2} - 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 139\cdot 367$	$3$	$6.71460911113$	$391.20199385994954$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.10237243409$
8.0.4237568.1	$x^{8} - x^{6} - 2 x^{3} + 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 16553$	$2$	$6.73580622678$	$257.3169252109157$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$4$	$3$	$1.44505539112$
8.0.4243509.1	$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 3 x^{3} - 2 x^{2} + 1$	$8$	[0,4]	$3^{6}\cdot 5821$	$2$	$6.73698593943$	$173.91608106375702$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.16326164535$
8.0.4383801.1	$x^{8} - 3 x^{6} - 2 x^{5} + 4 x^{4} + 3 x^{3} - 2 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 54121$	$2$	$6.76443228918$	$402.942923997928$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.36280464787$
8.0.4473088.1	$x^{8} - 2 x^{5} + x^{4} - 2 x^{3} + 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 101\cdot 173$	$3$	$6.78150256379$	$264.3709515056448$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$4$	$3$	$1.51070781357$
8.0.4532480.1	$x^{8} - x^{6} - 2 x^{5} + 2 x^{2} + 1$	$8$	[0,4]	$2^{8}\cdot 5\cdot 3541$	$3$	$6.79269300355$	$266.12027356065903$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$4$	$3$	$1.60282681328$
8.0.4540293.1	$x^{8} - 2 x^{7} + 2 x^{5} + x^{4} - 3 x^{3} - x^{2} + 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 56053$	$2$	$6.79415553977$	$410.0719449072321$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.57647619218$
8.0.4631661.1	$x^{8} - 3 x^{6} - x^{5} + 4 x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 211\cdot 271$	$3$	$6.81109747543$	$414.1774981816371$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.1969629745$
8.0.4705533.1	$x^{8} - 3 x^{7} + 5 x^{6} - 8 x^{5} + 8 x^{4} - 5 x^{3} + 5 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 43\cdot 193$	$4$	$6.82458273205$	$417.4673639938816$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.6972239063$
8.0.4807593.1	$x^{8} - x^{5} + x^{4} + x^{2} - 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 61\cdot 139$	$4$	$6.84291210674$	$421.970378107279$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.51445839838$
8.0.4830625.1	$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 6 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$	$8$	[0,4]	$5^{4}\cdot 59\cdot 131$	$3$	$6.84700138286$	$196.58331567048106$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$3$	$0.829684010287$
8.0.4842261.1	$x^{8} - x^{7} - x^{5} - x^{4} + x^{3} + x^{2} + 1$	$8$	[0,4]	$3^{5}\cdot 19927$	$2$	$6.84906084392$	$321.7821146789782$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.71317429153$
8.0.4900625.1	$x^{8} - x^{7} + 3 x^{5} - x^{4} - x^{3} + 3 x^{2} - x + 1$	$8$	[0,4]	$5^{4}\cdot 7841$	$2$	$6.85932584267$	$198.00252523642217$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$3$	$0.878208581759$
8.0.4967973.1	$x^{8} + x^{6} - x^{5} + x^{3} + 2 x^{2} + 2 x + 1$	$8$	[0,4]	$3^{4}\cdot 61333$	$2$	$6.87103883793$	$428.9510461579503$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.79092874997$
8.0.4987089.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x + 1$	$8$	[0,4]	$3^{6}\cdot 6841$	$2$	$6.87433812607$	$188.5387989877311$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.53004735949$
8.0.5040873.1	$x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 3 x^{3} + x + 1$	$8$	[0,4]	$3^{4}\cdot 62233$	$2$	$6.88356185813$	$432.0867968360061$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.58949567245$
8.0.5118208.1	$x^{8} - 3 x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{3} - x^{2} - 2 x + 1$	$8$	[0,4]	$2^{8}\cdot 19993$	$2$	$6.89667469356$	$282.79321066814884$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$4$	$3$	$1.64059012373$
8.0.5319837.1	$x^{8} - x^{7} - x^{5} - x^{3} + 2 x^{2} + 1$	$8$	[0,4]	$3^{4}\cdot 65677$	$2$	$6.93006472316$	$443.88174100766975$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.5355373112$
8.0.5467824.1	$x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 7 x^{4} - 6 x^{3} + 4 x^{2} - x + 1$	$8$	[0,4]	$2^{4}\cdot 3^{4}\cdot 4219$	$3$	$6.95387397758$	$318.2074794846909$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.71658558699$
8.0.5472441.1	$x^{8} - 3 x^{7} + 5 x^{6} - 5 x^{5} + 3 x^{4} + x^{3} - 3 x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 13\cdot 5197$	$3$	$6.95460768311$	$450.2032874158073$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.6579370044$
8.0.5481189.1	$x^{8} - x^{7} + x^{6} - 2 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 7^{2}\cdot 1381$	$3$	$6.95599637789$	$235.535384245302$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.59407059865$
8.0.5483133.1	$x^{8} - x^{6} - x^{5} - x^{4} - x^{3} + 2 x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 139\cdot 487$	$3$	$6.95630471334$	$450.64287412539875$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.96900114986$
8.0.5662953.1	$x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} - x^{4} + 3 x^{3} + x^{2} - 3 x + 1$	$8$	[0,4]	$3^{4}\cdot 151\cdot 463$	$3$	$6.98442035977$	$457.9727066103394$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.79658562792$
8.0.5714469.1	$x^{8} - x^{7} + x^{6} - x^{5} - 2 x^{3} + x^{2} + x + 1$	$8$	[0,4]	$3^{4}\cdot 70549$	$2$	$6.99233110586$	$460.0510841200138$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.56163841606$
8.2.5756875.1	$x^{8} - x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{3} + 2 x^{2} - 1$	$8$	[2,3]	$-\,5^{4}\cdot 61\cdot 151$	$3$	$6.99879624201$	$214.60428700284623$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$1.01211341069$
8.0.5765013.1	$x^{8} - x^{7} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 103\cdot 691$	$3$	$7.00003217752$	$462.08116170214083$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.58733763409$
8.2.5856875.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{3} + x^{2} + x - 1$	$8$	[2,3]	$-\,5^{4}\cdot 9371$	$2$	$7.0138785967$	$216.4601579968009$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$2$	$4$	$1.02990013853$
8.0.5868288.1	$x^{8} - 2 x^{6} - 2 x^{5} + 2 x^{3} + 5 x^{2} + 4 x + 1$	$8$	[0,4]	$2^{8}\cdot 3^{4}\cdot 283$	$3$	$7.01558559136$	$106.87720479506591$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$3.10452142763$
8.0.5923449.1	$x^{8} - x^{7} + 4 x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} + 1$	$8$	[0,4]	$3^{4}\cdot 7\cdot 31\cdot 337$	$4$	$7.02379506717$	$468.3876599570061$			?	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.86410363062$
8.0.5981769.1	$x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - x + 1$	$8$	[0,4]	$3^{4}\cdot 73849$	$2$	$7.03240225818$	$470.68779461549667$			✓	$S_4\wr C_2$ (as 8T47)	trivial	trivial	$6$	$3$	$2.89315764789$

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