Number field search results

Results (1-50 of 4316 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
8.0.1282789.1	$x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - 2 x + 1$	$8$	[0,4]	$1103\cdot 1163$	$2$	$5.80122090621$	$1132.6027547202946$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.313539838403$
8.0.1385533.1	$x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + x^{4} + 1$	$8$	[0,4]	$29\cdot 47777$	$2$	$5.85736259192$	$1177.0866578124144$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.331112529152$
8.0.1474013.1	$x^{8} - x^{7} + x^{6} - x^{4} + x^{3} - x^{2} + 1$	$8$	[0,4]	$617\cdot 2389$	$2$	$5.90286246256$	$1214.0893706807585$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.345105135911$
8.0.1590773.1	$x^{8} - x^{7} + 2 x^{5} - 2 x^{4} + x^{3} + x^{2} - 2 x + 1$	$8$	[0,4]	$179\cdot 8887$	$2$	$5.95937927669$	$1261.2584984847476$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.363609073488$
8.0.1740113.1	$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 3 x^{2} - x + 1$	$8$	[0,4]	$1740113$	$1$	$6.0265974216$	$1319.1334276713633$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.38876666774366264$
8.0.1867553.1	$x^{8} - x^{7} + x^{5} - 2 x^{4} + x^{3} + x^{2} - x + 1$	$8$	[0,4]	$1867553$	$1$	$6.08007752654$	$1366.5844284199934$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.40885972396034426$
8.0.2105893.1	$x^{8} - x^{7} + 2 x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - 2 x + 1$	$8$	[0,4]	$29\cdot 72617$	$2$	$6.17205144936$	$1451.1695283460165$			✓	$S_8$ (as 8T50)	trivial	$2$	$3$	$0.44069755405256955$
8.2.4296211.1	$x^{8} - x^{7} + 3 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$	$8$	[2,3]	$-\,199\cdot 21589$	$2$	$6.74738824726$	$2072.7303249578804$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.83312070768$
8.2.4297507.1	$x^{8} - x^{7} - 2 x^{6} + x^{5} + x^{3} + 2 x^{2} - 1$	$8$	[2,3]	$-\,2011\cdot 2137$	$2$	$6.74764264181$	$2073.0429325028463$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.83318984365$
8.2.4364587.1	$x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 1$	$8$	[2,3]	$-\,29\cdot 150503$	$2$	$6.76071913838$	$2089.159400333062$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8412077944090119$
8.2.4386467.1	$x^{8} - x^{7} - x^{6} + 3 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + x - 1$	$8$	[2,3]	$-\,41\cdot 83\cdot 1289$	$3$	$6.76494637444$	$2094.3894098280766$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8443442011032247$
8.2.4421387.1	$x^{8} - 2 x^{7} + 2 x^{6} + x^{5} - 2 x^{4} + x^{3} + x^{2} - 1$	$8$	[2,3]	$-\,1321\cdot 3347$	$2$	$6.77165488361$	$2102.7094426001895$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.848612129114202$
8.2.4423907.1	$x^{8} - x^{7} - 2 x^{6} + 3 x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} + x + 1$	$8$	[2,3]	$-\,4423907$	$1$	$6.772137207270576$	$2103.308584112184$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8486556559484179$
8.2.4456891.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - 2 x^{3} + x - 1$	$8$	[2,3]	$-\,4456891$	$1$	$6.778428222351358$	$2111.1350027887843$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8533890882180042$
8.2.4505651.1	$x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 5 x^{4} - 3 x^{3} + x^{2} + x - 1$	$8$	[2,3]	$-\,4505651$	$1$	$6.787653961428009$	$2122.6518791360963$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8590899748258677$
8.2.4542739.1	$x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 4 x^{4} - x^{3} - x^{2} + x - 1$	$8$	[2,3]	$-\,4542739$	$1$	$6.794612960385022$	$2131.370216550846$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8640907466005752$
8.2.4570091.1	$x^{8} - x^{6} - x^{5} + x^{4} - x^{3} - 2 x^{2} + x + 1$	$8$	[2,3]	$-\,1249\cdot 3659$	$2$	$6.799713367076283$	$2137.7771165395143$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8691071409989591$
8.2.4570723.1	$x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + 2 x^{3} - 4 x^{2} + 3 x - 1$	$8$	[2,3]	$-\,4570723$	$1$	$6.7998309019$	$2137.9249285229826$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8669605427357915$
8.2.4584491.1	$x^{8} - x^{7} + 2 x^{6} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$	$8$	[2,3]	$-\,19\cdot 101\cdot 2389$	$3$	$6.80238785315$	$2141.1424520568453$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8688179378958599$
8.2.4596992.1	$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} - 2 x + 1$	$8$	[2,3]	$-\,2^{8}\cdot 17957$	$2$	$6.804703687569884$	$491.52785359466174$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8711682249043199$
8.2.4603987.1	$x^{8} - x^{7} - 2 x^{6} + x^{5} + 2 x^{4} - x - 1$	$8$	[2,3]	$-\,4603987$	$1$	$6.8059971215378265$	$2145.690331804662$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8718212555217068$
8.2.4614499.1	$x^{8} - x^{7} + x^{5} + x^{4} - 2 x^{3} + 2 x - 1$	$8$	[2,3]	$-\,4614499$	$1$	$6.807937648205655$	$2148.1384964661847$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8729503709676886$
8.2.4623371.1	$x^{8} + x^{6} - x^{3} - x^{2} - 1$	$8$	[2,3]	$-\,17\cdot 31^{2}\cdot 283$	$3$	$6.809572421507061$	$684.4769184408666$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.873839750719525$
8.2.4648192.1	$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} - x^{2} + 1$	$8$	[2,3]	$-\,2^{8}\cdot 67\cdot 271$	$3$	$6.814131452560941$	$494.2575233501126$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8773171765831781$
8.2.4663051.1	$x^{8} - x^{6} - 2 x^{5} + x^{4} + x^{2} + 2 x - 1$	$8$	[2,3]	$-\,31\cdot 359\cdot 419$	$3$	$6.816850516631215$	$2159.409873090331$			?	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8785601974574553$
8.2.4690927.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} + x^{4} - 2 x^{3} + 2 x - 1$	$8$	[2,3]	$-\,443\cdot 10589$	$2$	$6.8219311864100645$	$2165.854796610336$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8833361607728416$
8.2.4761667.1	$x^{8} - x^{7} + x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 4 x^{2} + 3 x - 1$	$8$	[2,3]	$-\,23\cdot 207029$	$2$	$6.834706625519568$	$2182.1244235835866$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.892409675427044$
8.2.4775363.1	$x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 2 x^{4} - 3 x^{3} + 3 x^{2} - 1$	$8$	[2,3]	$-\,1931\cdot 2473$	$2$	$6.837160875217895$	$2185.2603963830034$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.892761210808111$
8.2.4785667.1	$x^{8} - x^{7} + 2 x^{6} - x^{5} + x^{3} - 2 x^{2} + 2 x - 1$	$8$	[2,3]	$-\,29\cdot 59\cdot 2797$	$3$	$6.839003240119339$	$2187.616739742133$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8954120433168544$
8.2.4809907.1	$x^{8} - 2 x^{7} + 3 x^{6} - 5 x^{5} + 5 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$	$8$	[2,3]	$-\,19\cdot 253153$	$2$	$6.843323725534318$	$2193.15001766865$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.8973516802448191$
8.2.4858379.1	$x^{8} + 3 x^{6} - x^{5} + 2 x^{4} - 3 x^{3} - 2 x + 1$	$8$	[2,3]	$-\,17^{2}\cdot 16811$	$2$	$6.851906434395191$	$534.5904974838218$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9045989163533711$
8.2.4931267.1	$x^{8} - 2 x^{7} + x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$	$8$	[2,3]	$-\,11\cdot 67\cdot 6691$	$3$	$6.864672373301241$	$2220.6456268391858$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9159002625287757$
8.2.5040467.1	$x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{4} + 4 x^{3} - x + 1$	$8$	[2,3]	$-\,5040467$	$1$	$6.883492554051752$	$2245.098438821781$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9288588955969742$
8.2.5040547.1	$x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{5} + 2 x^{4} - x^{3} + x^{2} + 1$	$8$	[2,3]	$-\,37\cdot 59\cdot 2309$	$3$	$6.883506210414857$	$2245.116255341803$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9268647190390614$
8.2.5103467.1	$x^{8} - x^{7} - x^{6} + x^{5} + x^{4} + x^{3} - 2 x^{2} + 1$	$8$	[2,3]	$-\,5103467$	$1$	$6.894188661972919$	$2259.0854344180966$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9341515370278446$
8.2.5107019.1	$x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} + 2 x - 1$	$8$	[2,3]	$-\,5107019$	$1$	$6.894788271629269$	$2259.871456521366$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9337002743186916$
8.2.5118587.1	$x^{8} - x^{7} - x^{6} + x^{5} + x^{2} - x - 1$	$8$	[2,3]	$-\,29\cdot 176503$	$2$	$6.896738528281753$	$2262.429446413744$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9358964080809821$
8.2.5155867.1	$x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} - x^{3} - 3 x^{2} + 1$	$8$	[2,3]	$-\,449\cdot 11483$	$2$	$6.902997454301547$	$2270.653430182598$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9405039275650298$
8.2.5165819.1	$x^{8} - 2 x^{6} - x^{5} + 2 x^{4} + 3 x^{3} - x - 1$	$8$	[2,3]	$-\,641\cdot 8059$	$2$	$6.904661594549214$	$2272.843813375657$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9414451308962976$
8.2.5204491.1	$x^{8} - x^{7} + x^{6} - 2 x^{4} + x^{3} - x^{2} - x + 1$	$8$	[2,3]	$-\,5204491$	$1$	$6.911101682109057$	$2281.335354567583$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9486003676975986$
8.2.5233147.1	$x^{8} - 2 x^{7} + 2 x^{5} + x^{4} - x^{3} - 2 x^{2} + x + 1$	$8$	[2,3]	$-\,5233147$	$1$	$6.915846841129293$	$2287.607265244627$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9515125685677428$
8.2.5272027.1	$x^{8} - x^{7} - x^{6} + 3 x^{5} - x^{4} - 3 x^{3} + 2 x^{2} - 1$	$8$	[2,3]	$-\,317\cdot 16631$	$2$	$6.922248776687624$	$2296.08950173986$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9542437305912765$
8.2.5286727.1	$x^{8} - x^{7} - x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} - 1$	$8$	[2,3]	$-\,5286727$	$1$	$6.924658503091751$	$2299.2883681695953$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9546924661447783$
8.2.5293867.1	$x^{8} - x^{7} + 2 x^{5} - x^{4} - x^{3} + x^{2} + x - 1$	$8$	[2,3]	$-\,227\cdot 23321$	$2$	$6.925826826912146$	$2300.840498600457$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9584670756759093$
8.2.5344939.1	$x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} - x^{3} - x^{2} + 2 x - 1$	$8$	[2,3]	$-\,521\cdot 10259$	$2$	$6.934143805490464$	$2311.912411835708$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9628254972480232$
8.2.5346947.1	$x^{8} - x^{6} - x^{5} + x^{4} + 2 x^{3} - 2 x - 1$	$8$	[2,3]	$-\,839\cdot 6373$	$2$	$6.934469381534787$	$2312.3466435636333$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9655694198061011$
8.2.5359051.1	$x^{8} - x^{7} + x^{6} - 2 x^{4} + 4 x^{3} - 4 x^{2} + 3 x - 1$	$8$	[2,3]	$-\,5359051$	$1$	$6.936429654555921$	$2314.9624187014356$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.966607895416933$
8.2.5371171.1	$x^{8} - x^{7} - 2 x^{6} + 2 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$	$8$	[2,3]	$-\,13\cdot 413167$	$2$	$6.938388640914016$	$2317.5786933780696$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9653280496288915$
8.2.5420747.1	$x^{8} - 2 x^{7} + 3 x^{5} - 2 x^{4} - x^{3} + 2 x^{2} - x - 1$	$8$	[2,3]	$-\,5420747$	$1$	$6.946361680883116$	$2328.2497718243203$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9711981530018224$
8.2.5525731.1	$x^{8} - 2 x^{6} - x^{5} + 3 x^{4} + 3 x^{3} - 2 x - 1$	$8$	[2,3]	$-\,17\cdot 325043$	$2$	$6.963037231804726$	$2350.687346288315$			✓	$S_8$ (as 8T50)	trivial	$2$	$4$	$0.9861710990807576$