Number field search results

Results (1-50 of 305609 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
10.0.216670707.1	$x^{10} - 3 x^{9} + 5 x^{8} - 6 x^{7} + 6 x^{6} - 4 x^{5} + 2 x^{4} - x^{3} + x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 11^{2}\cdot 7369$	$3$	$6.8167916456$	$493.1298003568634$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.74293786533$
10.0.226173952.1	$x^{10} - x^{8} - 2 x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 220873$	$2$	$6.84611608122$	$939.9425514359907$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.19443787527$
10.0.236184579.1	$x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 7 x^{6} - 6 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 37\cdot 109\cdot 241$	$4$	$6.87583036876$	$1707.5886507001621$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.84211740914$
10.0.246944619.1	$x^{10} - x^{9} + x^{6} - x^{5} - x^{4} + 3 x^{3} - x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 73\cdot 13921$	$3$	$6.90653086059$	$1746.0524047118402$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.90076515959$
10.0.260270739.1	$x^{10} - x^{8} - 2 x^{7} + x^{6} + 3 x^{5} - 2 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 163\cdot 6571$	$3$	$6.9429259695$	$1792.545396914678$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.96704129047$
10.0.262909719.1	$x^{10} - x^{8} - x^{7} - 2 x^{6} + 4 x^{4} + x^{3} - 2 x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 73\cdot 14821$	$3$	$6.94993374018$	$1801.610113204297$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.97569183141$
10.0.268043264.1	$x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 6 x^{5} + 7 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{10}\cdot 261761$	$2$	$6.96338631704$	$1023.2516796956651$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.33676061738$
10.0.284152779.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 2 x^{6} - 3 x^{5} - 2 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1169353$	$2$	$7.00414600793$	$1872.9813133077437$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.07998415618$
10.0.293950539.1	$x^{10} - x^{9} + 2 x^{7} - 2 x^{5} + x^{4} + 2 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 19\cdot 63667$	$3$	$7.02792998264$	$1904.9984251961994$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.12408409954$
10.0.298726947.1	$x^{10} + x^{8} - 2 x^{7} + x^{6} - 3 x^{5} + 4 x^{4} - x^{3} + 2 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1229329$	$2$	$7.0392670275$	$1920.4132367800426$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.14507565936$
10.0.310466763.1	$x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} + 2 x^{6} - x^{4} + 2 x^{3} - x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 643\cdot 1987$	$3$	$7.06645359577$	$1957.7852282617723$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.20892554614$
10.0.324037827.1	$x^{10} - 3 x^{9} + 3 x^{8} - x^{7} - 2 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1333489$	$2$	$7.09675105687$	$2000.1167465925582$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.28471092827$
10.0.328878387.1	$x^{10} - x^{9} - 3 x^{8} + 2 x^{7} + 6 x^{6} - 2 x^{5} - 5 x^{4} - x^{3} + x^{2} + 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 379\cdot 3571$	$3$	$7.10728176798$	$2015.0004962778546$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.34168673634$
10.0.334491687.1	$x^{10} - 3 x^{9} + 6 x^{8} - 8 x^{7} + 10 x^{6} - 11 x^{5} + 13 x^{4} - 13 x^{3} + 9 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1376509$	$2$	$7.11932030809$	$2032.123765915846$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.33321543714$
10.0.336597039.1	$x^{10} - x^{9} + x^{7} + x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 31\cdot 44683$	$3$	$7.12378869718$	$2038.509013960939$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.31395502357$
10.0.337121919.1	$x^{10} - x^{9} + x^{8} - x^{7} + 2 x^{5} - x^{4} + x^{3} - x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 307\cdot 4519$	$3$	$7.12489878211$	$2040.097791773718$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.32775666901$
10.0.359802567.1	$x^{10} - 3 x^{9} + 7 x^{8} - 10 x^{7} + 14 x^{6} - 13 x^{5} + 12 x^{4} - 6 x^{3} + 5 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1480669$	$2$	$7.17144093323$	$2107.606936788736$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.48495668105$
10.0.372491264.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{6} + 2 x^{5} - x^{4} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 363761$	$2$	$7.19633892683$	$1206.2520466303881$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.66804681887$
10.0.381570507.1	$x^{10} - 2 x^{9} + 2 x^{8} - 5 x^{7} + 5 x^{6} - 3 x^{5} + 5 x^{4} - 2 x^{3} + 2 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 151\cdot 10399$	$3$	$7.21369008023$	$2170.4255343134905$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.51157459686$
10.0.386017407.1	$x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 5 x^{6} - 5 x^{5} + 6 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 43\cdot 36943$	$3$	$7.22205329402$	$2183.036188431149$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.59702145251$
10.0.388323963.1	$x^{10} - 4 x^{9} + 8 x^{8} - 11 x^{7} + 13 x^{6} - 13 x^{5} + 11 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 127\cdot 12583$	$3$	$7.22635710195$	$2189.548583612613$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.535271131$
10.0.388496007.1	$x^{10} - 4 x^{9} + 8 x^{8} - 13 x^{7} + 17 x^{6} - 18 x^{5} + 17 x^{4} - 13 x^{3} + 8 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 61\cdot 26209$	$3$	$7.22667719643$	$2190.033561386674$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.53086209866$
10.0.388924659.1	$x^{10} - 2 x^{9} + 6 x^{7} - 5 x^{6} - 5 x^{5} + 8 x^{4} - 4 x^{2} + x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 571\cdot 2803$	$3$	$7.2274741654$	$2191.2414289621306$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.55136080635$
10.0.393584427.1	$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 3 x^{6} - 2 x^{5} - x^{4} + 2 x^{3} - x^{2} + x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1619689$	$2$	$7.23608718092$	$2204.3291496507504$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.63850385514$
10.0.395567307.1	$x^{10} - x^{9} - 3 x^{8} + 5 x^{7} + 3 x^{6} - 8 x^{5} + x^{4} + 5 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1627849$	$2$	$7.23972448615$	$2209.8748833361583$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.55652024571$
10.0.401836707.1	$x^{10} - 4 x^{9} + 10 x^{8} - 19 x^{7} + 28 x^{6} - 32 x^{5} + 30 x^{4} - 22 x^{3} + 12 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 61\cdot 27109$	$3$	$7.25111779974$	$2227.318342761088$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.65655309745$
10.0.402011667.1	$x^{10} - 3 x^{8} - 3 x^{7} + 4 x^{6} + 7 x^{5} - 6 x^{3} - 2 x^{2} + 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1654369$	$2$	$7.25143345211$	$2227.8031780208953$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.67086875589$
10.0.402381999.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 19 x^{6} - 19 x^{5} + 17 x^{4} - 12 x^{3} + 8 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1655893$	$2$	$7.25210117534$	$2228.829064778185$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.59500649905$
10.0.411465339.1	$x^{10} + x^{8} - 3 x^{7} - x^{5} + 4 x^{4} + 4 x^{3} + 4 x^{2} + 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1693273$	$2$	$7.26830805223$	$2253.8453806772104$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.65997292317$
10.0.412705792.1	$x^{10} + x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{10}\cdot 73\cdot 5521$	$3$	$7.27049627701$	$1269.6976017934348$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.75258368215$
10.0.418003011.1	$x^{10} + x^{8} - 2 x^{7} - x^{6} - 2 x^{5} + 2 x^{2} + x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1720177$	$2$	$7.2797747397$	$2271.680215171141$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.72555083841$
10.0.419790519.1	$x^{10} - 3 x^{9} + 4 x^{8} - 2 x^{7} + x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1727533$	$2$	$7.28288181839$	$2276.532231267548$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.65572384932$
10.0.422161227.1	$x^{10} - 3 x^{9} + 7 x^{8} - 10 x^{7} + 10 x^{6} - 6 x^{5} + x^{4} + x^{3} - x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 79\cdot 21991$	$3$	$7.28698430867$	$2282.951379245734$			?	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.754281509$
10.0.423858339.1	$x^{10} - 2 x^{9} + 2 x^{7} - 2 x^{6} - 2 x^{5} + 4 x^{4} + 3 x^{3} - 3 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1744273$	$2$	$7.28990843164$	$2287.5355734938857$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.76016816795$
10.0.424391967.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} - 2 x^{5} + x^{4} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 181\cdot 9649$	$3$	$7.29082569497$	$2288.9750981607467$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.75157645109$
10.0.433766907.1	$x^{10} - x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 2 x^{5} - 3 x^{4} + 4 x^{3} + x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7\cdot 255007$	$3$	$7.30677344198$	$2314.1190548457093$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.79735261034$
10.0.437003667.1	$x^{10} - x^{9} + 2 x^{8} - x^{7} - x^{6} + x^{5} - 3 x^{4} + x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 19\cdot 94651$	$3$	$7.31220751956$	$2322.736963153598$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.79931231235$
10.0.444182859.1	$x^{10} - 3 x^{9} + 4 x^{8} - 5 x^{6} + 4 x^{5} + 3 x^{4} - 7 x^{3} + 6 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 769\cdot 2377$	$3$	$7.32413228148$	$2341.7384567880335$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.78132496028$
10.0.449810739.1	$x^{10} - x^{9} + 4 x^{8} - 4 x^{7} + 7 x^{6} - 8 x^{5} + 6 x^{4} - 7 x^{3} + 3 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7^{2}\cdot 37\cdot 1021$	$4$	$7.33335960531$	$1231.8931881958936$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.86569253608$
10.0.450364779.1	$x^{10} + x^{8} - x^{7} + x^{6} - 3 x^{5} + x^{4} + x^{3} + 2 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 223\cdot 8311$	$3$	$7.33426236817$	$2357.9777352638425$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.77749183964$
10.0.451656567.1	$x^{10} - 3 x^{9} + 3 x^{8} - 2 x^{6} - x^{5} + 3 x^{4} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1858669$	$2$	$7.33636335516$	$2361.3570251023034$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.8607650601$
10.0.465544192.1	$x^{10} + 2 x^{6} - 2 x^{5} - 3 x^{4} - 2 x^{3} + 2 x^{2} + 2 x + 1$	$10$	[0,5]	$-\,2^{10}\cdot 29\cdot 61\cdot 257$	$4$	$7.35861516763$	$1348.5295695682762$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$2.0239321449$
10.0.473264127.1	$x^{10} - x^{9} - x^{8} + x^{7} + x^{6} + 2 x^{5} - 4 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7\cdot 278227$	$3$	$7.3707275556$	$2417.1816232960236$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.95122312256$
10.0.476626275.1	$x^{10} - 2 x^{9} + x^{8} + 2 x^{6} - 5 x^{4} + 3 x^{3} + 4 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 5^{2}\cdot 67\cdot 1171$	$4$	$7.37594717966$	$1084.829479687937$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.97188398821$
10.0.488663523.1	$x^{10} - 3 x^{9} + 3 x^{8} - 2 x^{7} + 2 x^{6} - x^{5} + x^{4} - 2 x^{3} - x^{2} + 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 877\cdot 2293$	$3$	$7.39436683537$	$2456.192785593183$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.93473179608$
10.0.494195904.1	$x^{10} - x^{9} - x^{8} + 2 x^{6} + 2 x^{5} - 2 x^{4} - 3 x^{3} + 2 x + 1$	$10$	[0,5]	$-\,2^{6}\cdot 3^{5}\cdot 43\cdot 739$	$4$	$7.4026959863$	$873.2972002703318$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$3.28587087017$
10.0.495519039.1	$x^{10} - x^{9} - x^{8} + x^{7} + x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 2039173$	$2$	$7.40467556267$	$2473.3618821353257$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$3.03730472202$
10.0.498152187.1	$x^{10} - 4 x^{9} + 9 x^{8} - 15 x^{7} + 19 x^{6} - 20 x^{5} + 16 x^{4} - 10 x^{3} + 6 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 13\cdot 103\cdot 1531$	$4$	$7.40860096967$	$2479.9247972468843$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$3.05216974516$
10.0.504404091.1	$x^{10} - x^{9} + 3 x^{8} - 4 x^{7} + 5 x^{6} - 7 x^{5} + 5 x^{4} - 5 x^{3} + 4 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 37\cdot 56101$	$3$	$7.41784680651$	$2495.4380376999948$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$3.11804596643$
10.0.505439271.1	$x^{10} - 3 x^{9} + 4 x^{8} - x^{7} - 2 x^{6} + 3 x^{5} - 5 x^{4} + 4 x^{3} + 2 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 2079997$	$2$	$7.41936775458$	$2497.9973979169795$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$3.07037385273$