Number field search results

Results (1-50 of 873 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
11.1.5781612911.1	$x^{11} - 2 x^{10} + 2 x^{9} - 3 x^{8} + 6 x^{7} - 8 x^{6} + 7 x^{5} - 7 x^{4} + 7 x^{3} - 6 x^{2} + 3 x - 1$	$11$	[1,5]	$-\,239\cdot 24190849$	$2$	$7.71718659147$	$76036.91807931197$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.38901958662$
11.1.5807103943.1	$x^{11} - x^{10} - x^{9} + 3 x^{8} - 4 x^{6} + 2 x^{5} + 2 x^{4} - 3 x^{3} + x - 1$	$11$	[1,5]	$-\,269\cdot 359\cdot 60133$	$3$	$7.72027358647$	$76204.35645683257$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.39244633936$
11.1.5901091967.1	$x^{11} - 2 x^{10} + x^{9} + 3 x^{8} - 5 x^{7} + 2 x^{6} + 4 x^{5} - 6 x^{4} + 2 x^{3} + 3 x^{2} - 3 x + 1$	$11$	[1,5]	$-\,5901091967$	$1$	$7.73155020404$	$76818.5652495541$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.40717627231$
11.1.5939843699.1	$x^{11} + x^{9} - 2 x^{8} - 2 x^{7} - x^{6} + 3 x^{4} + x^{3} + x^{2} - 1$	$11$	[1,5]	$-\,12917\cdot 459847$	$2$	$7.73615213135$	$77070.381463958$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.41278978844$
11.1.5960386319.1	$x^{11} - x^{10} + x^{9} - 2 x^{7} + x^{6} - 2 x^{5} + x^{3} + x + 1$	$11$	[1,5]	$-\,64661\cdot 92179$	$2$	$7.73858059371$	$77203.53825440904$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.416013299$
11.1.5999947987.1	$x^{11} - 2 x^{10} + x^{9} + 3 x^{8} - 5 x^{7} + x^{6} + 5 x^{5} - 5 x^{4} + x^{3} + 2 x^{2} - 2 x + 1$	$11$	[1,5]	$-\,11^{2}\cdot 49586347$	$2$	$7.74323604815$	$23354.867094462345$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.42155773768$
11.1.6046447999.1	$x^{11} + 3 x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 5 x^{5} - 6 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$	$11$	[1,5]	$-\,163\cdot 37094773$	$2$	$7.74867243441$	$77758.9094509433$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.4305918545$
11.1.6205948139.1	$x^{11} - x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - x^{5} - 2 x^{4} + 2 x^{2} - 1$	$11$	[1,5]	$-\,6205948139$	$1$	$7.76703541939$	$78777.84040578925$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.452878850509613$
11.1.6477690799.1	$x^{11} - x^{10} + 3 x^{9} - 4 x^{8} + 6 x^{7} - 7 x^{6} + 8 x^{5} - 8 x^{4} + 6 x^{3} - 5 x^{2} + 3 x - 1$	$11$	[1,5]	$-\,1609\cdot 4025911$	$2$	$7.79735472764$	$80484.10277191391$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.4917159142651446$
11.1.6660072199.1	$x^{11} - x^{9} - x^{8} - x^{5} + x^{4} + 3 x^{3} + x^{2} - x - 1$	$11$	[1,5]	$-\,11^{2}\cdot 181\cdot 304099$	$3$	$7.81706169806$	$24606.119340521782$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.5178724806066581$
11.1.9824914719.1	$x^{11} - x^{10} - x^{9} + 4 x^{8} - 3 x^{7} - x^{6} + 5 x^{5} - 5 x^{4} + x^{3} + 2 x^{2} - 2 x + 1$	$11$	[1,5]	$-\,3^{2}\cdot 131\cdot 8333261$	$3$	$8.0982937573$	$57227.36734290684$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.97043442549$
11.1.12696946299.1	$x^{11} - 2 x^{10} + 3 x^{9} - 3 x^{8} + 3 x^{7} - 3 x^{6} + 5 x^{5} - 9 x^{4} + 11 x^{3} - 8 x^{2} + 4 x - 1$	$11$	[1,5]	$-\,3^{2}\cdot 15731\cdot 89681$	$3$	$8.28930494428$	$65056.248224132934$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$2.30111811917$
11.1.26277078939.1	$x^{11} - x^{10} + x^{8} - 4 x^{7} + 2 x^{6} + x^{5} - 3 x^{4} + 5 x^{3} - 3 x^{2} + x - 1$	$11$	[1,5]	$-\,3\cdot 23\cdot 107\cdot 227\cdot 15679$	$5$	$8.85593214996$	$162102.06333973666$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$4.39349221591$
11.1.129891985607.1	$x^{11} - x^{10} + 5 x^{9} - 4 x^{8} + 10 x^{7} - 6 x^{6} + 11 x^{5} - 7 x^{4} + 9 x^{3} - 4 x^{2} + 2 x + 1$	$11$	[1,5]	$-\,167^{5}$	$1$	$10.2406062691$	$12.922847983320086$			?	$D_{11}$ (as 11T2)	trivial	$2$	$5$	$9.67372434998$
11.1.275311670611.1	$x^{11} - x - 1$	$11$	[1,5]	$-\,275311670611$	$1$	$10.9643794384$	$524701.5062023359$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$17.146941728$
11.1.1461660310351.1	$x^{11} + x^{9} - x^{8} + 3 x^{7} + 3 x^{6} - 6 x^{5} + 3 x^{4} + 5 x^{3} - 6 x^{2} + 5 x + 1$	$11$	[1,5]	$-\,271^{5}$	$1$	$12.7613062817$	$16.46207763315433$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$55.1714638864$
11.1.20765311670611.1	$x^{11} + 2 x - 1$	$11$	[1,5]	$-\,58451\cdot 355260161$	$2$	$16.2430332069$	$4556897.153832967$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$224.480601857$
11.1.34522712143931.1	$x^{11} - 11 x^{8} + 44 x^{5} + 33 x^{4} + 44 x^{3} - 11$	$11$	[1,5]	$-\,11^{13}$	$1$	$17.0112728223$	$20.6986330715433$			?	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$549.701696297$
11.1.37013238967296.1	$x^{11} + 4 x - 4$	$11$	[1,5]	$-\,2^{10}\cdot 3\cdot 59\cdot 97\cdot 397\cdot 5303$	$6$	$17.1193396424$	$357019.7155830808$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$616.335807376$
11.1.53339349076992.1	$x^{11} - 3 x^{10} + 11 x^{9} - 21 x^{8} + 36 x^{7} - 38 x^{6} + 32 x^{5} - 2 x^{4} - 17 x^{3} + 37 x^{2} - 23 x + 15$	$11$	[1,5]	$-\,2^{10}\cdot 3^{5}\cdot 11^{8}$	$3$	$17.6975614233$	$22.148198538243356$			?	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$701.357741363$
11.1.72100355223951.1	$x^{11} - 3 x^{10} + 8 x^{8} + 3 x^{7} - 42 x^{6} + 61 x^{5} - 21 x^{4} - 33 x^{3} + 45 x^{2} + 9 x - 27$	$11$	[1,5]	$-\,3^{5}\cdot 197^{5}$	$2$	$18.1891536377$	$24.310491562286437$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$1616.39133164$
11.1.73029787676416.1	$x^{11} - 4 x - 8$	$11$	[1,5]	$-\,2^{8}\cdot 16651\cdot 17132461$	$3$	$18.2103454852$	$929938.0819016622$				$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1746.89492098$
11.1.77265229938688.1	$x^{11} - 4 x^{10} + 6 x^{9} + 2 x^{8} - 14 x^{7} + 10 x^{6} + 7 x^{5} - 16 x^{4} + 2 x^{3} + 8 x^{2} - x - 8$	$11$	[1,5]	$-\,2^{15}\cdot 11^{9}$	$2$	$18.3039157958$	$24.479267048299516$			?	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$900.940644336$
11.1.93851287159343.1	$x^{11} - 5 x^{10} + 13 x^{9} - 22 x^{8} + 32 x^{7} - 44 x^{6} + 47 x^{5} - 30 x^{4} + 11 x^{3} + 6 x^{2} - 21 x + 17$	$11$	[1,5]	$-\,7^{5}\cdot 89^{5}$	$2$	$18.6303854133$	$24.95996794869737$			?	$D_{11}$ (as 11T2)	trivial	$2$	$5$	$582.446099571$
11.1.118098000000000.1	$x^{11} - 2 x^{10} + 4 x^{9} - 10 x^{8} + 8 x^{7} - 16 x^{6} + 12 x^{5} - 12 x^{4} + 15 x^{3} - 14 x^{2} + 4 x - 8$	$11$	[1,5]	$-\,2^{10}\cdot 3^{10}\cdot 5^{9}$	$3$	$19.0236907151$	$118.67065256545114$				$S_{11}$ (as 11T8)	trivial	$2$	$5$	$3246.69054219$
11.1.124287391407299.1	$x^{11} - x^{10} - 4 x^{9} - 15 x^{8} - 7 x^{7} + 14 x^{6} + 15 x^{5} - 35 x^{4} + 16 x^{3} - x^{2} + 3 x - 2$	$11$	[1,5]	$-\,659^{5}$	$1$	$19.1122383147$	$25.67099530598687$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$1763.45397868$
11.1.139234453205859.1	$x^{11} - 3$	$11$	[1,5]	$-\,3^{10}\cdot 11^{9}$	$2$	$19.31057278$	$23.496328849167636$			?	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$1213.74771242$
11.1.210239150705664.1	$x^{11} - 4 x^{6} - 8 x^{3} + 4 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 3\cdot 13327\cdot 5135231$	$4$	$20.0477146495$	$850884.1833276282$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1709.4620755$
11.1.236196000000000.1	$x^{11} - x^{10} + x^{9} - 5 x^{8} + 8 x^{7} - 8 x^{6} + 8 x^{5} - 14 x^{4} + 5 x^{3} - 7 x^{2} + x - 1$	$11$	[1,5]	$-\,2^{11}\cdot 3^{10}\cdot 5^{9}$	$3$	$20.2610122844$	$128.90766120636556$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$3697.30119308$
11.1.251199150705664.1	$x^{11} - 4 x - 4$	$11$	[1,5]	$-\,2^{10}\cdot 7\cdot 53\cdot 661217441$	$4$	$20.3747627608$	$930085.2080516538$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$939.193205333$
11.1.265446387748607.1	$x^{11} - x^{10} - 2 x^{9} + 4 x^{8} - 3 x^{7} + x^{6} + 20 x^{5} - 48 x^{4} + 35 x^{3} + 7 x^{2} - 26 x + 13$	$11$	[1,5]	$-\,13^{5}\cdot 59^{5}$	$2$	$20.47720226$	$27.694764848252458$			?	$D_{11}$ (as 11T2)	trivial	$2$	$5$	$782.000461973$
11.1.271679150705664.1	$x^{11} - 2 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 3\cdot 13\cdot 149\cdot 45656801$	$5$	$20.5204526942$	$967256.8400565436$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1358.54751598$
11.1.292149150705664.1	$x^{11} - x - 2$	$11$	[1,5]	$-\,2^{11}\cdot 7\cdot 20378707499$	$3$	$20.6564157583$	$1796614.20099493$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1806.33546131$
11.1.292159140940039.1	$x^{11} - x - 4$	$11$	[1,5]	$-\,19\cdot 397\cdot 38732485873$	$3$	$20.6564799718$	$17092663.365901727$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1210.10977477$
11.1.292159150705664.1	$x^{11} - 2$	$11$	[1,5]	$-\,2^{10}\cdot 11^{11}$	$2$	$20.6564800346$	$25.133974703275978$			✓	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$1650.51852107$
11.1.312639150705664.1	$x^{11} + 2 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 305311670611$	$2$	$20.7840995916$	$1037612.8350379699$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1341.88333263$
11.1.374079150705664.1	$x^{11} - 4 x^{6} + 8 x^{3} + 4 x - 2$	$11$	[1,5]	$-\,2^{10}\cdot 29\cdot 1613\cdot 1949\cdot 4007$	$5$	$21.1258826943$	$1134998.809089498$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1252.2429858$
11.1.415728505588199.1	$x^{11} - 2 x^{10} + x^{9} - 5 x^{8} + 18 x^{7} - 17 x^{6} + 17 x^{4} - 13 x^{3} - 5 x^{2} + 17 x - 1$	$11$	[1,5]	$-\,839^{5}$	$1$	$21.3295999209$	$28.965496715920477$			?	$D_{11}$ (as 11T2)	trivial	$2$	$5$	$636.945438741$
11.1.489776025600000.1	$x^{11} - x^{10} - 5 x^{9} + x^{8} + 11 x^{7} + 13 x^{6} - 8 x^{5} - 40 x^{4} + 16 x^{3} + 16 x^{2} + 32 x - 32$	$11$	[1,5]	$-\,2^{15}\cdot 3^{14}\cdot 5^{5}$	$3$	$21.6498215122$	$347.63601580572566$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$6420.43885993$
11.1.501292001353351.1	$x^{11} - 2 x^{10} + x^{9} + 11 x^{8} - 8 x^{7} - 5 x^{6} + 33 x^{5} - 16 x^{4} - 28 x^{3} + 29 x^{2} - 12 x + 9$	$11$	[1,5]	$-\,13^{5}\cdot 67^{5}$	$2$	$21.6956111617$	$29.512709126747414$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$1530.41505746$
11.1.524740246980399.1	$x^{11} - 4 x^{10} + 2 x^{9} + 13 x^{8} - 36 x^{7} + 69 x^{6} - 82 x^{5} + 103 x^{4} - 74 x^{3} + 50 x^{2} - 18 x + 3$	$11$	[1,5]	$-\,3^{5}\cdot 293^{5}$	$2$	$21.785962984$	$29.647934160747187$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$5287.62126732$
11.1.845536520469607.1	$x^{11} - 2 x^{10} - x^{9} - 13 x^{8} + 6 x^{7} + 18 x^{6} + 81 x^{5} + 99 x^{4} + 122 x^{3} + 68 x^{2} + 43 x + 1$	$11$	[1,5]	$-\,967^{5}$	$1$	$22.7516047132$	$31.096623610932426$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$2418.5369885$
11.1.891598970659375.1	$x^{11} + 11 x^{9} + 44 x^{7} + 77 x^{5} + 55 x^{3} + 11 x - 1$	$11$	[1,5]	$-\,5^{5}\cdot 11^{11}$	$2$	$22.8615842964$	$29.928334099511996$			✓	$F_{11}$ (as 11T4)	trivial	$2$	$5$	$3096.8070415454536$
11.1.1168796602822656.1	$x^{11} + 4 x - 8$	$11$	[1,5]	$-\,2^{12}\cdot 3\cdot 379\cdot 250968103$	$4$	$23.4311955827$	$1564177.3384463699$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$5493.8077231$
11.1.1278110063526912.1	$x^{11} - x^{10} - 6 x^{9} + 2 x^{8} + 16 x^{7} - 6 x^{6} + 5 x^{5} - 29 x^{4} + 39 x^{3} - 45 x^{2} + 21 x - 9$	$11$	[1,5]	$-\,2^{10}\cdot 3^{9}\cdot 7^{8}\cdot 11$	$4$	$23.6224199938$	$349.2314779575145$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$8467.09734169$
11.1.1442319106405376.1	$x^{11} - x^{10} - x^{9} + 3 x^{8} + 27 x^{7} + 51 x^{6} + 29 x^{5} - 31 x^{4} - 48 x^{3} - 22 x^{2} + 16 x - 8$	$11$	[1,5]	$-\,2^{10}\cdot 269^{5}$	$2$	$23.8834184058$	$32.802438933713454$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$42962.944817$
11.1.1692662195786551.1	$x^{11} - 3 x^{10} + 6 x^{9} - 11 x^{8} + 22 x^{7} - 19 x^{6} + 19 x^{5} - 37 x^{4} + 60 x^{3} - 46 x^{2} + 22 x - 11$	$11$	[1,5]	$-\,11^{5}\cdot 101^{5}$	$2$	$24.2334630781$	$33.331666624997915$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$3266.99243566$
11.1.1771755311670611.1	$x^{11} + 3 x - 1$	$11$	[1,5]	$-\,1771755311670611$	$1$	$24.3342811889$	$42092223.88601737$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$2963.21990148$
11.1.2063629150705664.1	$x^{11} + 3 x - 2$	$11$	[1,5]	$-\,2^{11}\cdot 19\cdot 79\cdot 179\cdot 3750317$	$5$	$24.6739818695$	$4774944.643524367$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$6791.73500403$
11.1.2164483503590607.1	$x^{11} - 4 x^{10} - x^{9} + 7 x^{8} + 30 x^{7} - 91 x^{5} - 95 x^{4} + 28 x^{3} + 200 x^{2} + 177 x - 9$	$11$	[1,5]	$-\,3^{5}\cdot 389^{5}$	$2$	$24.7812447154$	$34.161381705077446$				$D_{11}$ (as 11T2)	trivial	$2$	$5$	$12887.1088995$