Number field search results

Results (1-50 of 1596 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	$2$	$5$	$2.30111811917$
11.3.24963663301.1	$x^{11} - 2 x^{8} + 4 x^{4} - x^{3} - 3 x^{2} + x + 1$	$11$	[3,4]	$971\cdot 25709231$	$2$	$8.8147469027$	$157998.9344932427$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.33925469123$
11.3.26176773577.1	$x^{11} - x^{9} - x^{8} - 2 x^{7} + 2 x^{5} + 3 x^{4} - 2 x^{2} + 1$	$11$	[3,4]	$14851\cdot 1762627$	$2$	$8.85285362001$	$161792.37799414407$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.4712164339$
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	$2$	$5$	$4.39349221591$
11.3.26877166541.1	$x^{11} - x^{9} - x^{8} - 2 x^{7} + x^{5} + 2 x^{4} + 2 x^{3} - 1$	$11$	[3,4]	$1583\cdot 2731\cdot 6217$	$3$	$8.87412968486$	$163942.57086248221$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.543622789082196$
11.3.27095385033.1	$x^{11} - 2 x^{9} - x^{7} - x^{6} + 4 x^{5} + x^{4} - 2 x - 1$	$11$	[3,4]	$3^{3}\cdot 1003532779$	$2$	$8.88065563404$	$54868.91959023797$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.564346423290848$
11.3.27252765193.1	$x^{11} - 2 x^{8} - x^{7} + x^{6} + x^{5} - x^{4} - 2 x^{3} + x^{2} + 2 x + 1$	$11$	[3,4]	$1559\cdot 17480927$	$2$	$8.8853325881$	$165084.11550782225$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.581164668665217$
11.3.28208540809.1	$x^{11} - x^{10} + x^{9} - 3 x^{5} + x^{4} - 2 x^{2} + x + 1$	$11$	[3,4]	$28208540809$	$1$	$8.91321950394$	$167953.9842010305$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.678778945916857$
11.3.28385393161.1	$x^{11} - x^{10} + 2 x^{9} - x^{7} + 2 x^{6} - x^{5} - x^{4} + x^{3} - x^{2} - x + 1$	$11$	[3,4]	$28385393161$	$1$	$8.91828518293$	$168479.6520681355$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.707477044366799$
11.3.28868429753.1	$x^{11} - x^{9} - x^{6} - x^{5} + x^{4} - x^{3} + 2 x - 1$	$11$	[3,4]	$163\cdot 177106931$	$2$	$8.93197626131$	$169907.12096024698$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.748635444917281$
11.3.32252418553.1	$x^{11} - 4 x^{10} + 9 x^{9} - 15 x^{8} + 21 x^{7} - 21 x^{6} + 17 x^{5} - 8 x^{4} + 3 x^{2} - 3 x + 1$	$11$	[3,4]	$61\cdot 227\cdot 397\cdot 5867$	$4$	$9.02243671016$	$179589.583642816$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$5.07930695367$
11.3.64283038681.1	$x^{11} - x^{10} - 5 x^{9} + 3 x^{8} + 10 x^{7} - 3 x^{6} - 11 x^{5} + 3 x^{4} + 5 x^{3} - 2 x^{2} + 1$	$11$	[3,4]	$71^{2}\cdot 3571^{2}$	$2$	$9.6062573688$	$4005.8879678934163$			?	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$8.04640012169$
11.3.66355073541.1	$x^{11} - 5 x^{9} - x^{8} + 7 x^{7} + 4 x^{6} - x^{5} - 5 x^{4} - 2 x^{3} + 2 x^{2} - 1$	$11$	[3,4]	$3^{2}\cdot 7372785949$	$2$	$9.63400216401$	$148722.41877739885$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$8.00982507951$
11.3.118125032125.1	$x^{11} - 2 x^{10} + x^{9} + 4 x^{8} - 6 x^{7} + 2 x^{6} + 5 x^{5} - 5 x^{4} + 3 x^{2} - 3 x + 1$	$11$	[3,4]	$5^{3}\cdot 73\cdot 139\cdot 93131$	$4$	$10.1525827971$	$102788.2486816166$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$12.5932309979$
11.3.121321855232.1	$x^{11} + 2 x^{9} - x^{8} - x^{7} + 2 x^{6} - 4 x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$	$11$	[3,4]	$2^{8}\cdot 2927\cdot 161911$	$3$	$10.1772588853$	$87078.2174369687$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$18.3096406338$
11.3.127663872125.1	$x^{11} - 3 x^{10} + x^{9} + 3 x^{8} + 2 x^{7} - 3 x^{6} - 6 x^{5} - 2 x^{4} + 6 x^{3} + 4 x^{2} - x - 1$	$11$	[3,4]	$5^{3}\cdot 131\cdot 1297\cdot 6011$	$4$	$10.2245110026$	$106857.86753296934$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$13.1449090087$
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	$2$	$5$	$9.67372434998$
11.5.132326332471.1	$x^{11} - 2 x^{10} + 2 x^{7} + x^{6} - 3 x^{5} + 2 x^{2} + x - 1$	$11$	[5,3]	$-\,211441\cdot 625831$	$2$	$10.2579068817$	$363766.8655485268$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$15.3396861125$
11.3.133644778349.1	$x^{11} - 2 x^{10} + 2 x^{9} - 2 x^{8} + x^{6} - 3 x^{5} + 3 x^{4} - x^{3} + x^{2} - 1$	$11$	[3,4]	$401\cdot 333278749$	$2$	$10.2671564868$	$365574.58657434053$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$13.6774760578$
11.3.136113034225.1	$x^{11} - 2 x^{10} + x^{9} + 4 x^{8} - 6 x^{7} + 8 x^{5} - 7 x^{4} - 2 x^{3} + 5 x^{2} - 2 x - 1$	$11$	[3,4]	$5^{2}\cdot 7^{2}\cdot 83^{2}\cdot 127^{2}$	$4$	$10.2842518003$	$2844.1679033165196$			✓	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$13.1993869045$
11.5.145065457639.1	$x^{11} - x^{10} - 4 x^{9} + 7 x^{8} + 4 x^{7} - 9 x^{6} - 5 x^{5} + 2 x^{4} + 8 x^{3} + 2 x^{2} - 3 x - 1$	$11$	[5,3]	$-\,2389\cdot 2617\cdot 23203$	$3$	$10.3439791741$	$380874.5956860342$			?	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$16.2407020956$
11.5.157519649831.1	$x^{11} - x^{10} - x^{9} - x^{7} + x^{6} + 2 x^{4} + 3 x^{3} - 2 x - 1$	$11$	[5,3]	$-\,19457\cdot 8095783$	$2$	$10.4217228987$	$396887.4523476397$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.2118083495$
11.5.167050542839.1	$x^{11} - 2 x^{10} + 2 x^{9} - 3 x^{7} + x^{6} - x^{5} + 2 x + 1$	$11$	[5,3]	$-\,2089\cdot 79966751$	$2$	$10.4775296669$	$408718.1704292091$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.654115853304827$
11.5.167720394923.1	$x^{11} - 2 x^{10} - 3 x^{9} + 9 x^{8} - x^{7} - 13 x^{6} + 9 x^{5} + 7 x^{4} - 5 x^{3} - 1$	$11$	[5,3]	$-\,167720394923$	$1$	$10.4813421415$	$409536.80533378193$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.7118832979$
11.3.177546554301.1	$x^{11} + 2 x^{9} - 2 x^{8} + x^{7} - 4 x^{6} + x^{5} - x^{3} + 3 x^{2} - 3 x + 1$	$11$	[3,4]	$3\cdot 34963\cdot 1692709$	$3$	$10.5357328491$	$421362.734827132$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$17.7712884727$
11.5.200601609583.1	$x^{11} + x^{9} - 2 x^{7} - x^{6} - 3 x^{5} + x^{4} + x^{3} + x^{2} + x - 1$	$11$	[5,3]	$-\,200601609583$	$1$	$10.6533193695$	$447885.7104027767$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$19.635566037183242$
11.3.233856337233.1	$x^{11} - 4 x^{10} + 6 x^{9} - 5 x^{8} + 7 x^{6} - 9 x^{5} + 3 x^{4} + 4 x^{3} - 4 x^{2} + 3 x - 1$	$11$	[3,4]	$3\cdot 246941\cdot 315671$	$3$	$10.802911822$	$483586.94898952765$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$20.8515824211$
11.5.234360387559.1	$x^{11} + x^{9} - 2 x^{8} - x^{7} - x^{5} - x^{3} + 2 x^{2} + x - 1$	$11$	[5,3]	$-\,71\cdot 3300850529$	$2$	$10.8050265172$	$484107.8263765212$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$21.919668485422946$
11.5.236131740703.1	$x^{11} - x^{10} - 2 x^{9} + 2 x^{8} - x^{7} + 2 x^{5} - x^{4} + x^{3} + x^{2} - 1$	$11$	[5,3]	$-\,372881\cdot 633263$	$2$	$10.8124254085$	$485933.8851150432$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.027596379016778$
11.5.248686333151.1	$x^{11} - 2 x^{9} - x^{7} - x^{6} + 2 x^{3} + x + 1$	$11$	[5,3]	$-\,2381\cdot 104446171$	$2$	$10.863464669$	$498684.6028814204$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.52935578711483$
11.1.275311670611.1	$x^{11} - x - 1$	$11$	[1,5]	$-\,275311670611$	$1$	$10.9643794384$	$524701.5062023359$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$17.146941728$
11.3.303820448000.1	$x^{11} - 3 x^{10} + 9 x^{8} - 6 x^{7} - 11 x^{6} + 6 x^{5} + 13 x^{4} - 4 x^{3} - 8 x^{2} + 2$	$11$	[3,4]	$2^{8}\cdot 5^{3}\cdot 9494389$	$3$	$11.0630346521$	$41211.74513055835$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$34.9771751389$
11.3.337570274092.1	$x^{11} - 3 x^{10} + 6 x^{9} - 4 x^{8} + 2 x^{7} + 4 x^{6} - 3 x^{5} + x^{4} + 2 x^{3} + 5 x^{2} - 2 x - 1$	$11$	[3,4]	$2^{2}\cdot 89\cdot 4801\cdot 197507$	$4$	$11.1694839592$	$581007.9810914821$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$34.4297607586$
11.7.610429790897.1	$x^{11} - x^{10} - 4 x^{9} + x^{8} + 5 x^{7} + 7 x^{6} - 7 x^{5} - 5 x^{4} + 7 x^{3} - 3 x^{2} - x + 1$	$11$	[7,2]	$610429790897$	$1$	$11.7874924921$	$781300.0645699449$			?	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$49.9574794147$
11.7.808524990121.1	$x^{11} - 2 x^{10} - x^{9} + 4 x^{8} - x^{7} - 5 x^{6} - x^{5} + 8 x^{4} + 3 x^{3} - 5 x^{2} - x + 1$	$11$	[7,2]	$43\cdot 547\cdot 34374601$	$3$	$12.0925414904$	$899180.1766726177$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$59.1581764769$
11.7.835929782249.1	$x^{11} - x^{10} - x^{9} - 3 x^{7} + 4 x^{6} + 2 x^{5} + x^{4} + 4 x^{3} - 6 x^{2} - 3 x + 1$	$11$	[7,2]	$56509\cdot 14792861$	$2$	$12.1292407976$	$914291.956788968$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$60.09604192925153$
11.3.836463893056.1	$x^{11} - x^{9} + x^{7} - x^{6} + 2 x^{5} + x^{4} - 2 x^{3} - x - 1$	$11$	[3,4]	$2^{6}\cdot 11^{2}\cdot 19^{2}\cdot 547^{2}$	$4$	$12.129945128$	$800.4218167922659$			✓	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$42.63364030773609$
11.3.1013364643329.1	$x^{11} - 3 x^{10} + 5 x^{9} - 11 x^{8} + 11 x^{7} - 9 x^{6} + 7 x^{5} + x^{4} - 6 x^{3} + 3 x^{2} - 4 x + 1$	$11$	[3,4]	$3^{4}\cdot 33829\cdot 369821$	$3$	$12.3433558559$	$193731.83483103648$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$106.551564033$
11.7.1135258109569.1	$x^{11} - 2 x^{10} - x^{9} + 5 x^{8} - 3 x^{7} - 2 x^{6} - 3 x^{5} + 3 x^{4} + 11 x^{3} - 5 x^{2} - 4 x + 1$	$11$	[7,2]	$71\cdot 73\cdot 219034943$	$3$	$12.4714713129$	$1065484.9175699297$			?	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$72.38649544528622$