Number field search results

Results (1-50 of 1596 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
11.1.5781612911.1	x^11 - 2x^10 + 2x^9 - 3x^8 + 6x^7 - 8x^6 + 7x^5 - 7x^4 + 7x^3 - 6x^2 + 3x - 1	$11$	[1,5]	$-\,239\cdot 24190849$	$2$	$7.71718659147$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.38901958662$
11.1.5807103943.1	x^11 - x^10 - x^9 + 3x^8 - 4x^6 + 2x^5 + 2x^4 - 3x^3 + x - 1	$11$	[1,5]	$-\,269\cdot 359\cdot 60133$	$3$	$7.72027358647$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.39244633936$
11.1.5901091967.1	x^11 - 2x^10 + x^9 + 3x^8 - 5x^7 + 2x^6 + 4x^5 - 6x^4 + 2x^3 + 3x^2 - 3x + 1	$11$	[1,5]	$-\,5901091967$	$1$	$7.73155020404$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.40717627231$
11.1.5939843699.1	x^11 + x^9 - 2x^8 - 2x^7 - x^6 + 3x^4 + x^3 + x^2 - 1	$11$	[1,5]	$-\,12917\cdot 459847$	$2$	$7.73615213135$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.41278978844$
11.1.5960386319.1	x^11 - x^10 + x^9 - 2x^7 + x^6 - 2x^5 + x^3 + x + 1	$11$	[1,5]	$-\,64661\cdot 92179$	$2$	$7.73858059371$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.416013299$
11.1.5999947987.1	x^11 - 2x^10 + x^9 + 3x^8 - 5x^7 + x^6 + 5x^5 - 5x^4 + x^3 + 2x^2 - 2x + 1	$11$	[1,5]	$-\,11^{2}\cdot 49586347$	$2$	$7.74323604815$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.42155773768$
11.1.6046447999.1	x^11 + 3x^9 - 2x^8 + 4x^7 - 5x^6 + 5x^5 - 6x^4 + 4x^3 - 4x^2 + 2x - 1	$11$	[1,5]	$-\,163\cdot 37094773$	$2$	$7.74867243441$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.4305918545$
11.1.6205948139.1	x^11 - x^9 - x^8 + 2x^7 + 2x^6 - x^5 - 2x^4 + 2x^2 - 1	$11$	[1,5]	$-\,6205948139$	$1$	$7.76703541939$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.452878850509613$
11.1.6477690799.1	x^11 - x^10 + 3x^9 - 4x^8 + 6x^7 - 7x^6 + 8x^5 - 8x^4 + 6x^3 - 5x^2 + 3x - 1	$11$	[1,5]	$-\,1609\cdot 4025911$	$2$	$7.79735472764$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.4917159142651446$
11.1.6660072199.1	x^11 - x^9 - x^8 - x^5 + x^4 + 3x^3 + x^2 - x - 1	$11$	[1,5]	$-\,11^{2}\cdot 181\cdot 304099$	$3$	$7.81706169806$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.5178724806066581$
11.1.9824914719.1	x^11 - x^10 - x^9 + 4x^8 - 3x^7 - x^6 + 5x^5 - 5x^4 + x^3 + 2x^2 - 2x + 1	$11$	[1,5]	$-\,3^{2}\cdot 131\cdot 8333261$	$3$	$8.0982937573$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1.97043442549$
11.1.12696946299.1	x^11 - 2x^10 + 3x^9 - 3x^8 + 3x^7 - 3x^6 + 5x^5 - 9x^4 + 11x^3 - 8x^2 + 4x - 1	$11$	[1,5]	$-\,3^{2}\cdot 15731\cdot 89681$	$3$	$8.28930494428$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$2.30111811917$
11.3.24963663301.1	x^11 - 2x^8 + 4x^4 - x^3 - 3x^2 + x + 1	$11$	[3,4]	$971\cdot 25709231$	$2$	$8.8147469027$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.33925469123$
11.3.26176773577.1	x^11 - x^9 - x^8 - 2x^7 + 2x^5 + 3x^4 - 2x^2 + 1	$11$	[3,4]	$14851\cdot 1762627$	$2$	$8.85285362001$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.4712164339$
11.1.26277078939.1	x^11 - x^10 + x^8 - 4x^7 + 2x^6 + x^5 - 3x^4 + 5x^3 - 3x^2 + x - 1	$11$	[1,5]	$-\,3\cdot 23\cdot 107\cdot 227\cdot 15679$	$5$	$8.85593214996$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$4.39349221591$
11.3.26877166541.1	x^11 - x^9 - x^8 - 2x^7 + x^5 + 2x^4 + 2x^3 - 1	$11$	[3,4]	$1583\cdot 2731\cdot 6217$	$3$	$8.87412968486$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.543622789082196$
11.3.27095385033.1	x^11 - 2x^9 - x^7 - x^6 + 4x^5 + x^4 - 2x - 1	$11$	[3,4]	$3^{3}\cdot 1003532779$	$2$	$8.88065563404$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.564346423290848$
11.3.27252765193.1	x^11 - 2x^8 - x^7 + x^6 + x^5 - x^4 - 2x^3 + x^2 + 2x + 1	$11$	[3,4]	$1559\cdot 17480927$	$2$	$8.8853325881$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.581164668665217$
11.3.28208540809.1	x^11 - x^10 + x^9 - 3x^5 + x^4 - 2x^2 + x + 1	$11$	[3,4]	$28208540809$	$1$	$8.91321950394$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.678778945916857$
11.3.28385393161.1	x^11 - x^10 + 2x^9 - x^7 + 2x^6 - x^5 - x^4 + x^3 - x^2 - x + 1	$11$	[3,4]	$28385393161$	$1$	$8.91828518293$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.707477044366799$
11.3.28868429753.1	x^11 - x^9 - x^6 - x^5 + x^4 - x^3 + 2x - 1	$11$	[3,4]	$163\cdot 177106931$	$2$	$8.93197626131$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$4.748635444917281$
11.3.32252418553.1	x^11 - 4x^10 + 9x^9 - 15x^8 + 21x^7 - 21x^6 + 17x^5 - 8x^4 + 3x^2 - 3x + 1	$11$	[3,4]	$61\cdot 227\cdot 397\cdot 5867$	$4$	$9.02243671016$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$5.07930695367$
11.3.64283038681.1	x^11 - x^10 - 5x^9 + 3x^8 + 10x^7 - 3x^6 - 11x^5 + 3x^4 + 5x^3 - 2x^2 + 1	$11$	[3,4]	$71^{2}\cdot 3571^{2}$	$2$	$9.6062573688$			not computed	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$8.04640012169$
11.3.66355073541.1	x^11 - 5x^9 - x^8 + 7x^7 + 4x^6 - x^5 - 5x^4 - 2x^3 + 2x^2 - 1	$11$	[3,4]	$3^{2}\cdot 7372785949$	$2$	$9.63400216401$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$8.00982507951$
11.3.118125032125.1	x^11 - 2x^10 + x^9 + 4x^8 - 6x^7 + 2x^6 + 5x^5 - 5x^4 + 3x^2 - 3x + 1	$11$	[3,4]	$5^{3}\cdot 73\cdot 139\cdot 93131$	$4$	$10.1525827971$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$12.5932309979$
11.3.121321855232.1	x^11 + 2x^9 - x^8 - x^7 + 2x^6 - 4x^5 + 2x^4 - 2x^3 - 2x^2 + 2x - 1	$11$	[3,4]	$2^{8}\cdot 2927\cdot 161911$	$3$	$10.1772588853$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$18.3096406338$
11.3.127663872125.1	x^11 - 3x^10 + x^9 + 3x^8 + 2x^7 - 3x^6 - 6x^5 - 2x^4 + 6x^3 + 4x^2 - x - 1	$11$	[3,4]	$5^{3}\cdot 131\cdot 1297\cdot 6011$	$4$	$10.2245110026$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$13.1449090087$
11.1.129891985607.1	x^11 - x^10 + 5x^9 - 4x^8 + 10x^7 - 6x^6 + 11x^5 - 7x^4 + 9x^3 - 4x^2 + 2x + 1	$11$	[1,5]	$-\,167^{5}$	$1$	$10.2406062691$			not computed	$D_{11}$ (as 11T2)	trivial	$2$	$5$	$9.67372434998$
11.5.132326332471.1	x^11 - 2x^10 + 2x^7 + x^6 - 3x^5 + 2x^2 + x - 1	$11$	[5,3]	$-\,211441\cdot 625831$	$2$	$10.2579068817$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$15.3396861125$
11.3.133644778349.1	x^11 - 2x^10 + 2x^9 - 2x^8 + x^6 - 3x^5 + 3x^4 - x^3 + x^2 - 1	$11$	[3,4]	$401\cdot 333278749$	$2$	$10.2671564868$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$13.6774760578$
11.3.136113034225.1	x^11 - 2x^10 + x^9 + 4x^8 - 6x^7 + 8x^5 - 7x^4 - 2x^3 + 5x^2 - 2x - 1	$11$	[3,4]	$5^{2}\cdot 7^{2}\cdot 83^{2}\cdot 127^{2}$	$4$	$10.2842518003$			✓	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$13.1993869045$
11.5.145065457639.1	x^11 - x^10 - 4x^9 + 7x^8 + 4x^7 - 9x^6 - 5x^5 + 2x^4 + 8x^3 + 2x^2 - 3x - 1	$11$	[5,3]	$-\,2389\cdot 2617\cdot 23203$	$3$	$10.3439791741$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$16.2407020956$
11.5.157519649831.1	x^11 - x^10 - x^9 - x^7 + x^6 + 2x^4 + 3x^3 - 2x - 1	$11$	[5,3]	$-\,19457\cdot 8095783$	$2$	$10.4217228987$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.2118083495$
11.5.167050542839.1	x^11 - 2x^10 + 2x^9 - 3x^7 + x^6 - x^5 + 2x + 1	$11$	[5,3]	$-\,2089\cdot 79966751$	$2$	$10.4775296669$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.654115853304827$
11.5.167720394923.1	x^11 - 2x^10 - 3x^9 + 9x^8 - x^7 - 13x^6 + 9x^5 + 7x^4 - 5x^3 - 1	$11$	[5,3]	$-\,167720394923$	$1$	$10.4813421415$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$17.7118832979$
11.3.177546554301.1	x^11 + 2x^9 - 2x^8 + x^7 - 4x^6 + x^5 - x^3 + 3x^2 - 3x + 1	$11$	[3,4]	$3\cdot 34963\cdot 1692709$	$3$	$10.5357328491$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$17.7712884727$
11.5.200601609583.1	x^11 + x^9 - 2x^7 - x^6 - 3x^5 + x^4 + x^3 + x^2 + x - 1	$11$	[5,3]	$-\,200601609583$	$1$	$10.6533193695$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$19.635566037183242$
11.3.233856337233.1	x^11 - 4x^10 + 6x^9 - 5x^8 + 7x^6 - 9x^5 + 3x^4 + 4x^3 - 4x^2 + 3x - 1	$11$	[3,4]	$3\cdot 246941\cdot 315671$	$3$	$10.802911822$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$20.8515824211$
11.5.234360387559.1	x^11 + x^9 - 2x^8 - x^7 - x^5 - x^3 + 2x^2 + x - 1	$11$	[5,3]	$-\,71\cdot 3300850529$	$2$	$10.8050265172$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$21.919668485422946$
11.5.236131740703.1	x^11 - x^10 - 2x^9 + 2x^8 - x^7 + 2x^5 - x^4 + x^3 + x^2 - 1	$11$	[5,3]	$-\,372881\cdot 633263$	$2$	$10.8124254085$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.027596379016778$
11.5.248686333151.1	x^11 - 2x^9 - x^7 - x^6 + 2x^3 + x + 1	$11$	[5,3]	$-\,2381\cdot 104446171$	$2$	$10.863464669$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$7$	$22.52935578711483$
11.1.275311670611.1	x^11 - x - 1	$11$	[1,5]	$-\,275311670611$	$1$	$10.9643794384$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$17.146941728$
11.3.303820448000.1	x^11 - 3x^10 + 9x^8 - 6x^7 - 11x^6 + 6x^5 + 13x^4 - 4x^3 - 8x^2 + 2	$11$	[3,4]	$2^{8}\cdot 5^{3}\cdot 9494389$	$3$	$11.0630346521$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$34.9771751389$
11.3.337570274092.1	x^11 - 3x^10 + 6x^9 - 4x^8 + 2x^7 + 4x^6 - 3x^5 + x^4 + 2x^3 + 5x^2 - 2x - 1	$11$	[3,4]	$2^{2}\cdot 89\cdot 4801\cdot 197507$	$4$	$11.1694839592$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$34.4297607586$
11.7.610429790897.1	x^11 - x^10 - 4x^9 + x^8 + 5x^7 + 7x^6 - 7x^5 - 5x^4 + 7x^3 - 3x^2 - x + 1	$11$	[7,2]	$610429790897$	$1$	$11.7874924921$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$49.9574794147$
11.7.808524990121.1	x^11 - 2x^10 - x^9 + 4x^8 - x^7 - 5x^6 - x^5 + 8x^4 + 3x^3 - 5x^2 - x + 1	$11$	[7,2]	$43\cdot 547\cdot 34374601$	$3$	$12.0925414904$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$59.1581764769$
11.7.835929782249.1	x^11 - x^10 - x^9 - 3x^7 + 4x^6 + 2x^5 + x^4 + 4x^3 - 6x^2 - 3x + 1	$11$	[7,2]	$56509\cdot 14792861$	$2$	$12.1292407976$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$60.09604192925153$
11.3.836463893056.1	x^11 - x^9 + x^7 - x^6 + 2x^5 + x^4 - 2x^3 - x - 1	$11$	[3,4]	$2^{6}\cdot 11^{2}\cdot 19^{2}\cdot 547^{2}$	$4$	$12.129945128$			✓	$A_{11}$ (as 11T7)	trivial	$2$	$6$	$42.63364030773609$
11.3.1013364643329.1	x^11 - 3x^10 + 5x^9 - 11x^8 + 11x^7 - 9x^6 + 7x^5 + x^4 - 6x^3 + 3x^2 - 4x + 1	$11$	[3,4]	$3^{4}\cdot 33829\cdot 369821$	$3$	$12.3433558559$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$106.551564033$
11.7.1135258109569.1	x^11 - 2x^10 - x^9 + 5x^8 - 3x^7 - 2x^6 - 3x^5 + 3x^4 + 11x^3 - 5x^2 - 4x + 1	$11$	[7,2]	$71\cdot 73\cdot 219034943$	$3$	$12.4714713129$			not computed	$S_{11}$ (as 11T8)	trivial	$2$	$8$	$72.38649544528622$