Number field search results

Results (1-50 of 1211 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
10.2.1844444809.1	$x^{10} - 2 x^{7} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$	$10$	[2,4]	$67^{2}\cdot 641^{2}$	$2$	$8.44474551378$	$1226.371045017563$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$2.83451372423$
10.2.3176111449.1	$x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} - 6 x^{3} + 3 x^{2} - x - 1$	$10$	[2,4]	$7^{2}\cdot 83^{2}\cdot 97^{2}$	$3$	$8.91640061868$	$1469.936512753201$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$3.9936831862878965$
10.2.4473335689.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} - x^{6} + x^{5} - 3 x^{4} + 2 x^{3} + x^{2} + 1$	$10$	[2,4]	$66883^{2}$	$1$	$9.2270558424$	$1647.6962878643976$			✓	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$5.08623099681$
10.2.15249286144.1	$x^{10} + x^{8} - 2 x^{5} - x^{4} - 2 x^{3} - x^{2} + 1$	$10$	[2,4]	$2^{10}\cdot 17^{2}\cdot 227^{2}$	$3$	$10.4309761253$	$562.7812339299961$			✓	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$14.093069340833688$
10.6.51471358129.1	$x^{10} - x^{9} - 3 x^{8} - 2 x^{7} + 2 x^{6} + 6 x^{5} + 4 x^{4} - 2 x^{3} - 5 x^{2} + 1$	$10$	[6,2]	$307^{2}\cdot 739^{2}$	$2$	$11.7803057596$	$1237.1275245401118$			?	$A_{10}$ (as 10T44)	trivial	$2$	$7$	$35.7132422527$
10.6.527145698304.1	$x^{10} - 4 x^{9} + 2 x^{8} + 2 x^{7} + 5 x^{6} - 9 x^{4} + 4 x^{3} - 5 x^{2} + 1$	$10$	[6,2]	$2^{10}\cdot 3^{4}\cdot 2521^{2}$	$3$	$14.8659636551$	$2939.7347442925998$			?	$A_{10}$ (as 10T44)	trivial	$2$	$7$	$183.471364673$
10.2.7449493349376.1	$x^{10} - 4 x^{9} + 24 x^{7} - 42 x^{6} + 18 x^{5} + 12 x^{4} - 12 x^{3} + 9 x^{2} + 2 x + 1$	$10$	[2,4]	$2^{10}\cdot 3^{16}\cdot 13^{2}$	$3$	$19.3737046053$	$131.11336327214178$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$630.931619128$
10.2.19360000000000.1	$x^{10} + 5 x^{8} - 5 x^{6} - 32 x^{5} - 25 x^{4} + 40 x^{2} - 16$	$10$	[2,4]	$2^{14}\cdot 5^{10}\cdot 11^{2}$	$3$	$21.3152551327$	$117.56819608991158$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$1616.30834126$
10.2.35664401793024.1	$x^{10} - x^{9} + 3 x^{8} + 8 x^{7} - 38 x^{6} + 54 x^{5} - 122 x^{4} + 80 x^{3} - 102 x^{2} + 30 x - 42$	$10$	[2,4]	$2^{26}\cdot 3^{12}$	$2$	$22.6581002711$	$95.23418585255033$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$3649.74549655$
10.2.39062500000000.1	$x^{10} - 5 x^{9} + 20 x^{7} - 48 x^{5} - 10 x^{4} + 60 x^{3} + 35 x^{2} - 35 x - 26$	$10$	[2,4]	$2^{8}\cdot 5^{16}$	$2$	$22.8652525964$	$51.67645772044102$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$4052.59927268$
10.2.40960000000000.4	$x^{10} - 4 x^{9} + 8 x^{8} - 16 x^{7} + 37 x^{6} - 60 x^{5} + 52 x^{4} - 4 x^{3} - 42 x^{2} + 44 x - 14$	$10$	[2,4]	$2^{22}\cdot 5^{10}$	$2$	$22.9739670999$	$107.24911111313357$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$3543.00209689$
10.2.40960000000000.8	$x^{10} - 5 x^{8} - 16 x^{5} + 20 x^{4} + 16$	$10$	[2,4]	$2^{22}\cdot 5^{10}$	$2$	$22.9739670999$	$78.43749499118947$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$3543.07585885$
10.2.40960000000000.9	$x^{10} - 12 x^{5} - 50 x^{4} - 64$	$10$	[2,4]	$2^{22}\cdot 5^{10}$	$2$	$22.9739670999$	$70.89628976530283$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$2968.93095018$
10.2.69774697265625.1	$x^{10} - 10 x^{7} - 15 x^{6} + 39 x^{5} - 10 x^{4} + 15 x^{3} + 90 x^{2} - 65 x - 123$	$10$	[2,4]	$3^{10}\cdot 5^{10}\cdot 11^{2}$	$3$	$24.230913993$	$129.01385705267555$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$4575.95178602$
10.2.89302500000000.1	$x^{10} + 10 x^{8} - 10 x^{7} + 30 x^{6} - 36 x^{5} + 60 x^{4} - 60 x^{2} + 30 x + 12$	$10$	[2,4]	$2^{8}\cdot 3^{6}\cdot 5^{10}\cdot 7^{2}$	$4$	$24.8362693824$	$125.79839277648175$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$6700.47842416$
10.2.94478400000000.1	$x^{10} - x^{9} - 8 x^{8} + 11 x^{7} + 28 x^{6} - 43 x^{5} - 61 x^{4} + 112 x^{3} + 56 x^{2} - 192 x + 96$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{8}$	$3$	$24.9765962221$	$214.17533880095698$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$7088.05881287$
10.2.100000000000000.1	$x^{10} - 10 x^{7} + 5 x^{6} - 14 x^{5} + 25 x^{4} + 50 x^{3} - 30 x^{2} - 10 x - 1$	$10$	[2,4]	$2^{14}\cdot 5^{14}$	$2$	$25.1188643151$	$83.700463625635$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$4550.67205885$
10.2.104231337890625.1	$x^{10} - 15 x^{7} + 5 x^{6} + 6 x^{5} + 45 x^{4} - 45 x^{3} + 45 x - 9$	$10$	[2,4]	$3^{6}\cdot 5^{10}\cdot 11^{4}$	$3$	$25.22317954$	$226.73348469048673$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$2539.31192785$
10.2.108160000000000.1	$x^{10} - 6 x^{5} - 25 x^{4} - 16$	$10$	[2,4]	$2^{16}\cdot 5^{10}\cdot 13^{2}$	$3$	$25.3166750832$	$175.6051585652081$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$4628.07578446$
10.2.109222230491136.1	$x^{10} - 4 x^{9} + 3 x^{8} + 12 x^{7} - 27 x^{6} + 45 x^{4} - 36 x^{3} - 21 x^{2} + 28 x - 7$	$10$	[2,4]	$2^{22}\cdot 3^{12}\cdot 7^{2}$	$3$	$25.3414291796$	$153.320495401323$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$5221.54222574$
10.2.138234385465344.1	$x^{10} - 4 x^{9} + 24 x^{7} - 42 x^{6} + 84 x^{4} - 120 x^{3} + 81 x^{2} - 20 x + 8$	$10$	[2,4]	$2^{16}\cdot 3^{16}\cdot 7^{2}$	$3$	$25.9454739613$	$175.1521744322793$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$11827.7472793$
10.2.147622500000000.4	$x^{10} - 30 x^{6} - 30 x^{5} + 180 x^{2} + 270 x + 108$	$10$	[2,4]	$2^{8}\cdot 3^{10}\cdot 5^{10}$	$3$	$26.1165168989$	$116.31983870929686$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$11062.0700212$
10.2.207360000000000.1	$x^{10} - 16 x^{5} + 75 x^{2} - 36$	$10$	[2,4]	$2^{18}\cdot 3^{4}\cdot 5^{10}$	$3$	$27.0192007704$					$A_{10}$ (as 10T44)	trivial	$2$	$5$	$24462.0486839$
10.2.222902511206400.4	$x^{10} - 2 x^{9} + 9 x^{8} - 12 x^{7} + 30 x^{6} - 72 x^{5} + 60 x^{4} - 312 x^{3} + 54 x^{2} - 444 x - 66$	$10$	[2,4]	$2^{24}\cdot 3^{12}\cdot 5^{2}$	$3$	$27.2151978632$	$148.88337655490113$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$15247.7603232$
10.2.452093906250000.1	$x^{10} - 10 x^{7} - 9 x^{5} + 25 x^{4} - 60 x^{3} + 192$	$10$	[2,4]	$2^{4}\cdot 3^{10}\cdot 5^{10}\cdot 7^{2}$	$4$	$29.2094154185$	$169.77954108531165$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$6814.51644898$
10.2.485980261401600.1	$x^{10} - 2 x^{9} + 243 x^{2} - 486 x + 243$	$10$	[2,4]	$2^{10}\cdot 3^{18}\cdot 5^{2}\cdot 7^{2}$	$4$	$29.4213003129$	$387.0905348824428$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$10303.5364606$
10.2.590490000000000.16	$x^{10} - 5 x^{9} + 10 x^{8} + 10 x^{7} - 60 x^{6} + 86 x^{5} + 30 x^{4} - 110 x^{3} + 20 x^{2} + 40 x - 16$	$10$	[2,4]	$2^{10}\cdot 3^{10}\cdot 5^{10}$	$3$	$30.0$	$135.11534721965677$				$A_{10}$ (as 10T44)	$[2]$	$2$	$5$	$34142.2320222$
10.2.590490000000000.18	$x^{10} - 5 x^{8} - 5 x^{6} - 6 x^{5} + 25 x^{4} + 40 x^{2} + 16$	$10$	[2,4]	$2^{10}\cdot 3^{10}\cdot 5^{10}$	$3$	$30.0$	$84.45330482080361$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$18132.2987212$
10.2.590490000000000.27	$x^{10} - 5 x^{9} + 20 x^{7} + 5 x^{6} - 33 x^{5} + 10 x^{4} - 140 x^{3} + 30 x^{2} + 270 x + 120$	$10$	[2,4]	$2^{10}\cdot 3^{10}\cdot 5^{10}$	$3$	$30.0$	$84.74723971751452$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$55750.4412506$
10.2.729000000000000.1	$x^{10} + 5 x^{8} - 10 x^{7} + 55 x^{6} + 16 x^{5} + 25 x^{4} - 10 x^{3} + 20 x^{2} - 2$	$10$	[2,4]	$2^{12}\cdot 3^{6}\cdot 5^{12}$	$3$	$30.638870628$	$108.76958136314693$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$29046.1780366$
10.2.829440000000000.6	$x^{10} - 10 x^{8} + 50 x^{6} - 24 x^{5} - 80 x^{4} + 120 x^{2} - 72$	$10$	[2,4]	$2^{20}\cdot 3^{4}\cdot 5^{10}$	$3$	$31.0369114783$	$106.28440672191141$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$34395.0864289$
10.2.1049760000000000.19	$x^{10} - 5 x^{8} - 30 x^{7} - 35 x^{6} + 24 x^{5} + 185 x^{4} + 150 x^{3} - 160 x^{2} - 360 x - 112$	$10$	[2,4]	$2^{14}\cdot 3^{8}\cdot 5^{10}$	$3$	$31.7767152315$	$159.12336645288931$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$56365.4767049$
10.2.1239040000000000.2	$x^{10} - 10 x^{8} - 10 x^{7} + 30 x^{6} - 40 x^{5} - 25 x^{4} + 60 x^{3} - 140 x^{2} + 120 x - 58$	$10$	[2,4]	$2^{20}\cdot 5^{10}\cdot 11^{2}$	$3$	$32.307885324$	$192.0964924009864$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$15463.4545043$
10.2.1328602500000000.1	$x^{10} - 2 x^{9} + 6 x^{8} + 12 x^{7} - 66 x^{6} + 180 x^{5} - 288 x^{4} + 324 x^{3} - 252 x^{2} + 126 x - 36$	$10$	[2,4]	$2^{8}\cdot 3^{12}\cdot 5^{10}$	$3$	$32.5341531359$	$103.19392575635743$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$41537.8153712$
10.2.1328602500000000.5	$x^{10} - 30 x^{7} + 192 x^{5} - 180 x^{4} - 240 x^{3} + 600 x^{2} - 520 x + 96$	$10$	[2,4]	$2^{8}\cdot 3^{12}\cdot 5^{10}$	$3$	$32.5341531359$	$106.58179226787911$			?	$A_{10}$ (as 10T44)	$[2]$	$2$	$5$	$22053.0342072$
10.2.1474560000000000.13	$x^{10} + 5 x^{8} - 32 x^{5} - 20 x^{4} + 144$	$10$	[2,4]	$2^{24}\cdot 3^{2}\cdot 5^{10}$	$3$	$32.8750365903$	$100.31912134342569$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$17855.495664$
10.2.1640250000000000.8	$x^{10} + 10 x^{8} + 40 x^{6} - 12 x^{5} + 65 x^{4} - 60 x^{3} + 20 x^{2} - 120 x + 20$	$10$	[2,4]	$2^{10}\cdot 3^{8}\cdot 5^{12}$	$3$	$33.2269902974$	$157.8830840055145$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$57946.6700139$
10.2.1666598976000000.1	$x^{10} - 4 x^{9} + 17 x^{8} - 44 x^{7} + 88 x^{6} - 90 x^{5} + 24 x^{4} + 36 x^{3} - 21 x^{2} - 6 x + 3$	$10$	[2,4]	$2^{12}\cdot 3^{12}\cdot 5^{6}\cdot 7^{2}$	$4$	$33.2799841718$	$477.77312836089504$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$32395.9116704$
10.2.2007040000000000.1	$x^{10} - 5 x^{8} + 5 x^{6} - 8 x^{5} - 15 x^{4} + 5 x^{2} - 1$	$10$	[2,4]	$2^{22}\cdot 5^{10}\cdot 7^{2}$	$3$	$33.9043640614$	$241.3597847507842$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$12276.9498329$
10.2.2361960000000000.9	$x^{10} + 5 x^{8} - 5 x^{6} - 48 x^{5} - 25 x^{4} + 40 x^{2} - 16$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$130.24480093611996$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$36214.2753763$
10.2.2361960000000000.10	$x^{10} + 5 x^{8} - 5 x^{6} - 36 x^{5} - 25 x^{4} + 40 x^{2} - 16$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$156.105880799064$			?	$A_{10}$ (as 10T44)	$[2]$	$2$	$5$	$20672.2576595$
10.2.2361960000000000.17	$x^{10} - 5 x^{8} - 5 x^{6} - 24 x^{5} + 25 x^{4} + 40 x^{2} + 16$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$178.95031930863476$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$27876.3161743$
10.2.2361960000000000.20	$x^{10} - 18 x^{5} - 75 x^{4} - 144$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$135.9728385694479$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$94505.9541794$
10.2.2361960000000000.22	$x^{10} - 18 x^{5} + 150 x^{4} - 144$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$98.9646476218519$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$34137.0119179$
10.2.2361960000000000.23	$x^{10} - 5 x^{9} + 20 x^{7} - 40 x^{6} + 80 x^{4} - 160 x^{3} + 160 x - 128$	$10$	[2,4]	$2^{12}\cdot 3^{10}\cdot 5^{10}$	$3$	$34.4609506499$	$87.08289954653597$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$72067.5771506$
10.2.2538998916710400.1	$x^{10} - 4 x^{9} + 24 x^{7} - 42 x^{6} + 84 x^{4} - 120 x^{3} + 81 x^{2} - 156 x - 60$	$10$	[2,4]	$2^{18}\cdot 3^{18}\cdot 5^{2}$	$3$	$34.7109301441$	$151.52694353882393$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$36092.7062724$
10.2.2538998916710400.2	$x^{10} - 9 x^{8} + 18 x^{6} + 54 x^{4} - 243 x^{2} - 1024 x + 243$	$10$	[2,4]	$2^{18}\cdot 3^{18}\cdot 5^{2}$	$3$	$34.7109301441$	$251.50479774942383$				$A_{10}$ (as 10T44)	trivial	$2$	$5$	$23186.1775485$
10.2.2687385600000000.3	$x^{10} - 4 x^{9} + 10 x^{8} - 36 x^{7} + 78 x^{6} - 120 x^{5} + 164 x^{4} - 140 x^{3} + 41 x^{2} + 12 x - 306$	$10$	[2,4]	$2^{20}\cdot 3^{8}\cdot 5^{8}$	$3$	$34.9086455492$	$327.7544549834651$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$62819.4553191$
10.2.3317760000000000.4	$x^{10} - 10 x^{8} + 30 x^{6} - 16 x^{5} - 60 x^{4} + 40 x^{2} - 16$	$10$	[2,4]	$2^{22}\cdot 3^{4}\cdot 5^{10}$	$3$	$35.6520491593$	$105.03777197502482$				$A_{10}$ (as 10T44)	$[2]$	$2$	$5$	$20807.135662$
10.2.3690562500000000.2	$x^{10} + 10 x^{8} + 10 x^{6} - 60 x^{5} - 100 x^{4} - 180 x^{3} - 100 x^{2} - 60 x - 16$	$10$	[2,4]	$2^{8}\cdot 3^{10}\cdot 5^{12}$	$3$	$36.0337330194$	$168.42900859392978$			?	$A_{10}$ (as 10T44)	trivial	$2$	$5$	$103068.171247$