Number field search results

Results (1-50 of 3622 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
10.0.229345007.1	$x^{10} - x^{9} + 6 x^{8} - 3 x^{7} + 11 x^{6} - 3 x^{5} + 11 x^{4} - 3 x^{3} + 6 x^{2} - x + 1$	$10$	[0,5]	$-\,47^{5}$	$1$	$6.8556546004$	$6.855654600401044$		✓	?	$D_5$ (as 10T2)	trivial	$2$	$4$	$0.60186322759$
10.0.3077056399.1	$x^{10} - 2 x^{9} + 3 x^{8} - 7 x^{7} + x^{6} + 2 x^{5} + 19 x^{4} - 25 x^{3} + 21 x^{2} - 5 x + 1$	$10$	[0,5]	$-\,79^{5}$	$1$	$8.88819441732$	$8.888194417315589$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$3.2292468301$
10.0.11592740743.1	$x^{10} - 2 x^{9} + 3 x^{8} + x^{7} - 15 x^{6} + 22 x^{5} + 9 x^{4} - 65 x^{3} + 77 x^{2} - 39 x + 9$	$10$	[0,5]	$-\,103^{5}$	$1$	$10.1488915651$	$10.14889156509222$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$6.90703427277$
10.0.23863536599.2	$x^{10} - x^{9} + 6 x^{8} + 3 x^{7} - x^{6} + 37 x^{5} - 2 x^{4} + 12 x^{3} + 48 x^{2} - 16 x + 32$	$10$	[0,5]	$-\,7^{5}\cdot 17^{5}$	$2$	$10.9087121146$	$10.908712114635714$		✓	?	$D_5$ (as 10T2)	$[2]$	$2$	$4$	$6.25954076332$
10.0.33038369407.1	$x^{10} - 5 x^{9} + 18 x^{8} - 42 x^{7} + 76 x^{6} - 102 x^{5} + 99 x^{4} - 67 x^{3} + 22 x^{2} + 9$	$10$	[0,5]	$-\,127^{5}$	$1$	$11.2694276696$	$11.269427669584644$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$12.1999793748$
10.0.38579489651.1	$x^{10} - 4 x^{9} + 4 x^{8} - 4 x^{7} + 9 x^{6} - 6 x^{5} + 12 x^{4} - 2 x^{3} + 41 x^{2} - 2 x + 4$	$10$	[0,5]	$-\,131^{5}$	$1$	$11.4455231423$	$11.445523142259598$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$26.1311479413$
10.0.59797108943.2	$x^{10} + 6 x^{8} - x^{7} + 12 x^{6} - 13 x^{5} + 45 x^{4} + 40 x^{3} + 43 x^{2} - 15 x + 25$	$10$	[0,5]	$-\,11^{5}\cdot 13^{5}$	$2$	$11.9582607431$	$11.958260743101398$		✓	?	$D_5$ (as 10T2)	$[2]$	$2$	$4$	$9.26993706061$
10.0.101621504799.2	$x^{10} - 5 x^{9} + 22 x^{8} - 58 x^{7} + 119 x^{6} - 175 x^{5} + 181 x^{4} - 128 x^{3} + 37 x^{2} + 6 x + 9$	$10$	[0,5]	$-\,3^{5}\cdot 53^{5}$	$2$	$12.6095202129$	$12.609520212918492$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$37.9329762086$
10.0.183765996899.1	$x^{10} - x^{9} + 11 x^{8} + 4 x^{7} + 45 x^{6} + 49 x^{5} + 131 x^{4} + 148 x^{3} + 156 x^{2} + 144 x + 64$	$10$	[0,5]	$-\,179^{5}$	$1$	$13.3790881603$	$13.379088160259652$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$62.0097126537$
10.0.296630859375.1	$x^{10} + 5 x^{8} + 15 x^{6} + 20 x^{4} + 25 x^{2} + 15$	$10$	[0,5]	$-\,3^{5}\cdot 5^{13}$	$2$	$14.0352978355$	$14.035297835467638$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$79.1456128499$
10.0.602738989907.1	$x^{10} - 2 x^{9} + 5 x^{8} - 4 x^{7} - 9 x^{6} + 28 x^{5} - 41 x^{4} + 30 x^{3} + 99 x^{2} + 16 x + 113$	$10$	[0,5]	$-\,227^{5}$	$1$	$15.0665191733$	$15.066519173319364$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$120.244653403$
10.0.779811265199.1	$x^{10} - 2 x^{8} - 15 x^{7} - 30 x^{6} + x^{5} + 147 x^{4} + 366 x^{3} + 405 x^{2} + 217 x + 49$	$10$	[0,5]	$-\,239^{5}$	$1$	$15.4596248337$	$15.459624833740307$		✓	?	$D_5$ (as 10T2)	$[3]$	$2$	$4$	$19.2491145749$
10.0.1250000000000.1	$x^{10} + 5 x^{8} - 10 x^{7} + 5 x^{6} - 28 x^{5} + 15 x^{4} - 10 x^{3} + 30 x^{2} + 40 x + 16$	$10$	[0,5]	$-\,2^{10}\cdot 5^{13}$	$2$	$16.2065659669$	$16.206565966927624$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$666.652012769$
10.0.2272262782976.1	$x^{10} - 2 x^{9} - 5 x^{8} + 16 x^{7} - x^{6} - 42 x^{5} + 37 x^{4} + 36 x^{3} + 236 x^{2} - 592 x + 332$	$10$	[0,5]	$-\,2^{15}\cdot 37^{5}$	$2$	$17.2046505341$	$17.204650534085253$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$818.35662213$
10.0.2553954421743.1	$x^{10} - 2 x^{9} + 2 x^{8} + 13 x^{7} + 47 x^{6} + 4 x^{5} - 92 x^{4} - 114 x^{3} + 6 x^{2} + 135 x + 81$	$10$	[0,5]	$-\,3^{5}\cdot 101^{5}$	$2$	$17.4068951855$	$17.406895185529212$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$228.712161935$
10.0.3303341057599.3	$x^{10} + 5 x^{8} - 10 x^{7} + 47 x^{6} - 25 x^{5} + 87 x^{4} - 124 x^{3} + 460 x^{2} - 319 x + 319$	$10$	[0,5]	$-\,11^{5}\cdot 29^{5}$	$2$	$17.8605710995$	$17.86057109949175$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$94.192928741$
10.0.3602729712967.3	$x^{10} - 3 x^{8} + 19 x^{6} + 37 x^{4} - 54 x^{2} + 175$	$10$	[0,5]	$-\,7^{5}\cdot 11^{8}$	$2$	$18.0161989123$	$18.016198912314337$		✓		$D_5$ (as 10T2)	$[5]$	$2$	$4$	$55.0487330749$
10.0.4817172660224.1	$x^{10} + 2 x^{8} - 3 x^{6} - 4 x^{4} + 4 x^{2} + 1376$	$10$	[0,5]	$-\,2^{15}\cdot 43^{5}$	$2$	$18.547236991$	$18.547236990991408$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$1221.19051164$
10.0.5030919566507.1	$x^{10} - 2 x^{9} + x^{8} + 6 x^{7} + 2 x^{6} + 10 x^{5} - 9 x^{4} + 24 x^{3} + 417 x^{2} - 622 x + 428$	$10$	[0,5]	$-\,347^{5}$	$1$	$18.6279360102$	$18.627936010197157$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$358.048560296$
10.0.7024111812608.2	$x^{10} - 4 x^{8} + 13 x^{6} - 6 x^{4} + 64 x^{2} + 32$	$10$	[0,5]	$-\,2^{15}\cdot 11^{8}$	$2$	$19.2601267834$	$19.260126783385598$		✓		$D_5$ (as 10T2)	$[5]$	$2$	$4$	$683.618965914$
10.10.10368641602001.1	$x^{10} - 2 x^{9} - 20 x^{8} + 2 x^{7} + 69 x^{6} - x^{5} - 69 x^{4} + 2 x^{3} + 20 x^{2} - 2 x - 1$	$10$	[10,0]	$401^{5}$	$1$	$20.0249843945$	$20.024984394500787$		✓		$D_5$ (as 10T2)	trivial	$2$	$9$	$1552.90547638$
10.0.12309502009375.1	$x^{10} - 2 x^{9} - x^{8} - 5 x^{7} - 11 x^{6} + 46 x^{5} + 115 x^{4} - 161 x^{3} - 291 x^{2} + 225 x + 515$	$10$	[0,5]	$-\,5^{5}\cdot 83^{5}$	$2$	$20.3715487875$	$20.37154878746336$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$301.986905014$
10.0.16305067506199.1	$x^{10} - 4 x^{9} + 5 x^{8} + 15 x^{7} + 12 x^{6} - 79 x^{5} + 142 x^{4} - 103 x^{3} + 619 x^{2} - 128 x + 443$	$10$	[0,5]	$-\,439^{5}$	$1$	$20.9523268398$	$20.952326839756964$		✓		$D_5$ (as 10T2)	$[3]$	$2$	$4$	$159.412146987$
10.0.17061555810443.1	$x^{10} - 4 x^{9} + 4 x^{8} + 14 x^{7} - 70 x^{6} + 96 x^{5} + 25 x^{4} - 294 x^{3} + 968 x^{2} - 2024 x + 1808$	$10$	[0,5]	$-\,443^{5}$	$1$	$21.0475651798$	$21.047565179849187$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$651.452267301$
10.0.17391168553984.1	$x^{10} + 16 x^{8} + 110 x^{6} + 352 x^{4} + 529 x^{2} + 144$	$10$	[0,5]	$-\,2^{10}\cdot 19^{8}$	$2$	$21.0878778075$	$21.08787780747746$		✓		$D_5$ (as 10T2)	trivial	$4$	$4$	$13249.0898359$
10.0.19501004534375.1	$x^{10} - 4 x^{9} + 4 x^{8} - 5 x^{7} - 22 x^{6} + 43 x^{5} + 162 x^{4} + 80 x^{3} + 536 x^{2} + 336 x + 224$	$10$	[0,5]	$-\,5^{5}\cdot 7^{5}\cdot 13^{5}$	$3$	$21.3307290077$	$21.330729007701542$		✓	?	$D_5$ (as 10T2)	$[2, 2]$	$2$	$4$	$275.152080898$
10.0.20516357421875.1	$x^{10} - 5 x^{9} + 15 x^{8} - 30 x^{7} + 45 x^{6} - 51 x^{5} + 85 x^{4} - 110 x^{3} + 295 x^{2} - 245 x + 329$	$10$	[0,5]	$-\,5^{13}\cdot 7^{5}$	$2$	$21.4392715774$	$21.43927157742677$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$741.985232673$
10.0.25216079618399.1	$x^{10} + 18 x^{8} + 145 x^{6} + 576 x^{4} + 1024 x^{2} + 479$	$10$	[0,5]	$-\,479^{5}$	$1$	$21.8860686282$	$21.88606862823929$		✓	?	$D_5$ (as 10T2)	$[5]$	$2$	$4$	$35.7327151873$
10.0.27675731591168.1	$x^{10} - 10 x^{8} - 8 x^{7} - 3 x^{6} + 156 x^{4} + 312 x^{3} + 844 x^{2} + 560 x + 400$	$10$	[0,5]	$-\,2^{15}\cdot 61^{5}$	$2$	$22.0907220344$	$22.090722034374522$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$3135.83122994$
10.0.37078857421875.2	$x^{10} - 5 x^{8} + 10 x^{6} - 168 x^{5} + 225 x^{4} + 450 x^{3} + 405 x^{2} + 270 x + 108$	$10$	[0,5]	$-\,3^{5}\cdot 5^{16}$	$2$	$22.7463980236$	$22.746398023598275$		✓		$D_5$ (as 10T2)	trivial	$6$	$4$	$15823.0197762$
10.0.39129873538843.1	$x^{10} + 14 x^{8} - 15 x^{6} + 75 x^{4} - 22 x^{2} + 523$	$10$	[0,5]	$-\,523^{5}$	$1$	$22.8691932521$	$22.869193252058544$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$1557.16197396$
10.0.40000000000000.4	$x^{10} - 35 x^{6} + 130 x^{4} + 160$	$10$	[0,5]	$-\,2^{15}\cdot 5^{13}$	$2$	$22.9195453899$	$22.91954538992328$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$5980.98773157$
10.0.60698860931851.1	$x^{10} - 2 x^{8} - 13 x^{6} + 14 x^{4} + 49 x^{2} + 2284$	$10$	[0,5]	$-\,571^{5}$	$1$	$23.8956062907$	$23.895606290697042$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$1759.61468719$
10.0.77114156402999.1	$x^{10} + 14 x^{8} - 17 x^{6} + 137 x^{4} - 109 x^{2} + 599$	$10$	[0,5]	$-\,599^{5}$	$1$	$24.474476501$	$24.474476501040833$		✓		$D_5$ (as 10T2)	$[5]$	$2$	$4$	$542.706702994$
10.0.85154195684051.1	$x^{10} + 14 x^{8} - 31 x^{6} + 51 x^{4} + 378 x^{2} + 611$	$10$	[0,5]	$-\,13^{5}\cdot 47^{5}$	$2$	$24.7184141886$	$24.71841418861655$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$1055.79605151$
10.0.87978302634375.1	$x^{10} - x^{8} - 6 x^{7} + 99 x^{6} - 27 x^{5} - 271 x^{4} + 180 x^{3} + 1000 x^{2} + 825 x + 225$	$10$	[0,5]	$-\,3^{5}\cdot 5^{5}\cdot 41^{5}$	$3$	$24.7991935353$	$24.79919353527449$		✓		$D_5$ (as 10T2)	$[2, 2]$	$2$	$4$	$1625.74756239$
10.0.90876845839099.1	$x^{10} + 14 x^{8} - 15 x^{6} + 171 x^{4} - 214 x^{2} + 619$	$10$	[0,5]	$-\,619^{5}$	$1$	$24.8797106092$	$24.879710609249457$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$2054.49574254$
10.0.103244904396875.1	$x^{10} + 10 x^{8} - 67 x^{6} + 175 x^{4} + 846 x^{2} + 635$	$10$	[0,5]	$-\,5^{5}\cdot 127^{5}$	$2$	$25.1992063367$	$25.199206336708304$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$2024.6593919$
10.0.121559878349523.1	$x^{10} - 11 x^{8} + 31 x^{6} + 303 x^{4} - 1908 x^{2} + 3888$	$10$	[0,5]	$-\,3^{5}\cdot 29^{8}$	$2$	$25.6140955742$	$25.614095574192245$		✓		$D_5$ (as 10T2)	trivial	$6$	$4$	$31666.976075$
10.0.129074483789824.1	$x^{10} + 12 x^{8} - 4 x^{7} - 34 x^{6} - 28 x^{5} + 248 x^{4} + 116 x^{3} - 95 x^{2} + 140 x + 668$	$10$	[0,5]	$-\,2^{15}\cdot 83^{5}$	$2$	$25.7681974535$	$25.768197453450252$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$9497.55325285$
10.0.136023078872351.1	$x^{10} - 2 x^{8} + 99 x^{6} + 573 x^{4} + 1059 x^{2} + 671$	$10$	[0,5]	$-\,11^{5}\cdot 61^{5}$	$2$	$25.903667694$	$25.903667693977237$		✓		$D_5$ (as 10T2)	$[6]$	$2$	$4$	$413.262780858$
10.0.148628987203643.1	$x^{10} - 4 x^{9} - 8 x^{8} + 2 x^{7} + 66 x^{6} + 144 x^{5} + 237 x^{4} + 250 x^{3} + 908 x^{2} + 112 x + 64$	$10$	[0,5]	$-\,683^{5}$	$1$	$26.1342686907$	$26.13426869074396$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$1814.25436175$
10.0.156250000000000.3	$x^{10} - 10 x^{7} - 55 x^{6} - 106 x^{5} + 50 x^{4} + 680 x^{3} + 1600 x^{2} + 2240 x + 1568$	$10$	[0,5]	$-\,2^{10}\cdot 5^{16}$	$2$	$26.265278044$	$26.26527804403767$		✓		$D_5$ (as 10T2)	$[5]$	$4$	$4$	$11877.9665213$
10.0.157539780804451.1	$x^{10} + 2 x^{8} - 99 x^{6} + 591 x^{4} + 1118 x^{2} + 691$	$10$	[0,5]	$-\,691^{5}$	$1$	$26.2868788562$	$26.28687885618983$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$2669.10062662$
10.0.166872925103499.1	$x^{10} - 10 x^{8} + 129 x^{6} + 179 x^{4} + 1306 x^{2} + 699$	$10$	[0,5]	$-\,3^{5}\cdot 233^{5}$	$2$	$26.4386081328$	$26.43860813280457$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$5966.96565655$
10.0.196595458984375.1	$x^{10} - 5 x^{9} - 5 x^{8} + 40 x^{7} - 45 x^{6} + 67 x^{5} + 530 x^{4} + 85 x^{3} + 575 x^{2} + 495 x + 121$	$10$	[0,5]	$-\,5^{13}\cdot 11^{5}$	$2$	$26.8755492262$	$26.875549226221146$		✓		$D_5$ (as 10T2)	$[4]$	$2$	$4$	$692.559851723$
10.0.198926586778624.1	$x^{10} - 4 x^{8} + 102 x^{6} + 528 x^{4} + 953 x^{2} + 724$	$10$	[0,5]	$-\,2^{10}\cdot 181^{5}$	$2$	$26.9072480941$	$26.90724809414742$		✓		$D_5$ (as 10T2)	$[2]$	$2$	$4$	$11794.4144151$
10.0.207252522098163.3	$x^{10} - 4 x^{9} + 14 x^{8} - 22 x^{7} + 65 x^{6} + 164 x^{5} + 508 x^{4} + 888 x^{3} + 1671 x^{2} + 1890 x + 900$	$10$	[0,5]	$-\,3^{5}\cdot 31^{8}$	$2$	$27.0177999966$	$27.01779999660944$		✓		$D_5$ (as 10T2)	$[5]$	$6$	$4$	$8605.31566738$
10.0.220405380367699.1	$x^{10} - 14 x^{8} + 109 x^{6} + 319 x^{4} - 578 x^{2} + 739$	$10$	[0,5]	$-\,739^{5}$	$1$	$27.1845544381$	$27.184554438136374$		✓		$D_5$ (as 10T2)	trivial	$2$	$4$	$3282.00851578$
10.0.238890943128751.1	$x^{10} + 6 x^{8} - 19 x^{6} - 84 x^{4} + 196 x^{2} + 6759$	$10$	[0,5]	$-\,751^{5}$	$1$	$27.4043792121$	$27.40437921208944$		✓		$D_5$ (as 10T2)	$[3]$	$2$	$4$	$550.038348344$