Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 129866 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
10.0.37078857421875.1	$x^{10} + 10 x^{8} - 10 x^{7} + 90 x^{6} - 49 x^{5} + 125 x^{4} + 70 x^{3} + 95 x^{2} + 10 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 5^{16}$	$2$	$22.7463980236$	$22.746398023598275$	✓	✓		$C_{10}$ (as 10T1)	$[11]$	$6$	$4$	$257.113789169$
10.0.43913358828288.1	$x^{10} - 4 x^{9} + 5 x^{8} + 14 x^{7} - 52 x^{6} + 8 x^{5} + 337 x^{4} - 984 x^{3} + 1389 x^{2} - 1026 x + 324$	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 163^{4}$	$3$	$23.1344759229$	$44.22668877499196$				$D_{10}$ (as 10T3)	$[11]$	$6$	$4$	$1113.39252057$
10.0.47483866083328.2	$x^{10} - 4 x^{9} + 24 x^{7} - 29 x^{6} - 36 x^{5} + 78 x^{4} + 4 x^{3} - 22 x^{2} - 100 x + 112$	$10$	[0,5]	$-\,2^{12}\cdot 103^{5}$	$2$	$23.3160300917$	$28.705400188814647$				$A_5\times C_2$ (as 10T11)	$[15]$	$2$	$4$	$527.919428837$
10.0.49294471550063.1	$x^{10} - 4 x^{9} + 16 x^{8} - 42 x^{7} + 99 x^{6} - 181 x^{5} + 297 x^{4} - 378 x^{3} + 432 x^{2} - 324 x + 243$	$10$	[0,5]	$-\,23\cdot 1609\cdot 36497^{2}$	$3$	$23.4034466716$	$36751.11534361917$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$56.8105224918$
10.0.54025845694031.1	$x^{10} - 4 x^{9} + 16 x^{8} - 40 x^{7} + 93 x^{6} - 167 x^{5} + 279 x^{4} - 360 x^{3} + 432 x^{2} - 324 x + 243$	$10$	[0,5]	$-\,36497^{2}\cdot 40559$	$2$	$23.6189266472$	$38474.43076901853$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$56.8105224918$
10.0.54470105243231.1	$x^{10} - 2 x^{9} + 12 x^{8} - 18 x^{7} + 63 x^{6} - 73 x^{5} + 189 x^{4} - 162 x^{3} + 324 x^{2} - 162 x + 243$	$10$	[0,5]	$-\,61^{2}\cdot 131\cdot 397^{2}\cdot 709$	$4$	$23.6382772129$	$47426.26638267027$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$38.3907381012$
10.0.55534384018432.1	$x^{10} + 22 x^{8} + 176 x^{6} + 605 x^{4} + 792 x^{2} + 253$	$10$	[0,5]	$-\,2^{10}\cdot 11^{9}\cdot 23$	$3$	$23.6840623601$	$158.98748935426087$	✓		?	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 6]$	$2$	$4$	$26.1711060094$
10.0.57910048116275.1	$x^{10} - x^{9} + 9 x^{8} - 13 x^{7} + 39 x^{6} - 59 x^{5} + 117 x^{4} - 117 x^{3} + 243 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,5^{2}\cdot 37\cdot 47\cdot 36497^{2}$	$4$	$23.783479543$	$17814.07912298584$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$	$2$	$4$	$56.8105224918$
10.0.58551145104384.1	$x^{10} - 4 x^{9} + 17 x^{8} - 26 x^{7} + 25 x^{6} + 16 x^{5} + 19 x^{4} - 82 x^{3} + 282 x^{2} - 120 x + 16$	$10$	[0,5]	$-\,2^{10}\cdot 3^{4}\cdot 163^{4}$	$3$	$23.8096789446$	$44.22668877499196$				$D_{10}$ (as 10T3)	$[11]$	$4$	$4$	$2206.89336909$
10.0.64387371291203.1	$x^{10} - 3 x^{9} + 10 x^{8} - 15 x^{7} + 28 x^{6} - 32 x^{5} + 84 x^{4} - 135 x^{3} + 270 x^{2} - 243 x + 243$	$10$	[0,5]	$-\,59\cdot 73^{2}\cdot 97\cdot 1453^{2}$	$4$	$24.0369892631$	$24638.037401546415$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$146.78536797$
10.0.65537725589747.1	$x^{10} - 4 x^{9} + 12 x^{8} - 23 x^{7} + 42 x^{6} - 65 x^{5} + 126 x^{4} - 207 x^{3} + 324 x^{2} - 324 x + 243$	$10$	[0,5]	$-\,23\cdot 661\cdot 65657^{2}$	$3$	$24.079592694$	$31594.040118351437$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$88.0509066233$
10.0.68196858635907.1	$x^{10} - 2 x^{9} + 8 x^{8} - 17 x^{7} + 28 x^{6} - 67 x^{5} + 84 x^{4} - 153 x^{3} + 216 x^{2} - 162 x + 243$	$10$	[0,5]	$-\,3^{2}\cdot 37\cdot 43^{2}\cdot 71\cdot 1249^{2}$	$5$	$24.1755541101$	$20573.401930648222$	✓			$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$179.287993097$
10.0.68279420878511.1	$x^{10} + 6 x^{8} - 6 x^{7} + 15 x^{6} - 37 x^{5} + 45 x^{4} - 54 x^{3} + 162 x^{2} + 243$	$10$	[0,5]	$-\,47\cdot 337\cdot 65657^{2}$	$3$	$24.1784793202$	$32248.11968161865$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$88.0509066233$
10.0.69831323872151.1	$x^{10} + 7 x^{8} - 9 x^{7} + 18 x^{6} - 53 x^{5} + 54 x^{4} - 81 x^{3} + 189 x^{2} + 243$	$10$	[0,5]	$-\,97\cdot 167\cdot 65657^{2}$	$3$	$24.2328797681$	$32612.53965884902$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$88.0509066233$
10.0.71786961877952.1	$x^{10} - x^{9} + 5 x^{8} - 4 x^{7} + 14 x^{6} - 9 x^{5} + 28 x^{4} - 16 x^{3} + 40 x^{2} - 16 x + 32$	$10$	[0,5]	$-\,2^{6}\cdot 47^{2}\cdot 71\cdot 73\cdot 313^{2}$	$5$	$24.2999039729$	$24697.71050117804$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$155.415627048$
10.0.72230580325103.1	$x^{10} + 3 x^{8} - 2 x^{7} + 7 x^{6} - 7 x^{5} + 14 x^{4} - 8 x^{3} + 24 x^{2} + 32$	$10$	[0,5]	$-\,2087\cdot 186037^{2}$	$2$	$24.3148788722$	$19704.29443040273$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$206.228884508$
10.0.77265229938688.1	$x^{10} + 22 x^{8} + 176 x^{6} + 616 x^{4} + 880 x^{2} + 352$	$10$	[0,5]	$-\,2^{15}\cdot 11^{9}$	$2$	$24.4792670483$	$24.479267048299516$	✓	✓	?	$C_{10}$ (as 10T1)	$[22]$	$2$	$4$	$26.1711060094$
10.0.79184630786579.1	$x^{10} - 4 x^{9} + 14 x^{8} - 23 x^{7} + 46 x^{6} - 39 x^{5} + 77 x^{4} - 16 x^{3} + 97 x^{2} + 26 x + 64$	$10$	[0,5]	$-\,157^{2}\cdot 937^{2}\cdot 3659$	$3$	$24.539408464$	$23200.686002788796$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$186.670385026$
10.0.79937203918592.2	$x^{10} + 20 x^{8} + 113 x^{6} + 248 x^{4} + 203 x^{2} + 47$	$10$	[0,5]	$-\,2^{8}\cdot 47\cdot 81509^{2}$	$3$	$24.5626316432$	$6583.460040438933$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$122.10597583571828$
10.0.92023536681203.1	$x^{10} - 4 x^{9} + 15 x^{8} - 27 x^{7} + 57 x^{6} - 56 x^{5} + 100 x^{4} - 38 x^{3} + 113 x^{2} + 7 x + 75$	$10$	[0,5]	$-\,21347\cdot 65657^{2}$	$2$	$24.91092717$	$37437.681271681344$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[15]$	$2$	$4$	$88.0509066233$
10.0.92100620055287.1	$x^{10} + 9 x^{8} - x^{7} + 40 x^{6} - 7 x^{5} + 120 x^{4} - 9 x^{3} + 243 x^{2} + 243$	$10$	[0,5]	$-\,36497^{2}\cdot 69143$	$2$	$24.9130130438$	$50234.57047691361$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[16]$	$2$	$4$	$56.8105224918$
10.0.92108708193359.1	$x^{10} + 8 x^{8} - 2 x^{7} + 39 x^{6} - 5 x^{5} + 117 x^{4} - 18 x^{3} + 216 x^{2} + 243$	$10$	[0,5]	$-\,11\cdot 13\cdot 433\cdot 38569^{2}$	$4$	$24.9132318175$	$48868.74165558184$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$	$2$	$4$	$50.4870066613$
10.0.93289366800128.1	$x^{10} - x^{9} + 4 x^{8} - 4 x^{7} + 12 x^{6} - 10 x^{5} + 24 x^{4} - 16 x^{3} + 32 x^{2} - 16 x + 32$	$10$	[0,5]	$-\,2^{8}\cdot 863\cdot 20549^{2}$	$3$	$24.944983128$	$9453.712823150923$	✓			$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$456.501081731$
10.0.96032748066779.1	$x^{10} - 5 x^{9} + 15 x^{8} - 29 x^{7} + 54 x^{6} - 70 x^{5} + 108 x^{4} - 58 x^{3} + 145 x^{2} + x + 81$	$10$	[0,5]	$-\,12011\cdot 89417^{2}$	$2$	$25.0173863585$	$32771.749831218964$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$107.86378415$
10.0.99808561707863.1	$x^{10} - 3 x^{9} + 13 x^{8} - 28 x^{7} + 73 x^{6} - 118 x^{5} + 219 x^{4} - 252 x^{3} + 351 x^{2} - 243 x + 243$	$10$	[0,5]	$-\,83\cdot 181\cdot 81509^{2}$	$3$	$25.114051455$	$34992.99511330803$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[18]$	$2$	$4$	$122.105975836$
10.0.100716196621499.1	$x^{10} - 3 x^{9} + 14 x^{8} - 30 x^{7} + 80 x^{6} - 127 x^{5} + 240 x^{4} - 270 x^{3} + 378 x^{2} - 243 x + 243$	$10$	[0,5]	$-\,36497^{2}\cdot 75611$	$2$	$25.1367966426$	$52531.65395264078$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$56.8105224918$
10.0.102394555692839.1	$x^{10} - x^{9} + 10 x^{8} - 9 x^{7} + 47 x^{6} - 37 x^{5} + 141 x^{4} - 81 x^{3} + 270 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,36497^{2}\cdot 76871$	$2$	$25.1783743659$	$52967.5456010565$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[3, 6]$	$2$	$4$	$56.8105224918$
10.0.102602392460272.1	$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{5} + 8 x^{4} - 16 x^{3} + 24 x^{2} - 32 x + 32$	$10$	[0,5]	$-\,2^{4}\cdot 103\cdot 249517^{2}$	$3$	$25.1834803193$	$8047.395506930397$	✓			$C_2 \wr S_5$ (as 10T39)	$[17]$	$2$	$4$	$1420.76259834$
10.0.106079108279536.1	$x^{10} - 2 x^{9} + 5 x^{8} - 5 x^{7} + 8 x^{6} - 5 x^{5} + 16 x^{4} - 20 x^{3} + 40 x^{2} - 32 x + 32$	$10$	[0,5]	$-\,2^{4}\cdot 7\cdot 313\cdot 55009^{2}$	$4$	$25.2675414048$	$17427.08412217974$	✓			$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$259.01066264$
10.0.108266600324403.1	$x^{10} - x^{9} + 7 x^{8} - 4 x^{7} + 38 x^{6} - 25 x^{5} + 42 x^{4} + 3 x^{3} + 14 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 19^{4}\cdot 43^{4}$	$3$	$25.3191691379$	$49.50757517794625$	✓		?	$D_{10}$ (as 10T3)	$[11]$	$6$	$4$	$269.6129204212416$
10.0.109172417298176.1	$x^{10} - x^{9} + 2 x^{8} - 6 x^{7} + 8 x^{6} - 10 x^{5} + 16 x^{4} - 24 x^{3} + 16 x^{2} - 16 x + 32$	$10$	[0,5]	$-\,2^{8}\cdot 19^{2}\cdot 71\cdot 4079^{2}$	$4$	$25.3402731909$	$5266.044067966421$	✓			$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$1271.66265455$
10.0.111660952980367.1	$x^{10} - 3 x^{9} + 2 x^{8} + 2 x^{7} + 29 x^{6} - 57 x^{5} + 93 x^{4} - 128 x^{3} + 368 x^{2} - 111 x + 576$	$10$	[0,5]	$-\,7^{5}\cdot 81509^{2}$	$2$	$25.397451111385397$	$755.3562073617983$	✓		?	$S_5\times C_2$ (as 10T22)	$[15]$	$2$	$4$	$122.10597583571828$
10.0.111796920332863.1	$x^{10} + 3 x^{8} - 2 x^{7} + 3 x^{6} - 9 x^{5} + 6 x^{4} - 8 x^{3} + 24 x^{2} + 32$	$10$	[0,5]	$-\,1063\cdot 324301^{2}$	$2$	$25.4005420159$	$18566.9589055397$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[11]$	$2$	$4$	$302.113416135$
10.0.111880248027247.1	$x^{10} - x^{9} - 2 x^{8} - 2 x^{7} + 33 x^{6} + 9 x^{5} + 95 x^{4} + 78 x^{3} + 330 x^{2} + 33 x + 508$	$10$	[0,5]	$-\,7^{5}\cdot 83^{2}\cdot 983^{2}$	$3$	$25.402434607406672$	$755.7268024888359$	✓		?	$S_5\times C_2$ (as 10T22)	$[16]$	$2$	$4$	$121.72602244210606$
10.0.112708546547687.1	$x^{10} - x^{9} + 10 x^{8} - 11 x^{7} + 49 x^{6} - 47 x^{5} + 147 x^{4} - 99 x^{3} + 270 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,38569^{2}\cdot 75767$	$2$	$25.4211787806$	$54057.90805238397$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[20]$	$2$	$4$	$50.4870066613$
10.0.113647553656871.1	$x^{10} - x^{9} + 10 x^{8} - 9 x^{7} + 51 x^{6} - 37 x^{5} + 153 x^{4} - 81 x^{3} + 270 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,13\cdot 6563\cdot 36497^{2}$	$3$	$25.4422789054$	$55802.21808315508$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[18]$	$2$	$4$	$56.8105224918$
10.0.113700834897231.1	$x^{10} - x^{9} + 10 x^{8} - 7 x^{7} + 49 x^{6} - 27 x^{5} + 147 x^{4} - 63 x^{3} + 270 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,3\cdot 37\cdot 769\cdot 36497^{2}$	$4$	$25.443471461$	$55815.297392381595$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$	$2$	$4$	$56.8105224918$
10.0.114339955792896.1	$x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 10 x^{6} - 14 x^{5} + 20 x^{4} - 24 x^{3} + 24 x^{2} - 32 x + 32$	$10$	[0,5]	$-\,2^{10}\cdot 3^{2}\cdot 71\cdot 13219^{2}$	$4$	$25.4577373783$	$5979.67290728923$	✓			$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$1324.58365238$
10.0.114768614675312.1	$x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 11 x^{6} - 13 x^{5} + 22 x^{4} - 28 x^{3} + 32 x^{2} - 32 x + 32$	$10$	[0,5]	$-\,2^{4}\cdot 13^{2}\cdot 983\cdot 6571^{2}$	$4$	$25.467265385$	$18327.117503852045$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[11]$	$2$	$4$	$320.810827568$
10.0.115457271885167.1	$x^{10} - 4 x^{9} + 13 x^{8} - 29 x^{7} + 68 x^{6} - 121 x^{5} + 204 x^{4} - 261 x^{3} + 351 x^{2} - 324 x + 243$	$10$	[0,5]	$-\,26783\cdot 65657^{2}$	$2$	$25.4825056481$	$41934.37052108926$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$88.0509066233$
10.0.116117348402176.1	$x^{10} + 20 x^{8} + 149 x^{6} + 519 x^{4} + 851 x^{2} + 529$	$10$	[0,5]	$-\,2^{10}\cdot 11^{8}\cdot 23^{2}$	$3$	$25.4970368126$	$125.0903140152616$	✓		?	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 8]$	$2$	$4$	$26.1711060094$
10.0.116117348402176.2	$x^{10} + 25 x^{8} + 206 x^{6} + 711 x^{4} + 1035 x^{2} + 529$	$10$	[0,5]	$-\,2^{10}\cdot 11^{8}\cdot 23^{2}$	$3$	$25.4970368126$	$125.0903140152616$	✓		?	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 8]$	$2$	$4$	$26.1711060094$
10.0.117045666703175.1	$x^{10} - x^{9} + 4 x^{8} - 3 x^{7} - 7 x^{6} - x^{5} - 21 x^{4} - 27 x^{3} + 108 x^{2} - 81 x + 243$	$10$	[0,5]	$-\,5^{2}\cdot 7^{2}\cdot 983\cdot 9859^{2}$	$4$	$25.5173478532$	$18417.353094296694$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[11]$	$2$	$4$	$265.790133467$
10.0.117387761757872.1	$x^{10} - x^{9} + 3 x^{8} + 3 x^{7} + 27 x^{6} + 35 x^{5} + 38 x^{4} + 35 x^{3} + 17 x^{2} - 4 x + 24$	$10$	[0,5]	$-\,2^{4}\cdot 947\cdot 88019^{2}$	$3$	$25.5247961413$	$18259.68159634773$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$388.973349189$
10.0.120057286872179.1	$x^{10} - 2 x^{9} + 12 x^{8} - 19 x^{7} + 64 x^{6} - 79 x^{5} + 192 x^{4} - 171 x^{3} + 324 x^{2} - 162 x + 243$	$10$	[0,5]	$-\,193\cdot 467\cdot 36497^{2}$	$3$	$25.5822567004$	$57354.25971102757$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[2, 8]$	$2$	$4$	$56.8105224918$
10.0.120285414532047.1	$x^{10} - 5 x^{9} + 18 x^{8} - 39 x^{7} + 80 x^{6} - 108 x^{5} + 168 x^{4} - 130 x^{3} + 198 x^{2} - 49 x + 109$	$10$	[0,5]	$-\,3\cdot 71\cdot 131\cdot 65657^{2}$	$4$	$25.5871135785$	$42802.18768941607$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$	$2$	$4$	$88.0509066233$
10.0.120320641431296.1	$x^{10} - 2 x^{9} + 9 x^{8} - 16 x^{7} + 44 x^{6} - 64 x^{5} + 132 x^{4} - 144 x^{3} + 243 x^{2} - 162 x + 243$	$10$	[0,5]	$-\,2^{8}\cdot 2399\cdot 13997^{2}$	$3$	$25.5878628264$	$10089.196993883017$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[14]$	$2$	$4$	$247.188837628$
10.0.120560905159375.1	$x^{10} - 2 x^{9} + 7 x^{8} - 13 x^{7} - x^{6} + 67 x^{5} + 54 x^{4} - 55 x^{3} - 340 x^{2} - 276 x + 1424$	$10$	[0,5]	$-\,5^{5}\cdot 131^{5}$	$2$	$25.5929677841$	$25.592967784139454$				$D_{10}$ (as 10T3)	$[12]$	$2$	$4$	$458.38640509$
10.0.123121484415728.1	$x^{10} + 3 x^{8} - x^{7} + 8 x^{6} - 3 x^{5} + 16 x^{4} - 4 x^{3} + 24 x^{2} + 32$	$10$	[0,5]	$-\,2^{4}\cdot 2543\cdot 55009^{2}$	$3$	$25.6468117643$	$18774.86050316302$	✓			$C_2 \wr S_5$ (as 10T39)	$[13]$	$2$	$4$	$259.01066264$
10.0.129517482801911.1	$x^{10} - 2 x^{9} + 7 x^{8} - 13 x^{7} + 32 x^{6} - 59 x^{5} + 96 x^{4} - 117 x^{3} + 189 x^{2} - 162 x + 243$	$10$	[0,5]	$-\,97\cdot 167\cdot 89417^{2}$	$3$	$25.7770277765$	$38058.71756904061$	✓		?	$C_2 \wr S_5$ (as 10T39)	$[12]$	$2$	$4$	$107.86378415$