Number field search results

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

Results (24 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
16.0.683...328.1	$x^{16} + 4199 x^{14} + 5886131 x^{12} + 3978693634 x^{10} + 1482245714409 x^{8} + 318824584999742 x^{6} + 39051900730883446 x^{4} + 2486877913489246478 x^{2} + 61946512496156595137$	$16$	[0,8]	$2^{16}\cdot 17^{15}\cdot 43691^{4}$	$3$	$411.788160333$	$10012.541950101795$	✓		?	$C_2^5.C_8$ (as 16T591)	$[2, 2, 2, 2, 2, 1058994498]$	$2$	$7$	$3640.01221338$
16.0.683...328.2	$x^{16} + 4063 x^{14} + 6007715 x^{12} + 4216341258 x^{10} + 1588534344529 x^{8} + 337055877573450 x^{6} + 40036280260158564 x^{4} + 2475535254818828022 x^{2} + 61946512496156595137$	$16$	[0,8]	$2^{16}\cdot 17^{15}\cdot 43691^{4}$	$3$	$411.788160333$	$10012.541950101795$	✓		?	$C_2^5.C_8$ (as 16T591)	$[2, 2, 2, 2, 2, 1068746342]$	$2$	$7$	$3640.01221338$
16.0.186...936.1	$x^{16} + 3192 x^{14} - 3680 x^{13} + 3820332 x^{12} - 8222112 x^{11} + 2278069768 x^{10} - 6381521824 x^{9} + 749980009966 x^{8} - 2278581253952 x^{7} + 140107567212424 x^{6} - 406917584361472 x^{5} + 14342083431686636 x^{4} - 34925731551753120 x^{3} + 706802171767051960 x^{2} - 1124404063609193536 x + 11373046199801545201$	$16$	[0,8]	$2^{62}\cdot 7^{6}\cdot 193^{4}\cdot 223^{4}$	$4$	$438.397976799$	$13679.185028047033$	✓		?	$C_4^2.(C_2^2\times C_4)$ (as 16T471)	$[2, 2, 2, 2, 2, 2, 2, 2, 75774660]$	$2$	$7$	$20726.065235$
16.0.846...000.1	$x^{16} + 3366 x^{14} + 4288256 x^{12} + 2643188394 x^{10} + 843697669633 x^{8} + 140021879295672 x^{6} + 11844611939032629 x^{4} + 481407719903051007 x^{2} + 7448383238882771641$	$16$	[0,8]	$2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 89^{8}\cdot 109^{4}$	$5$	$481.909929555$	$23910.257213402874$	✓		?	$C_4^2.(C_2\times D_4)$ (as 16T493)	$[2, 2, 2, 2, 2, 2, 2, 252870404]$	$2$	$7$	$13345.9350553$
16.0.297...976.1	$x^{16} + 3464 x^{14} - 3216 x^{13} + 4898708 x^{12} - 7958096 x^{11} + 3643957168 x^{10} - 7631842416 x^{9} + 1528170097824 x^{8} - 3619337419376 x^{7} + 358605823359368 x^{6} - 892387439161696 x^{5} + 43925474650991112 x^{4} - 109475242669266480 x^{3} + 2467664760780016224 x^{2} - 5494406389961891840 x + 55151228745540959074$	$16$	[0,8]	$2^{66}\cdot 7^{6}\cdot 193^{4}\cdot 223^{4}$	$4$	$521.345993212$	$16267.384162792228$	✓		?	$C_4^2.(C_2^2\times C_4)$ (as 16T471)	$[2, 2, 2, 2, 2, 2, 2, 6, 106594380]$	$2$	$7$	$20726.065235$
16.0.468...664.1	$x^{16} + 1712 x^{14} + 1233350 x^{12} + 488006872 x^{10} + 115758148212 x^{8} + 16792514721616 x^{6} + 1446242915789840 x^{4} + 67056318133293792 x^{2} + 1270028532190841476$	$16$	[0,8]	$2^{48}\cdot 23^{6}\cdot 37^{4}\cdot 24499031^{2}$	$4$	$536.329851444$		✓		?	$C_2^4.C_2^5:S_4$ (as 16T1765)	$[2, 2, 2, 2723433000]$	$2$	$7$	$109226.925145$
16.0.964...184.1	$x^{16} + 1028 x^{14} + 255458 x^{12} + 23931840 x^{10} + 862829184 x^{8} + 12850493440 x^{6} + 71556958208 x^{4} + 147171966976 x^{2} + 69257396224$	$16$	[0,8]	$2^{44}\cdot 257^{14}$	$2$	$864.020349184$	$864.0203491841434$	✓	✓		$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 4, 4, 40, 687480]$	$2$	$7$	$112709711.05474126$
16.0.288...376.2	$x^{16} + 3092 x^{14} + 3763147 x^{12} + 2296419422 x^{10} + 744702238048 x^{8} + 127016546026864 x^{6} + 10768253589679158 x^{4} + 388439643284578428 x^{2} + 3207580110181323556$	$16$	[0,8]	$2^{46}\cdot 239^{4}\cdot 257^{10}$	$3$	$925.270923735$	$18080.560927787934$	✓		?	$C_4^2:C_2.C_4^2$ (as 16T875)	$[2, 2, 2, 2, 2, 2, 6, 149148972]$	$2$	$7$	$9996199.50284$
16.0.154...944.1	$x^{16} + 98688 x^{12} + 30716640 x^{10} + 2073969697 x^{8} + 2840635392 x^{6} + 164025558208 x^{4} - 2243290349568 x^{2} + 5648874013696$	$16$	[0,8]	$2^{48}\cdot 257^{14}$	$2$	$1027.49914676$	$1027.499146756919$	✓	✓	?	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 8, 24, 24, 32352]$	$2$	$7$	$56884691.566921$
16.0.154...944.3	$x^{16} + 123360 x^{12} + 3810894945 x^{8} - 521459496960 x^{4} + 17868678762496$	$16$	[0,8]	$2^{48}\cdot 257^{14}$	$2$	$1027.49914676$	$1027.499146756919$	✓	✓	?	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 4, 8, 16, 80880]$	$4$	$7$	$638360561.5229604$
16.0.905...248.1	$x^{16} + 3264 x^{14} + 3316496 x^{12} + 1304953472 x^{10} + 221639065992 x^{8} + 16702070265472 x^{6} + 490448945740944 x^{4} + 3874220981492640 x^{2} + 5934553794724178$	$16$	[0,8]	$2^{79}\cdot 23^{4}\cdot 31^{8}\cdot 89^{4}$	$4$	$1147.61419425$	$8061.015320665258$	✓		?	$D_8:D_4$ (as 16T385)	$[2, 2, 2, 4, 4, 20, 34192480]$	$2$	$7$	$30445425.2472$
16.0.905...248.2	$x^{16} + 3264 x^{14} + 4140208 x^{12} + 2581228928 x^{10} + 836309669640 x^{8} + 142366611859328 x^{6} + 12437574187407824 x^{4} + 512785191909377632 x^{2} + 7658348535725451218$	$16$	[0,8]	$2^{79}\cdot 23^{4}\cdot 31^{8}\cdot 89^{4}$	$4$	$1147.61419425$	$8061.015320665258$	✓		?	$D_8:D_4$ (as 16T385)	$[2, 2, 2, 2, 2, 4, 20, 34192480]$	$2$	$7$	$30445425.2472$
16.0.495...864.1	$x^{16} + 1928 x^{14} + 1288880 x^{12} + 405962108 x^{10} + 65834061236 x^{8} + 5383868719400 x^{6} + 189111188166776 x^{4} + 1503056414236448 x^{2} + 15977927617600$	$16$	[0,8]	$2^{36}\cdot 7687^{10}$	$2$	$1276.19059848$		✓			$(C_2\times C_4^3):\SL(2,3)$ (as 16T1543)	$[2, 2, 2, 2, 2, 4, 104987608]$	$2$	$7$	$381035207.312$
16.0.495...864.2	$x^{16} + 1500 x^{14} + 889640 x^{12} + 264096308 x^{10} + 40486683676 x^{8} + 2897987746232 x^{6} + 67780112968120 x^{4} + 460191898925712 x^{2} + 781198698804624$	$16$	[0,8]	$2^{36}\cdot 7687^{10}$	$2$	$1276.19059848$		✓			$(C_2\times C_4^3):\SL(2,3)$ (as 16T1543)	$[2, 2, 2, 2, 2, 4, 161966728]$	$2$	$7$	$381035207.312$
16.0.247...809.2	$x^{16} - x^{15} + 369 x^{14} - 7127 x^{13} - 24628 x^{12} - 3860358 x^{11} + 3847802 x^{10} - 31586510 x^{9} + 11790894313 x^{8} + 150438196003 x^{7} + 3045583313341 x^{6} + 28963391474261 x^{5} + 215319701431098 x^{4} + 1030855819624916 x^{3} + 5228711472095080 x^{2} + 2899855979953376 x + 99902637257197312$	$16$	[0,8]	$41^{14}\cdot 97^{14}$	$2$	$1411.2733551$	$1411.2733551005474$	✓	✓		$C_8\times C_2$ (as 16T5)	$[21, 4338913908]$	$2$	$7$	$1085553540910$
16.0.649...544.1	$x^{16} + 1501 x^{14} + 911285 x^{12} + 286021943 x^{10} + 49105808800 x^{8} + 4480851471638 x^{6} + 197363433219140 x^{4} + 3937312460664784 x^{2} + 28613530403758336$	$16$	[0,8]	$2^{28}\cdot 193^{8}\cdot 257^{10}$	$3$	$1498.95760197$	$9251.341920895136$	✓			$C_2^5.(C_2\times D_4)$ (as 16T813)	$[2, 2, 2, 2, 2, 4, 24, 8126040]$	$2$	$7$	$22245061053.3$
16.0.649...544.2	$x^{16} + 1244 x^{14} + 606551 x^{12} + 147646866 x^{10} + 18976436546 x^{8} + 1264961735700 x^{6} + 40283145849176 x^{4} + 511323407119984 x^{2} + 1009289184953344$	$16$	[0,8]	$2^{28}\cdot 193^{8}\cdot 257^{10}$	$3$	$1498.9576019681122$	$9251.341920895136$	✓			$C_2^5.(C_2\times D_4)$ (as 16T813)	$[2, 2, 2, 2, 2, 4, 4, 55415544]$	$2$	$7$	$22245061053.26185$
16.0.791...881.3	$x^{16} - 5 x^{15} + 536 x^{14} - 14970 x^{13} + 504403 x^{12} - 11045491 x^{11} + 220735521 x^{10} - 3445251317 x^{9} + 47662575288 x^{8} - 533426130836 x^{7} + 5232393557019 x^{6} - 40295189035117 x^{5} + 281733439507432 x^{4} - 1457129277599064 x^{3} + 7383199674276536 x^{2} - 21116314559719616 x + 31975694368889344$	$16$	[0,8]	$29^{14}\cdot 149^{14}$	$2$	$1517.52632279$	$1517.5263227935982$	✓			$\OD_{16}:C_2$ (as 16T41)	$[2, 24222, 242220]$	$2$	$7$	$88555507897.6$
16.0.791...881.4	$x^{16} - 3 x^{15} + 573 x^{14} + 9272 x^{13} + 337161 x^{12} + 6299195 x^{11} + 87537415 x^{10} + 1429221904 x^{9} + 16277482567 x^{8} + 215209853765 x^{7} + 2402287099291 x^{6} + 20641758474146 x^{5} + 168575519317340 x^{4} + 882336067964976 x^{3} + 4598319446544384 x^{2} + 12600832442989824 x + 49455952218418176$	$16$	[0,8]	$29^{14}\cdot 149^{14}$	$2$	$1517.52632279$	$1517.5263227935982$	✓			$\OD_{16}:C_2$ (as 16T41)	$[2, 24222, 242220]$	$2$	$7$	$27354159575.0$
16.0.791...881.5	$x^{16} - 5 x^{15} + 404 x^{14} - 7911 x^{13} + 85309 x^{12} - 1712558 x^{11} + 42103059 x^{10} - 763954787 x^{9} + 20065856528 x^{8} - 378903900861 x^{7} + 3069805875379 x^{6} - 16152690635942 x^{5} + 158678336760608 x^{4} - 1395404638505784 x^{3} + 4213301148768960 x^{2} + 9966977583135840 x + 414401005855515456$	$16$	[0,8]	$29^{14}\cdot 149^{14}$	$2$	$1517.52632279$	$1517.5263227935982$	✓			$\OD_{16}:C_2$ (as 16T36)	$[2, 24222, 242220]$	$2$	$7$	$6427573726.31$
16.0.259...176.1	$x^{16} + 1413 x^{14} + 640747 x^{12} + 122467295 x^{10} + 9850573750 x^{8} + 279518044450 x^{6} + 1590760453744 x^{4} + 708784500408 x^{2} + 1082146816$	$16$	[0,8]	$2^{30}\cdot 193^{8}\cdot 257^{10}$	$3$	$1634.62485588$	$9251.341920895136$	✓			$C_2^5.(C_2\times D_4)$ (as 16T813)	$[2, 2, 2, 2, 2, 4, 12, 32390040]$	$2$	$7$	$22245061053.3$
16.0.240...473.2	$x^{16} - x^{15} + 246 x^{14} - 5528 x^{13} - 102364 x^{12} + 2534658 x^{11} + 43785164 x^{10} - 994326206 x^{9} + 13045857327 x^{8} - 278639592799 x^{7} + 5130957769597 x^{6} - 53334252425244 x^{5} + 347355235431558 x^{4} - 1527640572701475 x^{3} + 4651932548849904 x^{2} - 9598577056412940 x + 13133394052911819$	$16$	[0,8]	$41^{14}\cdot 97^{15}$	$2$	$1878.38397934$	$1878.3839793438897$	✓	✓		$C_{16}$ (as 16T1)	$[13002309512]$	$2$	$7$	$1824756124090$
16.0.193...601.5	$x^{16} - x^{15} + 594 x^{14} + 2531 x^{13} + 47690 x^{12} - 5352141 x^{11} + 51739983 x^{10} + 192556636 x^{9} + 5083665532 x^{8} + 450226956190 x^{7} + 941787543275 x^{6} - 77428720044109 x^{5} - 764954674399913 x^{4} - 18683145716368537 x^{3} - 73879184588145834 x^{2} + 2427071999215910603 x + 33380320760954558557$	$16$	[0,8]	$37^{14}\cdot 173^{14}$	$2$	$2140.26154695$	$2140.2615469509783$	✓		?	$C_8.C_4$ (as 16T49)	$[6, 6, 1682050764]$	$2$	$7$	$1189759845.59$
16.0.366...169.4	$x^{16} - 7 x^{15} + 757 x^{14} + 17359 x^{13} + 505614 x^{12} + 12895156 x^{11} + 211899620 x^{10} + 7541456698 x^{9} - 1389972933 x^{8} + 1240781089975 x^{7} + 4371887866584 x^{6} - 55659562317467 x^{5} + 4297633387795179 x^{4} - 111896064809531971 x^{3} + 2220052595158974387 x^{2} - 20096776454760585706 x + 78442230270956678147$	$16$	[0,8]	$53^{14}\cdot 149^{14}$	$2$	$2572.04978592$	$2572.0497859216343$	✓			$C_8.C_4$ (as 16T49)	$[3, 6, 630, 1533420]$	$2$	$7$	$227392032558$
16.0.546...609.1	$x^{16} - 6 x^{15} + 3581 x^{14} + 35728 x^{13} + 3184374 x^{12} - 7157146 x^{11} + 1115337704 x^{10} - 3559324740 x^{9} - 413101870103 x^{8} - 19670422590640 x^{7} + 1180694075592 x^{6} + 4494586179489760 x^{5} + 79009337564951184 x^{4} - 636825223635723648 x^{3} - 12244752595015384320 x^{2} - 2796479624717236224 x + 944525217449845297152$	$16$	[0,8]	$61^{14}\cdot 157^{14}$	$2$	$3044.91940201$	$3044.919402009884$	✓	✓		$C_8: C_2$ (as 16T6)	$[168545, 337090]$	$2$	$7$	$10081352048400$