Number field search results

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

Results (27 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
14.0.104...504.1	$x^{14} - 2 x^{13} + 124 x^{12} - 214 x^{11} + 7557 x^{10} - 10668 x^{9} + 287927 x^{8} - 310308 x^{7} + 7248641 x^{6} - 5536192 x^{5} + 118383398 x^{4} - 58021334 x^{3} + 1144024522 x^{2} - 277132320 x + 4979767381$	$14$	[0,7]	$-\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 29^{12}$	$4$	$164.294733109$	$164.29473310917862$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 68966]$	$2$	$6$	$6020.985100147561$
14.0.177...304.1	$x^{14} + 406 x^{12} + 56840 x^{10} + 3421768 x^{8} + 86896992 x^{6} + 842232384 x^{4} + 2838635072 x^{2} + 3056991616$	$14$	[0,7]	$-\,2^{21}\cdot 7^{7}\cdot 29^{13}$	$3$	$170.621993392$	$170.62199339243452$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 109544]$	$2$	$6$	$6020.985100147561$
14.0.127...331.1	$x^{14} + 378 x^{12} - 847 x^{11} + 43729 x^{10} - 176134 x^{9} + 1941534 x^{8} - 8999703 x^{7} + 40933963 x^{6} - 146975164 x^{5} + 333745951 x^{4} - 521303860 x^{3} + 684084919 x^{2} - 722816269 x + 758859649$	$14$	[0,7]	$-\,7^{25}\cdot 37^{7}$	$2$	$196.428502121$	$196.42850212097045$	✓	✓	?	$C_{14}$ (as 14T1)	$[1044572]$	$2$	$6$	$35256.68973693789$
14.0.196...728.1	$x^{14} + 49 x^{12} - 42 x^{11} + 1988 x^{10} + 560 x^{9} + 59423 x^{8} + 56436 x^{7} + 1275554 x^{6} + 1649242 x^{5} + 18366768 x^{4} + 21707980 x^{3} + 161055601 x^{2} + 135111620 x + 665398601$	$14$	[0,7]	$-\,2^{14}\cdot 7^{24}\cdot 13^{7}$	$3$	$202.647462032$	$202.64746203246128$	✓	✓	?	$C_{14}$ (as 14T1)	$[1217566]$	$2$	$6$	$35256.68973693789$
14.0.219...000.1	$x^{14} + 420 x^{12} + 53900 x^{10} + 2401000 x^{8} + 37730000 x^{6} + 147000000 x^{4} + 196000000 x^{2} + 70000000$	$14$	[0,7]	$-\,2^{21}\cdot 5^{7}\cdot 7^{25}$	$3$	$204.236631295$	$204.23663129490222$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 515342]$	$2$	$6$	$35256.68973693789$
14.0.302...616.1	$x^{14} + 609 x^{12} + 127890 x^{10} + 11548467 x^{8} + 439916022 x^{6} + 6395702166 x^{4} + 32333827617 x^{2} + 52231567689$	$14$	[0,7]	$-\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 29^{13}$	$4$	$208.968411354$	$208.96841135399376$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 4, 4, 4, 8236]$	$2$	$6$	$6020.985100147561$
14.0.117...344.1	$x^{14} - 2 x^{13} + 112 x^{12} - 146 x^{11} + 6693 x^{10} - 9524 x^{9} + 276271 x^{8} - 461308 x^{7} + 7907601 x^{6} - 13385716 x^{5} + 147472662 x^{4} - 207970434 x^{3} + 1594403790 x^{2} - 1379805112 x + 7521613141$	$14$	[0,7]	$-\,2^{14}\cdot 3^{7}\cdot 7^{7}\cdot 43^{12}$	$4$	$230.279597716$	$230.27959771631453$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 21982]$	$2$	$6$	$35991.64185055774$
14.0.128...232.1	$x^{14} + 77 x^{12} - 42 x^{11} + 3836 x^{10} + 392 x^{9} + 135919 x^{8} + 93620 x^{7} + 3408482 x^{6} + 3494218 x^{5} + 57312920 x^{4} + 57285116 x^{3} + 584163825 x^{2} + 412653556 x + 2769616973$	$14$	[0,7]	$-\,2^{14}\cdot 7^{24}\cdot 17^{7}$	$3$	$231.736238619$	$231.73623861878355$	✓	✓	?	$C_{14}$ (as 14T1)	$[1515892]$	$2$	$6$	$35256.68973693789$
14.0.209...051.1	$x^{14} - x^{13} + 358 x^{12} - 366 x^{11} + 40159 x^{10} + 6901 x^{9} + 1703750 x^{8} + 1571901 x^{7} + 39941900 x^{6} + 54051465 x^{5} + 499919527 x^{4} + 560196080 x^{3} + 2982769075 x^{2} + 1543186750 x + 4370228125$	$14$	[0,7]	$-\,3^{7}\cdot 7^{7}\cdot 71^{13}$	$3$	$239.95801291$	$239.95801290996695$	✓	✓		$C_{14}$ (as 14T1)	$[2, 1046982]$	$2$	$6$	$315114.6966253571$
14.0.296...248.1	$x^{14} + 602 x^{12} + 117992 x^{10} + 9321368 x^{8} + 327073824 x^{6} + 4856550720 x^{4} + 22987673408 x^{2} + 4532780672$	$14$	[0,7]	$-\,2^{21}\cdot 7^{7}\cdot 43^{13}$	$3$	$245.972270969$	$245.97227096884077$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 2, 31764]$	$2$	$6$	$35991.64185055774$
14.0.375...000.1	$x^{14} + 630 x^{12} + 121275 x^{10} + 8103375 x^{8} + 191008125 x^{6} + 1116281250 x^{4} + 2232562500 x^{2} + 1196015625$	$14$	[0,7]	$-\,2^{14}\cdot 3^{7}\cdot 5^{7}\cdot 7^{25}$	$4$	$250.137766729$	$250.1377667287264$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 1454686]$	$2$	$6$	$35256.68973693789$
14.0.782...792.1	$x^{14} + 112 x^{12} - 42 x^{11} + 7091 x^{10} + 182 x^{9} + 303989 x^{8} + 151440 x^{7} + 9029657 x^{6} + 7273378 x^{5} + 178583580 x^{4} + 148149106 x^{3} + 2128994980 x^{2} + 1257735836 x + 11696930513$	$14$	[0,7]	$-\,2^{21}\cdot 7^{24}\cdot 11^{7}$	$3$	$263.621503894$	$263.62150389414694$	✓	✓	?	$C_{14}$ (as 14T1)	$[5904502]$	$2$	$6$	$35256.68973693789$
14.0.196...232.1	$x^{14} + 798 x^{12} + 194579 x^{10} + 16468459 x^{8} + 491701133 x^{6} + 3639865530 x^{4} + 9220992676 x^{2} + 6257102173$	$14$	[0,7]	$-\,2^{14}\cdot 7^{25}\cdot 19^{7}$	$3$	$281.520768273$	$281.5207682731608$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 2, 58, 1682]$	$2$	$6$	$35256.68973693789$
14.0.283...176.1	$x^{14} - 2 x^{13} + 39 x^{12} - 114 x^{11} + 2254 x^{10} - 1600 x^{9} + 65883 x^{8} - 46196 x^{7} + 1547230 x^{6} + 479562 x^{5} + 31057338 x^{4} + 34059520 x^{3} + 395200525 x^{2} + 349151250 x + 2163359375$	$14$	[0,7]	$-\,2^{21}\cdot 7^{7}\cdot 71^{12}$	$3$	$288.992707509$	$288.9927075086941$	✓	✓		$C_{14}$ (as 14T1)	$[7568372]$	$2$	$6$	$315114.6966253571$
14.0.119...791.1	$x^{14} - 5 x^{13} - 31 x^{12} + 309 x^{11} + 262 x^{10} - 8842 x^{9} + 67732 x^{8} - 350971 x^{7} + 1534032 x^{6} - 4949688 x^{5} + 19407809 x^{4} - 39113311 x^{3} + 126961596 x^{2} - 125321277 x + 300251687$	$14$	[0,7]	$-\,31^{7}\cdot 113^{12}$	$2$	$320.2302614292546$	$320.2302614292546$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 381066]$	$2$	$6$	$222748.97284811488$
14.0.251...391.1	$x^{14} - x^{13} + 23 x^{12} - 277 x^{11} - 5095 x^{10} + 31737 x^{9} + 490605 x^{8} - 1444591 x^{7} - 15658566 x^{6} + 26925836 x^{5} + 243943976 x^{4} - 414082048 x^{3} - 2583896960 x^{2} + 4799748096 x + 20455038976$	$14$	[0,7]	$-\,631^{13}$	$1$	$398.132161891$	$398.1321618914127$	✓	✓		$C_{14}$ (as 14T1)	$[3108937]$	$2$	$6$	$10178543858.108408$
14.0.560...663.1	$x^{14} - x^{13} + 432 x^{12} + 1683 x^{11} + 40299 x^{10} + 237027 x^{9} + 1186487 x^{8} + 10192584 x^{7} + 54209527 x^{6} + 22914955 x^{5} + 1968955430 x^{4} - 2618032473 x^{3} + 23452437113 x^{2} - 13674940874 x + 80838037483$	$14$	[0,7]	$-\,7^{7}\cdot 281^{13}$	$2$	$496.990109066$	$496.99010906616695$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 4, 4, 4, 4068]$	$2$	$6$	$12176100.831221418$
14.0.595...271.1	$x^{14} - x^{13} + 518 x^{12} - 1833 x^{11} + 102790 x^{10} - 520762 x^{9} + 8805688 x^{8} - 50472370 x^{7} + 317860920 x^{6} - 1273665671 x^{5} + 11573214816 x^{4} + 37382582628 x^{3} + 232439703661 x^{2} + 365724334139 x + 757415595679$	$14$	[0,7]	$-\,7^{7}\cdot 337^{13}$	$2$	$588.347521086$	$588.3475210861611$	✓	✓	?	$C_{14}$ (as 14T1)	$[2985668]$	$2$	$6$	$5486180.267403393$
14.0.137...523.2	$x^{14} - 2233 x^{11} - 1218 x^{10} - 249690 x^{9} + 5972260 x^{8} - 9384864 x^{7} - 13421345 x^{6} + 139144320 x^{5} + 959190225 x^{4} + 11388585418 x^{3} + 64346564856 x^{2} + 136319294454 x + 97550940167$	$14$	[0,7]	$-\,7^{25}\cdot 29^{13}$	$2$	$736.282775776$	$736.2827757757676$	✓	✓	?	$C_{14}$ (as 14T1)	$[2, 2, 2, 156044]$	$2$	$6$	$93363968.92853843$
14.0.137...523.4	$x^{14} - 2233 x^{11} + 15834 x^{10} + 276080 x^{9} + 6725390 x^{8} + 45617783 x^{7} + 410450166 x^{6} + 1371017746 x^{5} + 8530487112 x^{4} - 10631790456 x^{3} + 88403705502 x^{2} - 488778538759 x + 525016637623$	$14$	[0,7]	$-\,7^{25}\cdot 29^{13}$	$2$	$736.282775776$	$736.2827757757676$	✓	✓	?	$C_{14}$ (as 14T1)	$[1383004]$	$2$	$6$	$59811086.44175506$
14.0.137...523.6	$x^{14} - 2233 x^{11} + 24360 x^{10} + 125454 x^{9} + 1069810 x^{8} - 18378373 x^{7} - 133193172 x^{6} + 756770602 x^{5} + 5834381182 x^{4} - 26703542026 x^{3} + 188327791736 x^{2} - 2109103641127 x + 5899794618083$	$14$	[0,7]	$-\,7^{25}\cdot 29^{13}$	$2$	$736.282775776$	$736.2827757757676$	✓	✓	?	$C_{14}$ (as 14T1)	$[13, 163436]$	$2$	$6$	$78882035.29112078$
14.0.535...607.1	$x^{14} - 7224 x^{11} + 301 x^{10} - 68026 x^{9} + 13842689 x^{8} + 7961708 x^{7} + 210375522 x^{6} + 2524506264 x^{5} - 3402184037 x^{4} + 94982321987 x^{3} + 2062378028046 x^{2} - 2009656697825 x + 657479876713$	$14$	[0,7]	$-\,7^{25}\cdot 43^{12}$	$2$	$811.370964217$	$811.370964216572$	✓	✓		$C_{14}$ (as 14T1)	$[2, 14, 42742]$	$2$	$6$	$769768169.7365845$
14.0.535...607.2	$x^{14} - 7224 x^{11} + 25585 x^{10} + 176386 x^{9} + 16307879 x^{8} - 95951318 x^{7} - 935002320 x^{6} + 1542753828 x^{5} + 7724343571 x^{4} + 49362000457 x^{3} + 1628162950638 x^{2} - 164577661339 x + 16680217258567$	$14$	[0,7]	$-\,7^{25}\cdot 43^{12}$	$2$	$811.370964217$	$811.370964216572$	✓	✓	?	$C_{14}$ (as 14T1)	$[7, 172781]$	$2$	$6$	$301031344.50909585$
14.0.329...443.2	$x^{14} - 5719 x^{11} - 24080 x^{10} + 1193766 x^{9} + 24550764 x^{8} + 307265874 x^{7} + 2773555771 x^{6} + 18547361140 x^{5} + 94817302349 x^{4} + 366737247170 x^{3} + 1042967916088 x^{2} + 2126473677202 x + 2771555675837$	$14$	[0,7]	$-\,7^{24}\cdot 43^{13}$	$2$	$923.701469408$	$923.7014694075532$	✓	✓		$C_{14}$ (as 14T1)	$[2756257]$	$2$	$6$	$534504501.8334233$
14.0.329...443.3	$x^{14} - 1505 x^{11} + 39130 x^{10} + 131838 x^{9} + 6674976 x^{8} + 4397266 x^{7} - 85626373 x^{6} - 2202387502 x^{5} + 75633303333 x^{4} + 1283975888426 x^{3} + 5366060727678 x^{2} + 406889558152 x + 11968080874901$	$14$	[0,7]	$-\,7^{24}\cdot 43^{13}$	$2$	$923.701469408$	$923.7014694075532$	✓	✓	?	$C_{14}$ (as 14T1)	$[3112193]$	$2$	$6$	$301031344.50909585$
14.0.329...443.5	$x^{14} - 5719 x^{11} + 26488 x^{10} + 1147412 x^{9} + 383474 x^{8} - 156246735 x^{7} - 336846090 x^{6} + 13714379322 x^{5} + 49838686632 x^{4} - 498852081686 x^{3} - 2342604234320 x^{2} + 5856771467617 x + 38059805953523$	$14$	[0,7]	$-\,7^{24}\cdot 43^{13}$	$2$	$923.701469408$	$923.7014694075532$	✓	✓	?	$C_{14}$ (as 14T1)	$[1662773]$	$2$	$6$	$224277011.0596314$
14.0.329...443.6	$x^{14} - 1505 x^{11} + 64414 x^{10} + 721798 x^{9} + 13901986 x^{8} + 93883663 x^{7} + 1745978192 x^{6} + 12020663158 x^{5} + 128672845938 x^{4} + 540194248076 x^{3} + 4793924304218 x^{2} + 6892330333119 x + 65986926254491$	$14$	[0,7]	$-\,7^{24}\cdot 43^{13}$	$2$	$923.701469408$	$923.7014694075532$	✓	✓		$C_{14}$ (as 14T1)	$[2, 2, 1921402]$	$2$	$6$	$769768169.7365845$