Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 98)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.26706316588122320300180823322240000000000.1	x^16 + 1755x^14 + 1239334x^12 + 451082130x^10 + 89914939054x^8 + 9630554199795x^6 + 507257210716170x^4 + 10352297616322800x^2 + 23508342503733025	\( 2^{16}\cdot 5^{10}\cdot 29^{6}\cdot 89^{6}\cdot 109^{4} \)	16T790	$[2, 2, 2, 2, 2, 2, 6, 4723818]$ (GRH)
16.0.40198805069552937123844028608838939705344.1	x^16 + 1320x^14 + 695390x^12 + 188299712x^10 + 28176729004x^8 + 2334616894288x^6 + 100031244818584x^4 + 1742607190434464x^2 + 1089218734982596	\( 2^{48}\cdot 23^{4}\cdot 37^{4}\cdot 601^{2}\cdot 27457^{2} \)	16T1765	$[2, 2, 2, 135809000]$ (GRH)
16.0.120380606746796557474451161088000000000000.1	x^16 + 1040x^14 + 439400x^12 + 96668000x^10 + 11781412500x^8 + 779715300000x^6 + 25340747250000x^4 + 313742585000000x^2 + 979896528601250	\( 2^{79}\cdot 5^{12}\cdot 13^{8} \)	$C_{16}$ (as 16T1)	$[2, 505217732]$ (GRH)
16.0.199875058073008840373089541044249600000000.1	x^16 + 1736x^14 + 1211156x^12 + 430086456x^10 + 80387048099x^8 + 7216691979704x^6 + 230917087201933x^4 + 2822816545662095x^2 + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	$[2, 2, 2, 2, 2, 4, 23100260]$ (GRH)
16.0.199875058073008840373089541044249600000000.2	x^16 + 2000x^14 + 1449212x^12 + 493166662x^10 + 82609767019x^8 + 6431469174712x^6 + 205796436670039x^4 + 2611054203786213x^2 + 10285190654933041	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 139^{4}\cdot 181^{6} \)	16T868	$[2, 2, 2, 2, 2, 4, 25540748]$ (GRH)
16.0.215429589500286246610837301474983006961664.1	x^16 + 1304x^14 + 640710x^12 + 151171992x^10 + 18566685258x^8 + 1210767195416x^6 + 40931675101154x^4 + 666358713185624x^2 + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1189	$[2, 2, 2, 2, 2, 59292150]$ (GRH)
16.0.215429589500286246610837301474983006961664.2	x^16 + 1152x^14 + 541202x^12 + 135417804x^10 + 19597384553x^8 + 1649812386780x^6 + 75627238239712x^4 + 1521286853137908x^2 + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1189	$[2, 2, 2, 2, 2, 54061310]$ (GRH)
16.0.215429589500286246610837301474983006961664.3	x^16 + 1336x^14 + 723214x^12 + 202880976x^10 + 31228142425x^8 + 2556746204384x^6 + 97478917371936x^4 + 1157359870269768x^2 + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2, 2, 2, 2, 2, 67083750]$ (GRH)
16.0.215429589500286246610837301474983006961664.4	x^16 + 1816x^14 + 1120320x^12 + 323759520x^10 + 48091401945x^8 + 3668323194472x^6 + 133470657752078x^4 + 1858790094675688x^2 + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2, 2, 2, 2, 2, 73397938]$ (GRH)
16.0.682709662540737066595680412797349253873664.3	x^16 + 984x^14 + 338004x^12 + 50107248x^10 + 3459851010x^8 + 116832673728x^6 + 1884328811136x^4 + 12656515700736x^2 + 18984773551104	\( 2^{62}\cdot 3^{8}\cdot 41^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 77529736]$ (GRH)
16.0.1398629213800614161925350535491003636252672.1	x^16 + 1896x^14 + 1461230x^12 + 583460828x^10 + 126773588461x^8 + 14260732371956x^6 + 701771263583088x^4 + 11324769311543544x^2 + 29761106423144258	\( 2^{59}\cdot 113^{6}\cdot 1039^{4} \)	16T942	$[2, 2, 2, 2, 2, 181019886]$ (GRH)
16.0.1398629213800614161925350535491003636252672.2	x^16 + 2176x^14 + 1724014x^12 + 647707484x^10 + 123893802653x^8 + 12126531066564x^6 + 572663557369552x^4 + 10597769616281952x^2 + 29761106423144258	\( 2^{59}\cdot 113^{6}\cdot 1039^{4} \)	16T942	$[2, 2, 2, 2, 2, 189604294]$ (GRH)
16.0.3820736401648967194220515025487549637328896.22	x^16 + 168x^14 + 15552x^12 + 696016x^10 + 6123000x^8 - 149969952x^6 + 25613941120x^4 + 131763169728x^2 + 1310484615696	\( 2^{48}\cdot 13^{12}\cdot 17^{12} \)	$C_4^2$ (as 16T4)	$[2, 4, 8, 104, 104, 3016]$ (GRH)
16.0.9682510354914354784154938551289076131037184.1	x^16 - x^15 + 1333x^14 + 1304x^13 + 646954x^12 + 1514696x^11 + 144386740x^10 + 375878024x^9 + 16054876969x^8 + 33103102647x^7 + 891724768485x^6 + 1485492313944x^5 + 25049349509778x^4 + 37916090753304x^3 + 358906331026404x^2 + 405991720954560x + 2940120561720576	\( 2^{28}\cdot 3^{14}\cdot 11^{14}\cdot 2111^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T493)	$[2, 2, 2, 2, 2, 2, 2, 51068982]$ (GRH)
16.0.11400342036779277121730973270016000000000000.25	x^16 + 1220x^14 + 508130x^12 + 98978600x^10 + 10034792800x^8 + 543392514000x^6 + 15315089013000x^4 + 201872361780000x^2 + 908425628010000	\( 2^{44}\cdot 5^{12}\cdot 61^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 74, 1856290]$ (GRH)
16.0.44272035895977179125717718174809351883063296.1	x^16 + 1776x^14 + 1082972x^12 + 294264512x^10 + 40150581314x^8 + 2864580268288x^6 + 103065013482464x^4 + 1588496435904000x^2 + 5543020491743296	\( 2^{62}\cdot 127^{4}\cdot 577^{6} \)	$C_4:Q_8.C_2^3$ (as 16T520)	$[2, 2, 2, 2, 2, 4, 43619632]$ (GRH)
16.0.44272035895977179125717718174809351883063296.2	x^16 + 2288x^14 + 1816476x^12 + 641999728x^10 + 101963947458x^8 + 6294328954624x^6 + 168134672246112x^4 + 1833276172408064x^2 + 5543020491743296	\( 2^{62}\cdot 127^{4}\cdot 577^{6} \)	$C_4:Q_8.C_2^3$ (as 16T520)	$[2, 2, 2, 2, 2, 4, 27716476]$ (GRH)
16.0.69012051254784469945608052647868865324253184.6	x^16 + 884x^14 + 283322x^12 + 42405480x^10 + 3291492672x^8 + 134351822800x^6 + 2669893265000x^4 + 20635322500000x^2 + 51588306250000	\( 2^{44}\cdot 13^{12}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 4, 9512072]$ (GRH)
16.0.76098811128269790757290873194547302704873472.4	x^16 + 952x^14 + 323204x^12 + 51499392x^10 + 4085046994x^8 + 152944237824x^6 + 2124099047056x^4 + 2592170770112x^2 + 1568025872	\( 2^{62}\cdot 7^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 306101384]$ (GRH)
16.0.80661021875089306767964564881408000000000000.4	x^16 + 1020x^14 + 387090x^12 + 69859800x^10 + 6441606000x^8 + 316195002000x^6 + 8264854521000x^4 + 107755895700000x^2 + 548093933370000	\( 2^{44}\cdot 3^{8}\cdot 5^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 4, 74855876]$ (GRH)
16.0.162904790364716142536846429126656000000000000.2	x^16 + 820x^14 + 192290x^12 + 19384800x^10 + 899179200x^8 + 17643776000x^6 + 133834496000x^4 + 240988160000x^2 + 68853760000	\( 2^{44}\cdot 5^{12}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 6, 6, 6, 6, 12, 39576]$ (GRH)
16.0.182405472588468433947695572320256000000000000.20	x^16 + 976x^14 + 346724x^12 + 55785232x^10 + 4316728379x^8 + 153444603544x^6 + 2044575845776x^4 + 8014083537528x^2 + 202716958081	\( 2^{48}\cdot 5^{12}\cdot 61^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 20, 16642600]$ (GRH)
16.0.182405472588468433947695572320256000000000000.27	x^16 - 164x^14 + 15082x^12 - 777952x^10 + 27658415x^8 - 630293848x^6 + 15664045662x^4 - 152109439596x^2 + 2386255652001	\( 2^{48}\cdot 5^{12}\cdot 61^{12} \)	$C_4^2$ (as 16T4)	$[2, 2, 520, 3328520]$ (GRH)
16.0.182405472588468433947695572320256000000000000.28	x^16 + 976x^14 + 379664x^12 + 74539072x^10 + 7707154739x^8 + 400872052024x^6 + 9436607057716x^4 + 76635733034448x^2 + 156220976347921	\( 2^{48}\cdot 5^{12}\cdot 61^{12} \)	$C_4^2$ (as 16T4)	$[2, 20, 20, 1394900]$ (GRH)
16.0.189576579237593007104201322397696000000000000.5	x^16 + 680x^14 + 176460x^12 + 22344800x^10 + 1494203950x^8 + 52810704000x^6 + 911335779000x^4 + 5995981260000x^2 + 383966122500	\( 2^{62}\cdot 5^{12}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 34, 34, 1038088]$ (GRH)
16.0.201607431658701025979129418461200790453223424.1	x^16 + 1096x^14 + 388532x^12 + 49550160x^10 + 1983245154x^8 + 33736151360x^6 + 254419951232x^4 + 721459939328x^2 + 360729969664	\( 2^{62}\cdot 137^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 6, 139032408]$ (GRH)
16.0.225387523315734662028879718967317456742252544.6	x^16 + 584x^14 + 126144x^12 + 12925088x^10 + 701820613x^8 + 20830421520x^6 + 325634279004x^4 + 2354400118368x^2 + 5650252604676	\( 2^{48}\cdot 3^{8}\cdot 73^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 34, 68, 9928]$ (GRH)
16.0.225387523315734662028879718967317456742252544.8	x^16 + 584x^14 + 139284x^12 + 17392688x^10 + 1211607937x^8 + 46480731696x^6 + 912726990288x^4 + 7803495656064x^2 + 18734319395856	\( 2^{48}\cdot 3^{8}\cdot 73^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 2, 4, 2313224]$ (GRH)
16.0.257142839682757276401140868988052161101602113.1	x^16 - x^15 + 1604x^14 - 4849x^13 + 851534x^12 - 3460136x^11 + 220867782x^10 - 1005651829x^9 + 31950552532x^8 - 149369605348x^7 + 2679277607936x^6 - 11993916195144x^5 + 125839435016506x^4 - 486125527533824x^3 + 2817137139500788x^2 - 7283791516402294x + 16052774378388739	\( 67^{8}\cdot 97^{15} \)	$C_{16}$ (as 16T1)	$[1073881378]$ (GRH)
16.0.398360031450580799831535291203584000000000000.1	x^16 + 1160x^14 + 545780x^12 + 133550800x^10 + 18086924450x^8 + 1329298056000x^6 + 47949554448000x^4 + 659978046720000x^2 + 2969901210240000	\( 2^{62}\cdot 5^{12}\cdot 29^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 18, 107858376]$ (GRH)
16.0.398360031450580799831535291203584000000000000.2	x^16 + 1160x^14 + 521420x^12 + 117067200x^10 + 14357509950x^8 + 984437596000x^6 + 36868436687000x^4 + 689584829380000x^2 + 4996517664602500	\( 2^{62}\cdot 5^{12}\cdot 29^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 4, 175413508]$ (GRH)
16.0.398360031450580799831535291203584000000000000.3	x^16 + 1160x^14 + 437900x^12 + 60552000x^10 + 2057380350x^8 + 25657228000x^6 + 114018575000x^4 + 70728100000x^2 + 1768202500	\( 2^{62}\cdot 5^{12}\cdot 29^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 4, 774298372]$ (GRH)
16.0.398360031450580799831535291203584000000000000.4	x^16 + 1160x^14 + 521420x^12 + 117067200x^10 + 13863001950x^8 + 820543516000x^6 + 19044955487000x^4 + 410222980000x^2 + 1768202500	\( 2^{62}\cdot 5^{12}\cdot 29^{12} \)	$C_8\times C_2$ (as 16T5)	$[2, 36, 24789924]$ (GRH)
16.0.408924191550659033534214062789206959759730273.1	x^16 - x^15 + 1701x^14 - 5140x^13 + 957458x^12 - 3890525x^11 + 263030578x^10 - 1198723539x^9 + 40240148282x^8 - 188524940501x^7 + 3561203748047x^6 - 16001130613788x^5 + 176031116223380x^4 - 684237862730000x^3 + 4135020510780571x^2 - 10799903260538834x + 24670268999409811	\( 71^{8}\cdot 97^{15} \)	$C_{16}$ (as 16T1)	$[1546273474]$ (GRH)
16.0.552198156105754424298997471653759249446600704.1	x^16 + 1192x^14 + 533420x^12 + 115089984x^10 + 12963208302x^8 + 759505090400x^6 + 21418969775000x^4 + 246442200500000x^2 + 770131876562500	\( 2^{62}\cdot 149^{12} \)	$C_8\times C_2$ (as 16T5)	$[13, 146914690]$ (GRH)
16.0.667766448639661081824497937039393690193231872.4	x^16 + 816x^14 + 270504x^12 + 46693152x^10 + 4468073076x^8 + 233097458400x^6 + 6070515141456x^4 + 63887310947520x^2 + 211215000911202	\( 2^{79}\cdot 3^{8}\cdot 17^{14} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 190068616]$ (GRH)
16.0.1147634942730979008947338773912344095761629184.1	x^16 + 984x^14 + 373428x^12 + 70440624x^10 + 7238830194x^8 + 414992585088x^6 + 12938231720448x^4 + 200034687172608x^2 + 1185571438608384	\( 2^{62}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 4, 3495176]$ (GRH)
16.0.1147634942730979008947338773912344095761629184.4	x^16 + 328x^14 + 101516x^12 + 1931264x^10 + 27131422x^8 + 174770208x^6 + 831126744x^4 + 196071840x^2 + 44116164	\( 2^{62}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 4, 4, 4, 4, 28, 74256]$ (GRH)
16.0.1147634942730979008947338773912344095761629184.10	x^16 + 984x^14 + 373428x^12 + 70440624x^10 + 6974744274x^8 + 343883864448x^6 + 6663932840448x^4 + 2469564039168x^2 + 180699807744	\( 2^{62}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 700, 23800]$ (GRH)
16.0.1173204871331335989075336895013770710512304128.1	x^16 + 884x^14 + 288626x^12 + 44336136x^10 + 3323256560x^8 + 113320451504x^6 + 1370532909096x^4 + 3771231912032x^2 + 2900178534032	\( 2^{44}\cdot 13^{12}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 2, 4, 4, 4881092]$ (GRH)
16.0.3373848744484085385907843975364516141319847936.1	x^16 + 676x^14 + 177450x^12 + 22726756x^10 + 1452550700x^8 + 42136023800x^6 + 451304077972x^4 + 260354061768x^2 + 9841036804	\( 2^{56}\cdot 193^{2}\cdot 257^{10} \)	16T1435	$[2, 2, 2, 2, 2, 2, 4, 28600944]$ (GRH)
16.0.3373848744484085385907843975364516141319847936.2	x^16 + 1348x^14 + 746298x^12 + 220686820x^10 + 37699023596x^8 + 3727038571256x^6 + 199890202805044x^4 + 4937542579833672x^2 + 41236000985452036	\( 2^{56}\cdot 193^{2}\cdot 257^{10} \)	16T1435	$[2, 2, 2, 2, 2, 2, 4, 17502456]$ (GRH)
16.0.3438190509295256478027799611834368000000000000.2	x^16 + 1040x^14 + 439400x^12 + 96668000x^10 + 11781412500x^8 + 779715300000x^6 + 25340747250000x^4 + 313742585000000x^2 + 1177500376861250	\( 2^{79}\cdot 5^{12}\cdot 13^{12} \)	$C_{16}$ (as 16T1)	$[4, 398831044]$ (GRH)
16.0.3438190509295256478027799611834368000000000000.4	x^16 + 1040x^14 + 439400x^12 + 96668000x^10 + 11781412500x^8 + 779715300000x^6 + 25340747250000x^4 + 313742585000000x^2 + 102812781061250	\( 2^{79}\cdot 5^{12}\cdot 13^{12} \)	$C_{16}$ (as 16T1)	$[3, 3, 12, 13442124]$ (GRH)
16.0.3613016314808050004408591512141771336587411456.2	x^16 + 712x^14 + 133856x^12 + 9597760x^10 + 259143525x^8 + 2571346704x^6 + 8488999068x^4 + 9471488224x^2 + 2225008900	\( 2^{48}\cdot 3^{8}\cdot 89^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 4, 29438152]$ (GRH)
16.0.4590539770923916035789355095649376383046516736.6	x^16 + 656x^14 + 144648x^12 + 12664736x^10 + 405682372x^8 + 5736432672x^6 + 36798327216x^4 + 89879331456x^2 + 16775171361	\( 2^{64}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 8, 8, 3218056]$ (GRH)
16.0.4590539770923916035789355095649376383046516736.9	x^16 + 656x^14 + 155144x^12 + 16296352x^10 + 793516132x^8 + 16786170144x^6 + 140306830128x^4 + 284382596736x^2 + 161476189281	\( 2^{64}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 4, 4, 28, 169456]$ (GRH)
16.0.4590539770923916035789355095649376383046516736.11	x^16 + 656x^14 + 168264x^12 + 21800192x^10 + 1543733476x^8 + 59754143904x^6 + 1163849279472x^4 + 8655861520224x^2 + 1353632190849	\( 2^{64}\cdot 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 8, 8, 7498888]$ (GRH)
16.0.11352029626874238391016464929669692733284941824.2	x^16 + 816x^14 + 138312x^12 + 10046592x^10 + 366177348x^8 + 6765454368x^6 + 57355398864x^4 + 173471860224x^2 + 127157756850	\( 2^{79}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 434975504]$ (GRH)
16.0.11352029626874238391016464929669692733284941824.3	x^16 + 816x^14 + 246024x^12 + 33547392x^10 + 2007605412x^8 + 43864874784x^6 + 378786592080x^4 + 1110011465088x^2 + 359229669714	\( 2^{79}\cdot 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 2, 2, 2, 2, 2, 8186128]$ (GRH)