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 )

Label	Polynomial	Discriminant	Galois group	Class group
16.0.480777155608471076297548800000000.1	x^16 + 255x^14 + 26775x^12 + 1491750x^10 + 47334375x^8 + 852018750x^6 + 8132906250x^4 + 34855312500x^2 + 43569140625	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 139714]$ (GRH)
16.0.548747431866424450523939019858833.1	x^16 - x^15 + 256x^14 - 256x^13 + 27031x^12 - 27031x^11 + 1518781x^10 - 1518781x^9 + 48853156x^8 - 48853156x^7 + 900871906x^6 - 900871906x^5 + 9033778156x^4 - 9033778156x^3 + 43889090656x^2 - 43889090656x + 87458231281	\( 17^{15}\cdot 61^{8} \)	$C_{16}$ (as 16T1)	$[1265378]$ (GRH)
16.0.605544796424780341033364025769984.7	x^16 - 2x^15 + 163x^14 - 282x^13 + 12233x^12 - 18086x^11 + 549386x^10 - 679232x^9 + 16099839x^8 - 16070158x^7 + 314665218x^6 - 238996272x^5 + 4001369686x^4 - 2066649212x^3 + 30257685388x^2 - 8015671568x + 104203730401	\( 2^{24}\cdot 11^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[5, 120, 1680]$ (GRH)
16.0.1192550062163720610398944075186176.5	x^16 - 8x^15 + 156x^14 - 952x^13 + 10486x^12 - 50904x^11 + 404700x^10 - 1578616x^9 + 9888039x^8 - 30603224x^7 + 157206132x^6 - 370616376x^5 + 1590906842x^4 - 2596926520x^3 + 9376658828x^2 - 8135298584x + 24635195998	\( 2^{48}\cdot 3^{8}\cdot 71^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 8, 37128]$ (GRH)
16.0.1722945145525970304337872614249761.1	x^16 - 2x^15 + 53x^14 - 404x^13 + 3150x^12 - 16220x^11 + 43602x^10 - 147216x^9 + 562581x^8 - 1745730x^7 + 3929497x^6 - 4677356x^5 + 6836220x^4 - 10615248x^3 + 18312704x^2 - 3638272x + 7929856	\( 17^{8}\cdot 89^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[301, 3913]$ (GRH)
16.0.2055505143594254982418411202543616.5	x^16 + 224x^14 + 20384x^12 + 965888x^10 + 25354560x^8 + 361417728x^6 + 2529924096x^4 + 6746464256x^2 + 15567303361	\( 2^{64}\cdot 3^{8}\cdot 19^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 539552]$ (GRH)
16.0.2282105044722241146451513778896896.66	x^16 + 132x^14 + 8438x^12 - 24x^11 + 337124x^10 + 3528x^9 + 9103527x^8 + 183072x^7 + 168416588x^6 + 1983264x^5 + 2065793754x^4 - 25740600x^3 + 15254320436x^2 - 472415544x + 51546056158	\( 2^{48}\cdot 3^{8}\cdot 7^{8}\cdot 11^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 24, 48, 240]$ (GRH)
16.0.2304366822037031859005514783391744.4	x^16 - 2x^15 + 195x^14 - 338x^13 + 17357x^12 - 25718x^11 + 917938x^10 - 1136632x^9 + 31478439x^8 - 31424078x^7 + 715763506x^6 - 542563352x^5 + 10530368990x^4 - 5412835164x^3 + 91622805660x^2 - 24069872832x + 361048092497	\( 2^{24}\cdot 13^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[4, 4, 20, 40, 120]$ (GRH)
16.0.2308429957160341796132964777021233.1	x^16 - x^15 + 307x^14 - 307x^13 + 38863x^12 - 38863x^11 + 2616607x^10 - 2616607x^9 + 100769167x^8 - 100769167x^7 + 2220864463x^6 - 2220864463x^5 + 26505592399x^4 - 26505592399x^3 + 151398478927x^2 - 151398478927x + 338737808719	\( 17^{15}\cdot 73^{8} \)	$C_{16}$ (as 16T1)	$[1356226]$ (GRH)
16.0.2740458020629184239370240000000000.1	x^16 + 206x^14 + 16665x^12 + 700728x^10 + 16860739x^8 + 237751620x^6 + 1901560165x^4 + 7673353250x^2 + 11017777025	\( 2^{40}\cdot 5^{10}\cdot 761^{5} \)	16T1360	$[2, 2, 2, 142756]$ (GRH)
16.0.2801731803266966736034164664958976.6	x^16 - 8x^15 + 172x^14 - 1064x^13 + 12790x^12 - 63272x^11 + 545756x^10 - 2173192x^9 + 14717223x^8 - 46483976x^7 + 257685716x^6 - 618838472x^5 + 2865167258x^4 - 4749147848x^3 + 18507674124x^2 - 16229095208x + 53156046238	\( 2^{48}\cdot 3^{8}\cdot 79^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 80, 4080]$ (GRH)
16.0.2978012531396189373689422302674944.2	x^16 - 8x^15 + 156x^14 - 952x^13 + 10486x^12 - 50904x^11 + 404700x^10 - 1578616x^9 + 9888041x^8 - 30603232x^7 + 157205136x^6 - 370613360x^5 + 1590951472x^4 - 2597020816x^3 + 9376337416x^2 - 8134929520x + 24635401918	\( 2^{62}\cdot 71^{8} \)	$C_8\times C_2$ (as 16T5)	$[1223768]$ (GRH)
16.0.3536375739919375385601751537156096.2	x^16 + 240x^14 + 23400x^12 + 1188000x^10 + 33412500x^8 + 510300000x^6 + 3827250000x^4 + 10935000000x^2 + 25558736641	\( 2^{64}\cdot 61^{8} \)	$C_8\times C_2$ (as 16T5)	$[15, 15, 6630]$ (GRH)
16.0.5032238723456334453905817600000000.61	x^16 + 148x^14 + 10486x^12 - 24x^11 + 460196x^10 + 3864x^9 + 13557351x^8 + 224640x^7 + 272216812x^6 + 2718048x^5 + 3610023514x^4 - 36903144x^3 + 28731561716x^2 - 747884040x + 104415192286	\( 2^{48}\cdot 3^{8}\cdot 5^{8}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 24, 6240]$ (GRH)
16.0.5066254935343120593523840000000000.1	x^16 + 283x^14 + 32768x^12 + 2004498x^10 + 69707006x^8 + 1378919860x^6 + 14648741955x^4 + 71931672375x^2 + 106485151525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 1621^{5} \)	16T1574	$[2, 4, 290880]$ (GRH)
16.0.5066254935343120593523840000000000.2	x^16 + 222x^14 + 20794x^12 + 1070793x^10 + 33060731x^8 + 624287625x^6 + 7006261885x^4 + 42502093175x^2 + 106485151525	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 1621^{5} \)	16T1574	$[2, 8, 115608]$ (GRH)
16.0.5381489931190917922816000000000000.14	x^16 + 368x^14 + 55016x^12 + 4282784x^10 + 184415219x^8 + 4273731752x^6 + 46779340924x^4 + 163431621456x^2 + 78310985281	\( 2^{48}\cdot 5^{12}\cdot 23^{8} \)	$C_4^2$ (as 16T4)	$[2, 16, 42640]$ (GRH)
16.0.5877959313808425657932185600000000.8	x^16 + 256x^14 + 26624x^12 + 1441792x^10 + 43253760x^8 + 704643072x^6 + 5637144576x^4 + 17179869184x^2 + 40746248449	\( 2^{64}\cdot 5^{8}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 1005472]$ (GRH)
16.0.6040479020157644046336000000000000.32	x^16 - 4x^15 + 154x^14 - 604x^13 + 10903x^12 - 40348x^11 + 456524x^10 - 1514672x^9 + 12191031x^8 - 34028752x^7 + 209524964x^6 - 454064500x^5 + 2240623355x^4 - 3374395156x^3 + 13770521718x^2 - 10856135284x + 37766834191	\( 2^{44}\cdot 3^{8}\cdot 5^{12}\cdot 11^{8} \)	$C_4^2$ (as 16T4)	$[16, 16, 48, 96]$ (GRH)
16.0.6490588908866265677824000000000000.9	x^16 + 280x^14 + 30380x^12 + 1646400x^10 + 47899950x^8 + 739508000x^6 + 5529503000x^4 + 16470860000x^2 + 14412002500	\( 2^{62}\cdot 5^{12}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 4, 4, 8, 5576]$ (GRH)
16.0.6845525354902535215356313600000000.8	x^16 - 8x^15 + 228x^14 - 1456x^13 + 20938x^12 - 107064x^11 + 993728x^10 - 4020968x^9 + 26143449x^8 - 81567920x^7 + 393089516x^6 - 909551832x^5 + 3650673056x^4 - 5873105256x^3 + 19910692468x^2 - 17113258880x + 45036203521	\( 2^{48}\cdot 5^{8}\cdot 53^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[6, 360528]$ (GRH)
16.0.6996429487079101204569997541638144.2	x^16 - 8x^15 + 172x^14 - 1064x^13 + 12790x^12 - 63272x^11 + 545756x^10 - 2173192x^9 + 14717225x^8 - 46483984x^7 + 257684608x^6 - 618835120x^5 + 2865222448x^4 - 4749263824x^3 + 18507232360x^2 - 16228594896x + 53156361278	\( 2^{62}\cdot 79^{8} \)	$C_8\times C_2$ (as 16T5)	$[4, 432, 2160]$ (GRH)
16.0.7239938343280505619539558400000000.21	x^16 - 2x^15 + 227x^14 - 394x^13 + 23377x^12 - 34694x^11 + 1422906x^10 - 1763952x^9 + 55896239x^8 - 55806478x^7 + 1449580514x^6 - 1097221888x^5 + 24220970150x^4 - 12405931900x^3 + 238353759596x^2 - 62226612592x + 1057852414081	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[8, 24, 24672]$ (GRH)
16.0.7269924201415415149428216006967296.6	x^16 + 156x^14 + 11594x^12 - 24x^11 + 531680x^10 + 4032x^9 + 16317753x^8 + 247008x^7 + 340542452x^6 + 3145200x^5 + 4685677056x^4 - 43671120x^3 + 38637575756x^2 - 926997912x + 145330457809	\( 2^{48}\cdot 3^{8}\cdot 89^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 52, 6240]$ (GRH)
16.0.8684422986556880818624724610318336.63	x^16 - 8x^15 + 196x^14 - 1232x^13 + 16666x^12 - 84344x^11 + 812720x^10 - 3318856x^9 + 24998649x^8 - 80960624x^7 + 498037052x^6 - 1223811416x^5 + 6284020592x^4 - 10616609960x^3 + 45933051828x^2 - 40816151264x + 148857727873	\( 2^{48}\cdot 3^{8}\cdot 7^{8}\cdot 13^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 48, 1248]$ (GRH)
16.0.8926609275800253364594278400000000.1	x^16 + 244x^14 + 20637x^12 + 815784x^10 + 16689063x^8 + 188396254x^6 + 1187687160x^4 + 3924173404x^2 + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	$[2, 2, 2, 136716]$ (GRH)
16.0.8926609275800253364594278400000000.2	x^16 + 192x^14 + 15178x^12 + 640620x^10 + 15610103x^8 + 220323372x^6 + 1690250170x^4 + 5883712036x^2 + 5300131204	\( 2^{38}\cdot 5^{8}\cdot 89^{6}\cdot 409^{2} \)	16T1127	$[2, 2, 2, 137196]$ (GRH)
16.0.9477907118573134595068808298233856.5	x^16 + 272x^14 + 30056x^12 + 1729376x^10 + 55123860x^8 + 954143904x^6 + 8110223184x^4 + 26261675072x^2 + 63285955489	\( 2^{64}\cdot 3^{8}\cdot 23^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 16, 32080]$ (GRH)
16.0.9477907118573134595068808298233856.6	x^16 + 368x^14 + 55016x^12 + 4282784x^10 + 184695060x^8 + 4325222496x^6 + 49740058704x^4 + 217908828608x^2 + 78310985281	\( 2^{64}\cdot 3^{8}\cdot 23^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 206114]$ (GRH)
16.0.10265933934658824457230071374020608.1	x^16 + 304x^14 + 37544x^12 + 2414368x^10 + 86011860x^8 + 1663938528x^6 + 15807416016x^4 + 57207791296x^2 + 33967126082	\( 2^{79}\cdot 19^{8} \)	$C_{16}$ (as 16T1)	$[2319554]$ (GRH)
16.0.10294261539221265797567188438089728.1	x^16 + 374x^14 + 57596x^12 + 4706416x^10 + 219029360x^8 + 5782375104x^6 + 80953251456x^4 + 508849009152x^2 + 932889850112	\( 2^{24}\cdot 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 736258]$ (GRH)
16.0.10386864596368228067918124169560064.2	x^16 - 8x^15 + 180x^14 - 1120x^13 + 14026x^12 - 69960x^11 + 627024x^10 - 2519560x^9 + 17702027x^8 - 56416264x^7 + 324191712x^6 - 784977032x^5 + 3766659562x^4 - 6286165360x^3 + 25396479484x^2 - 22375524712x + 76059908671	\( 2^{62}\cdot 83^{8} \)	$C_8\times C_2$ (as 16T5)	$[5, 5, 65535]$ (GRH)
16.0.11268182541757132036763060346765233.2	x^16 - x^15 + 375x^14 - 375x^13 + 57971x^12 - 57971x^11 + 4764387x^10 - 4764387x^9 + 223793747x^8 - 223793747x^7 + 6006168851x^6 - 6006168851x^5 + 86959420307x^4 - 86959420307x^3 + 595808429459x^2 - 595808429459x + 1528698279571	\( 17^{15}\cdot 89^{8} \)	$C_{16}$ (as 16T1)	$[2, 2, 2, 370658]$ (GRH)
16.0.12213777651561724066555110400000000.1	x^16 + 356x^14 + 49410x^12 + 3419732x^10 + 125045630x^8 + 2344543474x^6 + 19807098481x^4 + 51865194328x^2 + 32527204609	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{4}\cdot 103^{8} \)	16T1665	$[2, 2, 2, 300472]$ (GRH)
16.0.12251765391792386665453977600000000.56	x^16 - 8x^15 + 244x^14 - 1568x^13 + 24010x^12 - 124040x^11 + 1221920x^10 - 5008984x^9 + 34483221x^8 - 109181072x^7 + 555347828x^6 - 1303648472x^5 + 5479602212x^4 - 8904466088x^3 + 31536986508x^2 - 27285235712x + 75639875521	\( 2^{48}\cdot 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 16, 16, 6032]$ (GRH)
16.0.12251765391792386665453977600000000.59	x^16 - 8x^15 + 324x^14 - 2128x^13 + 42490x^12 - 227640x^11 + 2888720x^10 - 12406664x^9 + 108025401x^8 - 360080432x^7 + 2140710428x^6 - 5211543192x^5 + 18830100752x^4 - 29370783528x^3 + 31429508788x^2 - 17556233312x + 81433551601	\( 2^{48}\cdot 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 10, 18850]$ (GRH)
16.0.12251765391792386665453977600000000.64	x^16 - 8x^15 + 204x^14 - 1288x^13 + 18070x^12 - 92040x^11 + 917820x^10 - 3775144x^9 + 29390151x^8 - 95871272x^7 + 609155508x^6 - 1506813672x^5 + 7990422842x^4 - 13574268328x^3 + 60672375788x^2 - 54121458632x + 204097777726	\( 2^{48}\cdot 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[8, 16, 46400]$ (GRH)
16.0.12566407444765825894344294400000000.3	x^16 - 8x^15 + 292x^14 - 1904x^13 + 34474x^12 - 182456x^11 + 2108384x^10 - 8913832x^9 + 71059739x^8 - 232686904x^7 + 1292149168x^6 - 3097554280x^5 + 11477990842x^4 - 18047994784x^3 + 37498043644x^2 - 28954052376x + 82125187631	\( 2^{62}\cdot 5^{8}\cdot 17^{8} \)	$C_8\times C_2$ (as 16T5)	$[4, 4, 60, 2040]$ (GRH)
16.0.14473837877661054916170965242085376.6	x^16 + 172x^14 + 13978x^12 - 24x^11 + 696224x^10 + 4368x^9 + 23084937x^8 + 294912x^7 + 518313508x^6 + 4129104x^5 + 7647922624x^4 - 59931840x^3 + 67451890556x^2 - 1387724424x + 270839247073	\( 2^{48}\cdot 3^{8}\cdot 97^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 2, 2, 2, 10, 2720]$ (GRH)
16.0.14876562920830399091974866674384896.2	x^16 + 288x^14 + 33696x^12 + 2052864x^10 + 69284160x^8 + 1269789696x^6 + 11428107264x^4 + 39182082048x^2 + 96031192321	\( 2^{64}\cdot 73^{8} \)	$C_8\times C_2$ (as 16T5)	$[6, 468672]$ (GRH)
16.0.15085984382462633967616000000000000.5	x^16 - 4x^15 + 174x^14 - 684x^13 + 13793x^12 - 51308x^11 + 642284x^10 - 2150452x^9 + 18981756x^8 - 53702132x^7 + 359963494x^6 - 793737240x^5 + 4239589780x^4 - 6503562836x^3 + 28576785148x^2 - 22976725744x + 85468811201	\( 2^{44}\cdot 5^{12}\cdot 37^{8} \)	$C_4^2$ (as 16T4)	$[40, 30160]$ (GRH)
16.0.15136091767428192657568213587984384.5	x^16 - 8x^15 + 188x^14 - 1176x^13 + 15318x^12 - 76984x^11 + 715900x^10 - 2900888x^9 + 21116169x^8 - 67859840x^7 + 403705168x^6 - 984991600x^5 + 4892167536x^4 - 8216449296x^3 + 34371364936x^2 - 30416805424x + 107162335102	\( 2^{62}\cdot 3^{8}\cdot 29^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 944112]$ (GRH)
16.0.15256656512850458090056729600000000.1	x^16 + 268x^14 + 29251x^12 + 1682196x^10 + 54789202x^8 + 1002211012x^6 + 9430297664x^4 + 36291649124x^2 + 40630868041	\( 2^{16}\cdot 5^{8}\cdot 19^{6}\cdot 103^{8} \)	16T1048	$[2, 2, 2, 2, 134740]$ (GRH)
16.0.18682108719227553550336000000000000.1	x^16 - 2x^15 + 194x^14 - 226x^13 + 15312x^12 - 4102x^11 + 637218x^10 + 369154x^9 + 15396726x^8 + 19606386x^7 + 222224758x^6 + 413636482x^5 + 1758527272x^4 + 4162184006x^3 + 5715260614x^2 + 11160522222x + 18098212481	\( 2^{24}\cdot 5^{12}\cdot 61^{6}\cdot 97^{4} \)	16T864	$[2, 2, 4, 65864]$ (GRH)
16.0.19997735500105260525348149910306816.7	x^16 + 180x^14 + 15254x^12 - 24x^11 + 789956x^10 + 4536x^9 + 27168519x^8 + 320448x^7 + 631526924x^6 + 4689888x^5 + 9632982138x^4 - 69573768x^3 + 87721316756x^2 - 1678274856x + 363345076222	\( 2^{48}\cdot 3^{8}\cdot 101^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 2168040]$ (GRH)
16.0.20900613426398125371268864579469312.1	x^16 + 224x^14 - 192x^13 + 20314x^12 - 35512x^11 + 970632x^10 - 2489256x^9 + 27814397x^8 - 82717776x^7 + 504053312x^6 - 1361814944x^5 + 5267824628x^4 - 9998030224x^3 + 21102481608x^2 - 15119234336x + 13719758722	\( 2^{57}\cdot 449^{4}\cdot 1889^{2} \)	16T1584	$[2, 2, 2, 2, 85042]$ (GRH)
16.0.21078441977020355377207705600000000.9	x^16 - 8x^15 + 260x^14 - 1680x^13 + 27290x^12 - 142264x^11 + 1482352x^10 - 6146760x^9 + 44663097x^8 - 143269808x^7 + 767003836x^6 - 1823888920x^5 + 8014040880x^4 - 13143868456x^3 + 48544576244x^2 - 42254476064x + 123000632449	\( 2^{48}\cdot 5^{8}\cdot 61^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[6, 605280]$ (GRH)
16.0.21686570067329360666414797746601984.7	x^16 - 8x^15 + 196x^14 - 1232x^13 + 16666x^12 - 84344x^11 + 812720x^10 - 3318856x^9 + 24998651x^8 - 80960632x^7 + 498035776x^6 - 1223807560x^5 + 6284093722x^4 - 10616762656x^3 + 45932378476x^2 - 40815400920x + 148858281023	\( 2^{62}\cdot 7^{8}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	$[16, 184416]$ (GRH)
16.0.22434050585222044572730141713145073.1	x^16 - x^15 + 409x^14 - 409x^13 + 68953x^12 - 68953x^11 + 6179161x^10 - 6179161x^9 + 316389721x^8 - 316389721x^7 + 9250453849x^6 - 9250453849x^5 + 145697978713x^4 - 145697978713x^3 + 1081338149209x^2 - 1081338149209x + 2952618490201	\( 17^{15}\cdot 97^{8} \)	$C_{16}$ (as 16T1)	$[17, 17, 20162]$ (GRH)
16.0.22795311112775003166262217194602496.7	x^16 + 304x^14 + 37544x^12 + 2414368x^10 + 86011860x^8 + 1663938528x^6 + 15807416016x^4 + 57207791296x^2 + 142701862081	\( 2^{64}\cdot 7^{8}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 48, 32304]$ (GRH)

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