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
16.0.4009292695690170390860412175969.21	x^16 - 6x^15 + 96x^14 - 446x^13 + 4135x^12 - 15442x^11 + 105440x^10 - 318139x^9 + 1747266x^8 - 4186200x^7 + 19309779x^6 - 35078044x^5 + 139303886x^4 - 173184835x^3 + 601821142x^2 - 389008031x + 1198719131	\( 17^{14}\cdot 47^{8} \)	$C_8\times C_2$ (as 16T5)	$[4, 4, 6560]$ (GRH)
16.0.5611988462318125056000000000000.44	x^16 - 8x^15 + 92x^14 - 504x^13 + 3508x^12 - 14860x^11 + 77626x^10 - 262972x^9 + 1107333x^8 - 2996084x^7 + 10483974x^6 - 21926452x^5 + 64443548x^4 - 95384228x^3 + 234422198x^2 - 189953172x + 382482481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 13^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 8, 2080]$ (GRH)
16.0.6486697150600796010022736756736.5	x^16 + 52x^14 + 1558x^12 - 24x^11 + 32324x^10 + 1848x^9 + 483207x^8 + 38592x^7 + 5163148x^6 + 175584x^5 + 37553914x^4 - 1933320x^3 + 168754196x^2 - 17519784x + 350398078	\( 2^{48}\cdot 3^{8}\cdot 37^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[106080]$ (GRH)
16.0.7400341554413735321499328643072.2	x^16 + 155x^14 + 9384x^12 + 284936x^10 + 4684188x^8 + 42761137x^6 + 212450356x^4 + 524089873x^2 + 483345053	\( 2^{16}\cdot 483345053^{3} \)	16T1946	$[115424]$ (GRH)
16.0.9001432898582155699240292122624.3	x^16 - 2x^15 + 91x^14 - 156x^13 + 3980x^12 - 5828x^11 + 107531x^10 - 132122x^9 + 1947249x^8 - 1943848x^7 + 24090615x^6 - 18462918x^5 + 198368818x^4 - 104591990x^3 + 993282715x^2 - 272656064x + 2317576561	\( 2^{16}\cdot 13^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[4, 4, 4, 8, 272]$ (GRH)
16.0.11939508427262544380953600000000.1	x^16 - 2x^15 + 113x^14 - 170x^13 + 5670x^12 - 5200x^11 + 162976x^10 - 45672x^9 + 2933108x^8 + 851928x^7 + 34322677x^6 + 21797522x^5 + 263102522x^4 + 148225950x^3 + 1229052881x^2 + 112463354x + 2667232231	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	$[4, 37960]$ (GRH)
16.0.11939508427262544380953600000000.2	x^16 - 2x^15 + 113x^14 - 172x^13 + 5830x^12 - 6642x^11 + 175264x^10 - 161942x^9 + 3284104x^8 - 2727984x^7 + 38554411x^6 - 29815402x^5 + 273976211x^4 - 167301256x^3 + 1092003662x^2 - 247972336x + 2265405829	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 941^{4} \)	16T1025	$[4, 36920]$ (GRH)
16.0.12255966294285746176000000000000.5	x^16 - 8x^15 + 100x^14 - 560x^13 + 4184x^12 - 18188x^11 + 101298x^10 - 352160x^9 + 1574821x^8 - 4365228x^7 + 16182278x^6 - 34569744x^5 + 107501834x^4 - 161864696x^3 + 421058284x^2 - 345252216x + 738052316	\( 2^{32}\cdot 5^{12}\cdot 43^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 30, 2100]$ (GRH)
16.0.14098938471283305926093925390625.4	x^16 - 6x^15 + 112x^14 - 530x^13 + 5619x^12 - 21510x^11 + 166080x^10 - 514575x^9 + 3172440x^8 - 7799164x^7 + 40179631x^6 - 74720456x^5 + 330143602x^4 - 418732795x^3 + 1613418232x^2 - 1059674139x + 3605932049	\( 5^{8}\cdot 11^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[126560]$ (GRH)
16.0.14730630136034492416000000000000.12	x^16 + 176x^14 + 12584x^12 + 468512x^10 + 9648419x^8 + 106937864x^6 + 559813276x^4 + 935384208x^2 + 214358881	\( 2^{48}\cdot 5^{12}\cdot 11^{8} \)	$C_4^2$ (as 16T4)	$[2, 2, 30, 870]$ (GRH)
16.0.16285050713501206114103002660864.7	x^16 - 2x^15 + 99x^14 - 170x^13 + 4673x^12 - 6854x^11 + 135514x^10 - 166672x^9 + 2622159x^8 - 2617358x^7 + 34526242x^6 - 26419040x^5 + 301456646x^4 - 158389884x^3 + 1594732716x^2 - 435146928x + 3916322369	\( 2^{24}\cdot 7^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[16, 9040]$ (GRH)
16.0.17117414167613859856000000000000.1	x^16 + 180x^14 + 12415x^12 + 417875x^10 + 7355100x^8 + 69576750x^6 + 347255625x^4 + 844226250x^2 + 768675625	\( 2^{16}\cdot 5^{12}\cdot 29^{4}\cdot 1109^{4} \)	16T1744	$[2, 2, 30520]$ (GRH)
16.0.18759175710374728781004800000000.1	x^16 + 170x^14 + 11900x^12 + 442000x^10 + 9350000x^8 + 112200000x^6 + 714000000x^4 + 2040000000x^2 + 1700000000	\( 2^{24}\cdot 5^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 2, 38978]$ (GRH)
16.0.21585269445983519741468649455616.5	x^16 - 8x^15 + 100x^14 - 560x^13 + 4186x^12 - 18200x^11 + 101264x^10 - 351880x^9 + 1570905x^8 - 4351376x^7 + 16097276x^6 - 34361912x^5 + 106654352x^4 - 160500584x^3 + 418672980x^2 - 343516544x + 745807489	\( 2^{48}\cdot 3^{8}\cdot 43^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[5, 20400]$ (GRH)
16.0.22368513682624478383882080078125.1	x^16 - 6x^15 + 114x^14 - 436x^13 + 4479x^12 - 10309x^11 + 80393x^10 - 82748x^9 + 763006x^8 + 192135x^7 + 5523873x^6 + 5112247x^5 + 40963734x^4 + 18571065x^3 + 207616495x^2 + 13494377x + 431724841	\( 5^{12}\cdot 13^{6}\cdot 29^{7}\cdot 1049^{2} \)	16T1558	$[2, 2, 2, 2, 6448]$ (GRH)
16.0.22856234040418247855901029307953.1	x^16 - x^15 + 171x^14 - 171x^13 + 12071x^12 - 12071x^11 + 454071x^10 - 454071x^9 + 9804071x^8 - 9804071x^7 + 122004071x^6 - 122004071x^5 + 836004071x^4 - 836004071x^3 + 2876004071x^2 - 2876004071x + 4576004071	\( 17^{15}\cdot 41^{8} \)	$C_{16}$ (as 16T1)	$[220354]$ (GRH)
16.0.24681786277054131674683564621824.5	x^16 - 8x^15 + 92x^14 - 504x^13 + 3510x^12 - 14872x^11 + 77596x^10 - 262712x^9 + 1104105x^8 - 2984864x^7 + 10419088x^6 - 21769840x^5 + 63853488x^4 - 94452624x^3 + 232760200x^2 - 188732656x + 387186238	\( 2^{62}\cdot 3^{8}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 43104]$ (GRH)
16.0.24722989956581301387479701814209.6	x^16 - 6x^15 + 120x^14 - 572x^13 + 6445x^12 - 24922x^11 + 203540x^10 - 637603x^9 + 4145112x^8 - 10300950x^7 + 55839765x^6 - 104874598x^5 + 486803774x^4 - 622686499x^3 + 2517198244x^2 - 1664461289x + 5933446319	\( 17^{14}\cdot 59^{8} \)	$C_8\times C_2$ (as 16T5)	$[217848]$ (GRH)
16.0.24967943722642702336000000000000.5	x^16 - 8x^15 + 108x^14 - 616x^13 + 4916x^12 - 21852x^11 + 129218x^10 - 459508x^9 + 2174117x^8 - 6156340x^7 + 24095662x^6 - 52453964x^5 + 172046412x^4 - 263040692x^3 + 722028526x^2 - 598345980x + 1353436561	\( 2^{32}\cdot 5^{12}\cdot 47^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[10, 17680]$ (GRH)
16.0.25943659843751205943422228627456.4	x^16 + 176x^14 + 12584x^12 + 468512x^10 + 9663060x^8 + 108226272x^6 + 595244496x^4 + 1247178944x^2 + 214358881	\( 2^{64}\cdot 3^{8}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 52658]$ (GRH)
16.0.36778727586648064367001600000000.15	x^16 - 8x^15 + 84x^14 - 448x^13 + 3038x^12 - 12768x^11 + 69340x^10 - 239384x^9 + 1097171x^8 - 3076240x^7 + 11902356x^6 - 25822592x^5 + 83442994x^4 - 127019952x^3 + 338600600x^2 - 278944192x + 606644476	\( 2^{44}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 24, 1248]$ (GRH)
16.0.40211959137583069521746829836288.1	x^16 + 187x^14 + 14399x^12 + 588302x^10 + 13689335x^8 + 180699222x^6 + 1264894554x^4 + 3975382884x^2 + 3644100977	\( 2^{16}\cdot 11^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	$[2, 94, 1598]$ (GRH)
16.0.43973667993577319434061585842176.5	x^16 - 8x^15 + 108x^14 - 616x^13 + 4918x^12 - 21864x^11 + 129180x^10 - 459208x^9 + 2169447x^8 - 6139592x^7 + 23986068x^6 - 52182408x^5 + 170888666x^4 - 261158920x^3 + 718599116x^2 - 595814888x + 1365774814	\( 2^{48}\cdot 3^{8}\cdot 47^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 8, 40, 40]$ (GRH)
16.0.47991168245852798976000000000000.6	x^16 + 56x^14 + 1581x^12 + 24416x^10 + 221976x^8 + 961100x^6 + 2238125x^4 + 1312500x^2 + 390625	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[6, 6, 12, 240]$ (GRH)
16.0.47991168245852798976000000000000.26	x^16 - 12x^14 - 60x^13 + 284x^12 + 1440x^11 + 4442x^10 - 2100x^9 - 2019x^8 + 49800x^7 + 700670x^6 + 2631000x^5 + 8159670x^4 + 15805800x^3 + 26809700x^2 + 26637000x + 24022900	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 6, 12, 816]$ (GRH)
16.0.47991168245852798976000000000000.39	x^16 - 4x^15 + 54x^14 - 164x^13 + 1529x^12 - 4056x^11 + 30078x^10 - 70272x^9 + 426051x^8 - 854320x^7 + 4275808x^6 - 6891612x^5 + 28648659x^4 - 33425040x^3 + 115796640x^2 - 76098832x + 210560401	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 8, 4080]$ (GRH)
16.0.47991168245852798976000000000000.49	x^16 - 8x^15 + 116x^14 - 672x^13 + 5704x^12 - 25852x^11 + 161722x^10 - 586696x^9 + 2927421x^8 - 8448140x^7 + 34806462x^6 - 77057656x^5 + 265837154x^4 - 412056200x^3 + 1190242220x^2 - 995805576x + 2376274876	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 8160]$ (GRH)
16.0.47991168245852798976000000000000.58	x^16 + 272x^14 + 30345x^12 + 1788332x^10 + 59633994x^8 + 1113167888x^6 + 10620530360x^4 + 39392512608x^2 + 6975757441	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 17^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[12, 48, 816]$ (GRH)
16.0.50345559205004654867065673828125.1	x^16 - 7x^15 + 169x^14 - 721x^13 + 10352x^12 - 32647x^11 + 314218x^10 - 802681x^9 + 5362186x^8 - 11468099x^7 + 53717753x^6 - 95434883x^5 + 311549332x^4 - 428392404x^3 + 959344879x^2 - 794857148x + 1187058641	\( 5^{12}\cdot 101^{6}\cdot 181^{5} \)	16T994	$[2, 2, 2, 2, 10974]$ (GRH)
16.0.50345559205004654867065673828125.2	x^16 - 5x^15 + 124x^14 - 604x^13 + 6872x^12 - 30262x^11 + 214133x^10 - 801805x^9 + 4005147x^8 - 12138424x^7 + 45602362x^6 - 105886889x^5 + 306325756x^4 - 497742168x^3 + 1090515202x^2 - 981056326x + 1503349111	\( 5^{12}\cdot 101^{6}\cdot 181^{5} \)	16T994	$[2, 2, 2, 2, 10838]$ (GRH)
16.0.53902309800791645700994109538304.2	x^16 - 8x^15 + 100x^14 - 560x^13 + 4186x^12 - 18200x^11 + 101264x^10 - 351880x^9 + 1570907x^8 - 4351384x^7 + 16096672x^6 - 34360072x^5 + 106670842x^4 - 160536640x^3 + 418600684x^2 - 343425912x + 745835231	\( 2^{62}\cdot 43^{8} \)	$C_8\times C_2$ (as 16T5)	$[5, 23225]$ (GRH)
16.0.55002674780385421400473600000000.7	x^16 - 8x^15 + 132x^14 - 784x^13 + 6874x^12 - 31416x^11 + 183344x^10 - 646472x^9 + 2702073x^8 - 7244720x^7 + 23236220x^6 - 46753560x^5 + 136884272x^4 - 203161896x^3 + 502723444x^2 - 407897504x + 702991681	\( 2^{48}\cdot 5^{8}\cdot 29^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[5, 10, 4080]$ (GRH)
16.0.56056588304600006656000000000000.13	x^16 + 208x^14 + 17576x^12 + 773344x^10 + 18821699x^8 + 246538552x^6 + 1525271644x^4 + 3011928816x^2 + 815730721	\( 2^{48}\cdot 5^{12}\cdot 13^{8} \)	$C_4^2$ (as 16T4)	$[2, 104, 1040]$ (GRH)
16.0.63032584989723012513503859703808.1	x^16 + 150x^14 + 9022x^12 + 280004x^10 + 4809504x^8 + 45653880x^6 + 226136664x^4 + 493550656x^2 + 246775328	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2, 4, 13224]$ (GRH)
16.0.63032584989723012513503859703808.2	x^16 + 138x^14 + 7449x^12 + 200900x^10 + 2870766x^8 + 21354056x^6 + 77612932x^4 + 118011392x^2 + 61693832	\( 2^{37}\cdot 2777^{6} \)	16T1540	$[2, 57110]$ (GRH)
16.0.64793809550643768832929443086336.2	x^16 + 144x^14 + 8424x^12 + 256608x^10 + 4330260x^8 + 39680928x^6 + 178564176x^4 + 306110016x^2 + 701137441	\( 2^{64}\cdot 37^{8} \)	$C_8\times C_2$ (as 16T5)	$[161330]$ (GRH)
16.0.65284017132783271936000000000000.5	x^16 + 80x^14 - 20x^13 + 3434x^12 - 160x^11 + 99940x^10 + 22440x^9 + 2045996x^8 + 925040x^7 + 29864470x^6 + 18829560x^5 + 298724599x^4 + 194588720x^3 + 1780212660x^2 + 775588320x + 4571966921	\( 2^{32}\cdot 5^{12}\cdot 53^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[6, 28560]$ (GRH)
16.0.68372792983010839504523425519489.27	x^16 - 6x^15 + 136x^14 - 656x^13 + 8265x^12 - 32502x^11 + 294420x^10 - 939579x^9 + 6738726x^8 - 17057530x^7 + 101632369x^6 - 194147354x^5 + 987871066x^4 - 1282215295x^3 + 5669585782x^2 - 3792717441x + 14754909041	\( 17^{14}\cdot 67^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 24, 480]$ (GRH)
16.0.78039659508312536877345552728064.1	x^16 - 8x^15 + 166x^14 - 968x^13 + 10922x^12 - 48692x^11 + 381910x^10 - 1294564x^9 + 7667398x^8 - 18508272x^7 + 86507434x^6 - 122570424x^5 + 495625354x^4 - 153572468x^3 + 1237648906x^2 + 1155456948x + 1587808969	\( 2^{36}\cdot 3^{12}\cdot 17^{6}\cdot 97^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T657)	$[2, 2, 2, 2, 2, 5634]$ (GRH)
16.0.78039659508312536877345552728064.2	x^16 + 174x^14 - 164x^13 + 11648x^12 - 15708x^11 + 401124x^10 - 506040x^9 + 7714170x^8 - 7237928x^7 + 83714568x^6 - 33396192x^5 + 466924080x^4 + 125673152x^3 + 1316168472x^2 + 808621280x + 1171252804	\( 2^{36}\cdot 3^{12}\cdot 17^{6}\cdot 97^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T657)	$[2, 2, 2, 2, 2, 5926]$ (GRH)
16.0.79688620999701608976000000000000.1	x^16 - 8x^15 + 323x^14 - 1972x^13 + 39783x^12 - 185618x^11 + 2417269x^10 - 8510506x^9 + 77623693x^8 - 201140128x^7 + 1308764896x^6 - 2362029700x^5 + 10813266968x^4 - 10291651056x^3 + 35038013272x^2 + 10096911248x + 18671230096	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 181^{4} \)	$C_2^4.C_2^3$ (as 16T203)	$[2, 2, 2, 2, 27880]$ (GRH)
16.0.80320700706231066139033600000000.2	x^16 - 8x^15 + 92x^14 - 504x^13 + 3674x^12 - 15856x^11 + 91312x^10 - 322272x^9 + 1555101x^8 - 4442312x^7 + 18083476x^6 - 39901264x^5 + 135999792x^4 - 210112840x^3 + 592976072x^2 - 493914464x + 1140903199	\( 2^{44}\cdot 5^{8}\cdot 43^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[5, 60900]$ (GRH)
16.0.98727145108216526698734258487296.5	x^16 + 208x^14 + 17576x^12 + 773344x^10 + 18850260x^8 + 249508896x^6 + 1621807824x^4 + 4015905088x^2 + 815730721	\( 2^{64}\cdot 3^{8}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	$[18, 8082]$ (GRH)
16.0.107586731453760569991937021444096.1	x^16 - 8x^15 + 204x^14 - 1260x^13 + 15852x^12 - 77252x^11 + 610208x^10 - 2252232x^9 + 11890001x^8 - 29764972x^7 + 104949032x^6 - 121487192x^5 + 325754186x^4 - 21775820x^3 + 464127720x^2 + 125219124x + 530507567	\( 2^{44}\cdot 223^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	$[2, 2, 2, 2, 8626]$ (GRH)
16.0.108730576084219434179495230711969.1	x^16 - 6x^15 + 144x^14 - 698x^13 + 9259x^12 - 36670x^11 + 348512x^10 - 1121047x^9 + 8415948x^8 - 21472404x^7 + 133700199x^6 - 257288560x^5 + 1366555346x^4 - 1785014155x^3 + 8231592580x^2 - 5534375147x + 22435022501	\( 17^{14}\cdot 71^{8} \)	$C_8\times C_2$ (as 16T5)	$[21, 21, 1071]$ (GRH)
16.0.109810177778809754855611190738944.2	x^16 - 8x^15 + 108x^14 - 616x^13 + 4918x^12 - 21864x^11 + 129180x^10 - 459208x^9 + 2169449x^8 - 6139600x^7 + 23985408x^6 - 52180400x^5 + 170908336x^4 - 261201616x^3 + 718504936x^2 - 595699024x + 1365814462	\( 2^{62}\cdot 47^{8} \)	$C_8\times C_2$ (as 16T5)	$[8, 8, 4520]$ (GRH)
16.0.114978539144999765882759100235776.5	x^16 + 84x^14 + 3638x^12 - 24x^11 + 102884x^10 + 2520x^9 + 2027175x^8 + 83712x^7 + 27955244x^6 + 589920x^5 + 259368858x^4 - 6750888x^3 + 1466638388x^2 - 85763016x + 3821989918	\( 2^{48}\cdot 3^{8}\cdot 53^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[3, 3, 59160]$ (GRH)
16.0.116841939847873560576000000000000.14	x^16 - 8x^15 + 28x^14 - 56x^13 + 340x^12 - 1676x^11 + 7958x^10 - 24808x^9 + 95421x^8 - 250700x^7 + 870290x^6 - 1819760x^5 + 5551070x^4 - 8321000x^3 + 19889100x^2 - 15996200x + 31810900	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 4, 4, 80, 80]$ (GRH)
16.0.116841939847873560576000000000000.24	x^16 - 8x^15 + 20x^14 + 296x^12 - 2140x^11 + 6826x^10 - 13560x^9 + 60301x^8 - 185100x^7 + 729070x^6 - 1570952x^5 + 5955986x^4 - 9495240x^3 + 31551500x^2 - 27037000x + 79747180	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 2, 2, 4, 4, 16, 80]$ (GRH)
16.0.116841939847873560576000000000000.41	x^16 + 124x^14 + 5985x^12 + 143756x^10 + 1842554x^8 + 12966476x^6 + 59620320x^4 + 130137424x^2 + 542004961	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[4, 4, 8, 16, 80]$ (GRH)

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