Global number field search results

Further refine search

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

Results (displaying all 21 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.9517173136000000000000.7	x^16 - 2x^15 + 9x^14 - 2x^13 + 22x^12 + 12x^11 + 34x^10 - 86x^9 + 204x^8 - 494x^7 + 697x^6 - 930x^5 + 1151x^4 - 950x^3 + 490x^2 - 140x + 20	\( 2^{16}\cdot 5^{12}\cdot 29^{6} \)	16T813	$[2]$ (GRH)
16.0.8003942607376000000000000.6	x^16 - 4x^15 - 5x^14 + 8x^13 - 6x^12 - 8x^11 + 220x^10 + 960x^9 + 3011x^8 + 10170x^7 + 28265x^6 + 57154x^5 + 81851x^4 + 81152x^3 + 53082x^2 + 20168x + 4001	\( 2^{16}\cdot 5^{12}\cdot 29^{8} \)	16T813	$[2, 4]$ (GRH)
16.0.11228907791089540625062500000000.1	x^16 - 2x^14 - 57x^13 + 219x^12 + 998x^11 + 4501x^10 + 1831x^9 + 7422x^8 + 43601x^7 + 399911x^6 + 1206459x^5 + 2853056x^4 + 4059920x^3 + 5288565x^2 + 4391325x + 4352275	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 7^{8}\cdot 41^{6} \)	16T813	$[2, 2, 2, 6]$ (GRH)
16.0.18875793996821517790730062500000000.1	x^16 + 9x^14 - 25x^13 - 29x^12 + 1005x^11 - 5461x^10 + 21415x^9 - 49309x^8 - 172835x^7 + 3262910x^6 - 16653470x^5 + 66855015x^4 - 186256050x^3 + 474767975x^2 - 744073275x + 862485775	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 7^{8}\cdot 41^{8} \)	16T813	$[2, 2, 2, 2, 12]$ (GRH)
16.0.18397442524921103360102400000000000000.1	x^16 + 30x^14 + 2080x^12 + 12320x^10 + 20240x^8 - 1020800x^6 + 258988800x^4 + 3940854400x^2 + 37449990400	\( 2^{24}\cdot 3^{8}\cdot 5^{14}\cdot 7^{8}\cdot 41^{6} \)	16T813	$[2, 4, 12]$ (GRH)
16.0.18397442524921103360102400000000000000.2	x^16 - 70x^14 + 3220x^12 - 102040x^10 + 2828640x^8 - 59208800x^6 + 910331200x^4 - 8271372800x^2 + 37449990400	\( 2^{24}\cdot 3^{8}\cdot 5^{14}\cdot 7^{8}\cdot 41^{6} \)	16T813	$[2, 4, 12]$ (GRH)
16.8.14009685799460036277781846932413291015625.1	x^16 - 114x^14 - 246x^13 + 2908x^12 + 9471x^11 + 13226x^10 - 48585x^9 - 246448x^8 + 2069598x^7 - 3949556x^6 - 11279715x^5 - 48085035x^4 + 153830565x^3 + 73641130x^2 - 36260400x + 3013600	\( 3^{8}\cdot 5^{10}\cdot 7^{8}\cdot 41^{14} \)	16T813	$[2, 4, 8]$ (GRH)
16.8.14009685799460036277781846932413291015625.2	x^16 - 8x^15 - 142x^14 + 1052x^13 + 7883x^12 - 51539x^11 - 216639x^10 + 1162594x^9 + 2984096x^8 - 11815071x^7 - 16940841x^6 + 54157635x^5 + 19776230x^4 - 484341650x^3 - 599158350x^2 + 1880620875x - 791780750	\( 3^{8}\cdot 5^{10}\cdot 7^{8}\cdot 41^{14} \)	16T813	$[2, 4, 8]$ (GRH)
16.12.112309106399498694797369730826240000000000.1	x^16 - 310x^14 + 25877x^12 - 67600x^10 - 32992534x^8 + 166231270x^6 + 8646624140x^4 - 39508786100x^2 + 25951599025	\( 2^{24}\cdot 5^{10}\cdot 71^{8}\cdot 101^{6} \)	16T813	$[2, 2]$ (GRH)
16.4.112309106399498694797369730826240000000000.1	x^16 + 50x^14 - 19303x^12 - 1539640x^10 - 42903454x^8 - 497016410x^6 - 1747851460x^4 + 4458422800x^2 + 25951599025	\( 2^{24}\cdot 5^{10}\cdot 71^{8}\cdot 101^{6} \)	16T813	$[2, 2, 2, 2]$ (GRH)
16.12.112309106399498694797369730826240000000000.2	x^16 - 50x^14 - 19303x^12 + 1539640x^10 - 42903454x^8 + 497016410x^6 - 1747851460x^4 - 4458422800x^2 + 25951599025	\( 2^{24}\cdot 5^{10}\cdot 71^{8}\cdot 101^{6} \)	16T813	$[2, 2]$ (GRH)
16.4.1145665194381286185627968624158474240000000000.1	x^16 - 18x^14 - 5214x^13 + 73695x^12 - 1032102x^11 + 13090654x^10 - 34026026x^9 - 1092134344x^8 - 18844746598x^7 + 120057079608x^6 - 778584634754x^5 + 12138022544004x^4 + 25818046094220x^3 - 669485660464680x^2 + 2187279234337270x - 444209861085895	\( 2^{24}\cdot 5^{10}\cdot 71^{8}\cdot 101^{8} \)	16T813	$[2, 2, 2, 2, 4, 4]$ (GRH)
16.8.420102507961629136806462464459178014450156250000.1	x^16 - 4x^15 - 1038x^14 + 3917x^13 + 245444x^12 - 216786x^11 + 3587876x^10 - 145368967x^9 - 1562627365x^8 + 3884178456x^7 - 5170631142x^6 - 60744177080x^5 + 104223811504x^4 + 101334149360x^3 + 615788347520x^2 - 2334652019200x + 1480098257920	\( 2^{4}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8}\cdot 37^{4}\cdot 41^{14} \)	16T813	$[2, 2, 2, 8, 8]$ (GRH)
16.8.420102507961629136806462464459178014450156250000.2	x^16 - 6x^15 - 511x^14 + 2893x^13 - 95772x^12 + 3821262x^11 - 31999820x^10 - 127119113x^9 + 4325628545x^8 - 31134488218x^7 + 185224572711x^6 - 1648592706546x^5 + 9840293716774x^4 - 5131102198184x^3 - 221066965507360x^2 + 391275792985264x + 1284521964547264	\( 2^{4}\cdot 3^{8}\cdot 5^{10}\cdot 7^{8}\cdot 37^{4}\cdot 41^{14} \)	16T813	$[2, 2, 4, 8, 8]$ (GRH)
16.16.162393855437479514050983820757859401106269862363136.1	x^16 - 1244x^14 + 606551x^12 - 147646866x^10 + 18976436546x^8 - 1264961735700x^6 + 40283145849176x^4 - 511323407119984x^2 + 1009289184953344	\( 2^{26}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 12]$ (GRH)
16.8.162393855437479514050983820757859401106269862363136.1	x^16 - 862x^14 + 138966x^12 + 3513246x^10 - 558556815x^8 - 9719978496x^6 + 533135995896x^4 + 10352687231872x^2 + 6668459216896	\( 2^{26}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 12]$ (GRH)
16.16.162393855437479514050983820757859401106269862363136.2	x^16 - 1501x^14 + 911285x^12 - 286021943x^10 + 49105808800x^8 - 4480851471638x^6 + 197363433219140x^4 - 3937312460664784x^2 + 28613530403758336	\( 2^{26}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 12]$ (GRH)
16.0.649575421749918056203935283031437604425079449452544.1	x^16 + 1501x^14 + 911285x^12 + 286021943x^10 + 49105808800x^8 + 4480851471638x^6 + 197363433219140x^4 + 3937312460664784x^2 + 28613530403758336	\( 2^{28}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 2, 2, 4, 24, 8126040]$ (GRH)
16.8.649575421749918056203935283031437604425079449452544.1	x^16 + 862x^14 + 138966x^12 - 3513246x^10 - 558556815x^8 + 9719978496x^6 + 533135995896x^4 - 10352687231872x^2 + 6668459216896	\( 2^{28}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 4, 12]$ (GRH)
16.0.2598301686999672224815741132125750417700317797810176.1	x^16 + 1413x^14 + 640747x^12 + 122467295x^10 + 9850573750x^8 + 279518044450x^6 + 1590760453744x^4 + 708784500408x^2 + 1082146816	\( 2^{30}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 2, 2, 4, 12, 32390040]$ (GRH)
16.8.187381214367639282787301532684742893490174895091410698240000000000.1	x^16 - 86874x^14 - 8522437947x^12 + 549770950990792x^10 + 12945257956415288274x^8 - 403100026764513865076870x^6 - 4195653086671836716753682900x^4 + 82597434109237025018114418481500x^2 + 43298734145286098398063387496619025	\( 2^{24}\cdot 5^{10}\cdot 11^{2}\cdot 71^{8}\cdot 101^{6}\cdot 1579^{2}\cdot 4159^{2}\cdot 17881^{2} \)	16T813	n/a