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 all 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.610923695025433870336.1	x^16 - 6x^15 + 16x^14 - 26x^13 + 34x^12 - 46x^11 + 69x^10 - 104x^9 + 82x^8 + 52x^7 - 95x^6 - 86x^5 + 190x^4 - 112x^3 + 56x^2 - 8x - 13	\( 2^{20}\cdot 17^{12} \)	16T1161	Trivial
16.8.610923695025433870336.1	x^16 + 5x^14 + 7x^12 + 9x^10 - 26x^8 - 25x^6 + 41x^4 - 12x^2 + 1	\( 2^{20}\cdot 17^{12} \)	16T1161	Trivial
16.4.9774779120406941925376.1	x^16 - 5x^14 + 7x^12 - 9x^10 - 26x^8 + 25x^6 + 41x^4 + 12x^2 + 1	\( 2^{24}\cdot 17^{12} \)	16T1161	$[2]$
16.8.9774779120406941925376.1	x^16 + 2x^14 - 22x^12 + 12x^10 - 15x^8 + 74x^6 + 20x^4 - 72x^2 + 16	\( 2^{24}\cdot 17^{12} \)	16T1161	Trivial
16.0.146202125884644293212890625.1	x^16 + 11x^14 - 25x^13 + 97x^12 + 125x^11 - 132x^10 - 200x^9 - 1880x^8 + 3705x^7 - 528x^6 - 8605x^5 + 20497x^4 - 14930x^3 + 4339x^2 - 11125x + 14771	\( 5^{14}\cdot 11^{10}\cdot 31^{4} \)	16T1161	$[2, 2, 4]$ (GRH)
16.8.146202125884644293212890625.1	x^16 - 7x^15 + 14x^14 - 7x^13 - 32x^12 + 178x^11 - 259x^10 + 574x^9 - 1722x^8 - 462x^7 + 6204x^6 - 12056x^5 + 17028x^4 + 1936x^3 - 32549x^2 + 24079x - 3509	\( 5^{14}\cdot 11^{10}\cdot 31^{4} \)	16T1161	$[2]$ (GRH)
16.0.749636144106256000000000000.1	x^16 - 4x^15 - 25x^14 - 64x^13 + 600x^12 + 2070x^11 + 1977x^10 - 10446x^9 + 9097x^8 + 52332x^7 + 67733x^6 - 395902x^5 + 134818x^4 + 331560x^3 + 760059x^2 - 1804726x + 1021031	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 61^{2}\cdot 101^{4} \)	16T1161	$[4]$ (GRH)
16.12.751923235065182967870521344.1	x^16 - 32x^14 - 48x^13 + 196x^12 + 688x^11 + 1208x^10 + 496x^9 - 4352x^8 - 8000x^7 - 1952x^6 + 6112x^5 + 9112x^4 + 6560x^3 + 1200x^2 - 672x - 196	\( 2^{62}\cdot 113^{4} \)	16T1161	Trivial (GRH)
16.4.751923235065182967870521344.1	x^16 - 8x^15 + 20x^14 - 8x^13 - 42x^12 + 184x^11 - 28x^10 - 2056x^9 - 1043x^8 + 5104x^7 + 8088x^6 - 5760x^5 - 13748x^4 + 1008x^3 + 8736x^2 + 800x - 862	\( 2^{62}\cdot 113^{4} \)	16T1161	$[2]$ (GRH)
16.0.1635131882791696000000000000.1	x^16 - 8x^15 + 49x^14 - 194x^13 + 952x^12 - 4478x^11 + 21258x^10 - 79934x^9 + 275476x^8 - 842176x^7 + 2544433x^6 - 6811142x^5 + 16013087x^4 - 29495626x^3 + 43412784x^2 - 43770752x + 28550621	\( 2^{16}\cdot 5^{12}\cdot 101^{4}\cdot 991^{2} \)	16T1161	$[2]$ (GRH)
16.12.3007692940260731871482085376.1	x^16 - 48x^14 - 32x^13 + 712x^12 + 784x^11 - 3720x^10 - 4496x^9 + 9130x^8 + 16800x^7 - 6384x^6 - 43664x^5 - 8852x^4 + 55360x^3 + 6616x^2 - 16400x - 2686	\( 2^{64}\cdot 113^{4} \)	16T1161	Trivial (GRH)
16.4.3007692940260731871482085376.1	x^16 + 16x^14 - 16x^13 + 28x^12 - 432x^11 - 432x^10 - 1632x^9 - 1876x^8 + 2176x^7 + 9776x^6 + 9536x^5 + 40112x^4 + 12480x^3 - 1536x^2 + 14848x - 4216	\( 2^{64}\cdot 113^{4} \)	16T1161	$[2]$ (GRH)
16.0.11463919801532416000000000000.1	x^16 - 6x^15 + 64x^14 - 340x^13 + 1948x^12 - 8352x^11 + 33828x^10 - 113188x^9 + 352922x^8 - 904216x^7 + 2222292x^6 - 4249040x^5 + 8233280x^4 - 10858344x^3 + 16315160x^2 - 11583064x + 13011916	\( 2^{28}\cdot 5^{12}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2, 2, 2, 130]$ (GRH)
16.0.11463919801532416000000000000.2	x^16 + 32x^14 - 8x^13 + 482x^12 - 252x^11 + 3724x^10 - 1724x^9 + 15990x^8 + 1164x^7 + 40612x^6 + 86476x^5 + 67782x^4 + 165288x^3 + 3152x^2 - 46464x + 581341	\( 2^{28}\cdot 5^{12}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2, 2, 2, 144]$ (GRH)
16.0.17690457232041959478759765625.1	x^16 - 2x^15 + 6x^14 + 2x^13 + 36x^12 - 36x^11 + 209x^10 + 121x^9 + 1407x^8 + 991x^7 + 4304x^6 + 8509x^5 + 32641x^4 + 28017x^3 + 27016x^2 + 22638x + 7051	\( 5^{14}\cdot 11^{12}\cdot 31^{4} \)	16T1161	$[2, 2, 4]$ (GRH)
16.8.17690457232041959478759765625.1	x^16 - 6x^15 - 9x^14 + 206x^13 - 667x^12 - 996x^11 + 12624x^10 - 29212x^9 - 28502x^8 + 281034x^7 - 509054x^6 - 55712x^5 + 1428728x^4 - 1607112x^3 - 305141x^2 + 1482888x - 668819	\( 5^{14}\cdot 11^{12}\cdot 31^{4} \)	16T1161	$[2]$ (GRH)
16.0.25376112779001856000000000000.1	x^16 - 4x^15 + 48x^14 - 124x^13 + 572x^12 - 720x^11 + 1872x^10 - 192x^9 + 8220x^8 + 5168x^7 + 35392x^6 + 153760x^5 + 118432x^4 - 73184x^3 - 63872x^2 + 49696x + 41936	\( 2^{28}\cdot 5^{12}\cdot 61^{2}\cdot 101^{4} \)	16T1161	$[2, 4]$ (GRH)
16.0.25376112779001856000000000000.2	x^16 - 8x^15 + 32x^14 + 44x^13 - 472x^12 + 1296x^11 + 2144x^10 - 5628x^9 + 5738x^8 + 24x^7 - 18944x^6 + 50868x^5 + 85328x^4 - 73952x^3 - 832x^2 + 244956x + 198301	\( 2^{28}\cdot 5^{12}\cdot 61^{2}\cdot 101^{4} \)	16T1161	$[2, 4]$ (GRH)
16.8.286597995038310400000000000000.1	x^16 - 2x^15 - 16x^14 + 58x^13 - 92x^12 - 132x^11 + 1226x^10 - 3726x^9 + 10063x^8 - 20052x^7 + 21174x^6 + 136214x^5 - 738912x^4 + 1644726x^3 - 2066094x^2 + 1426384x - 410419	\( 2^{28}\cdot 5^{14}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2]$ (GRH)
16.8.286597995038310400000000000000.2	x^16 - 2x^15 - 60x^14 + 50x^13 + 1030x^12 + 704x^11 - 2378x^10 - 28590x^9 - 41115x^8 + 277040x^7 - 101178x^6 - 1427454x^5 + 792520x^4 + 2128630x^3 - 646350x^2 - 2877768x + 857261	\( 2^{28}\cdot 5^{14}\cdot 41^{2}\cdot 101^{4} \)	16T1161	$[2]$ (GRH)
16.0.698337529849446400000000000000.1	x^16 + 28x^14 + 398x^12 + 6436x^10 + 46595x^8 + 108916x^6 + 123538x^4 + 65448x^2 + 10201	\( 2^{40}\cdot 5^{14}\cdot 101^{4} \)	16T1161	$[2, 2]$ (GRH)
16.8.698337529849446400000000000000.1	x^16 - 32x^14 + 58x^12 + 3436x^10 + 195x^8 - 81204x^6 + 262758x^4 - 352692x^2 + 10201	\( 2^{40}\cdot 5^{14}\cdot 101^{4} \)	16T1161	Trivial (GRH)
16.0.698337529849446400000000000000.2	x^16 + 44x^14 + 702x^12 + 5812x^10 + 21715x^8 + 81428x^6 + 186402x^4 + 143016x^2 + 10201	\( 2^{40}\cdot 5^{14}\cdot 101^{4} \)	16T1161	$[2, 2]$ (GRH)
16.8.698337529849446400000000000000.2	x^16 - 24x^14 - 20x^13 - 318x^12 + 1120x^11 + 9668x^10 - 7480x^9 - 81135x^8 + 11200x^7 + 304472x^6 - 33880x^5 - 388788x^4 + 178840x^3 - 23276x^2 - 313580x - 5279	\( 2^{40}\cdot 5^{14}\cdot 101^{4} \)	16T1161	Trivial (GRH)
16.0.1096614972044148736000000000000.1	x^16 - 8x^15 + 112x^14 - 596x^13 + 3868x^12 - 15024x^11 + 57824x^10 - 158208x^9 + 397768x^8 - 773696x^7 + 1322496x^6 - 1888832x^5 + 3030528x^4 - 3840832x^3 + 6567808x^2 + 2194816x + 180416	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 401^{2} \)	16T1161	$[2, 4]$ (GRH)
16.0.1096614972044148736000000000000.2	x^16 - 8x^15 + 40x^14 - 64x^13 - 362x^12 + 2836x^11 - 6096x^10 + 4624x^9 + 70415x^8 - 47372x^7 + 244888x^6 + 46256x^5 + 1536022x^4 + 1200356x^3 + 1874192x^2 + 95552x + 409781	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 401^{2} \)	16T1161	$[2, 4]$ (GRH)
16.16.2802086158223343616000000000000.1	x^16 - 2x^15 - 118x^14 + 212x^13 + 5262x^12 - 6530x^11 - 116802x^10 + 54126x^9 + 1336235x^8 + 544174x^7 - 6580482x^6 - 8196670x^5 + 3280572x^4 + 7052948x^3 + 385812x^2 - 1016658x + 125561	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 641^{2} \)	16T1161	Trivial (GRH)
16.8.2802086158223343616000000000000.1	x^16 - 6x^15 + 12x^14 - 48x^13 - 648x^12 + 2724x^11 + 4892x^10 + 8816x^9 - 18510x^8 - 286176x^7 + 139904x^6 - 127328x^5 + 675772x^4 + 716008x^3 - 5902568x^2 + 4399080x - 826564	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 641^{2} \)	16T1161	Trivial (GRH)
16.16.2802086158223343616000000000000.2	x^16 - 2x^15 - 94x^14 + 310x^13 + 3058x^12 - 13934x^11 - 38738x^10 + 266166x^9 + 83602x^8 - 2407142x^7 + 2128918x^6 + 9687290x^5 - 16400650x^4 - 11366298x^3 + 34410890x^2 - 6290462x - 12845159	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 641^{2} \)	16T1161	Trivial (GRH)
16.8.2802086158223343616000000000000.2	x^16 - 110x^13 - 766x^12 + 250x^11 - 940x^10 + 18540x^9 + 18321x^8 + 36470x^7 + 38600x^6 - 860760x^5 + 677094x^4 - 1927690x^3 + 1945660x^2 + 3510750x - 1556119	\( 2^{28}\cdot 5^{12}\cdot 101^{4}\cdot 641^{2} \)	16T1161	Trivial (GRH)
16.0.5335806592471429065121743241216.1	x^16 + 120x^12 + 320x^10 + 2072x^8 + 6656x^6 + 23520x^4 + 45824x^2 + 35344	\( 2^{74}\cdot 7^{10} \)	16T1161	$[2, 10]$ (GRH)
16.4.5335806592471429065121743241216.1	x^16 - 24x^14 + 140x^12 + 680x^10 - 5806x^8 + 14184x^6 - 8748x^4 - 3448x^2 + 529	\( 2^{74}\cdot 7^{10} \)	16T1161	$[2]$ (GRH)
16.0.5335806592471429065121743241216.2	x^16 + 120x^12 - 320x^10 + 2072x^8 - 6656x^6 + 23520x^4 - 45824x^2 + 35344	\( 2^{74}\cdot 7^{10} \)	16T1161	$[2, 10]$ (GRH)
16.4.5335806592471429065121743241216.2	x^16 + 24x^14 + 140x^12 - 680x^10 - 5806x^8 - 14184x^6 - 8748x^4 + 3448x^2 + 529	\( 2^{74}\cdot 7^{10} \)	16T1161	$[2]$ (GRH)
16.4.162407121785611878400000000000000.1	x^16 + 120x^14 + 5770x^12 + 102740x^10 - 317165x^8 - 19444500x^6 - 46530250x^4 - 938320300x^2 + 948948025	\( 2^{36}\cdot 5^{14}\cdot 61^{2}\cdot 101^{4} \)	16T1161	$[2, 4]$ (GRH)
16.4.162407121785611878400000000000000.2	x^16 + 60x^14 + 880x^12 - 37820x^10 - 1146490x^8 - 10099500x^6 - 55698400x^4 - 284022100x^2 + 948948025	\( 2^{36}\cdot 5^{14}\cdot 61^{2}\cdot 101^{4} \)	16T1161	$[2, 2]$ (GRH)