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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.9091934501760000000000.1	x^16 - 2x^14 - 25x^12 + 71x^10 + 119x^8 - 495x^6 - 330x^4 + 2475x^2 - 2475	\( -\,2^{16}\cdot 3^{6}\cdot 5^{10}\cdot 11^{7} \)	16T1558	Trivial
16.2.9091934501760000000000.2	x^16 - 7x^14 + 28x^12 - 62x^10 + 26x^8 + 330x^6 - 1155x^4 + 2475x^2 - 2475	\( -\,2^{16}\cdot 3^{6}\cdot 5^{10}\cdot 11^{7} \)	16T1558	Trivial
16.12.2131503570359500313600000000.1	x^16 - 39x^14 + 570x^12 - 3546x^10 + 4474x^8 + 44109x^6 - 143260x^4 + 4901x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	Trivial (GRH)
16.4.2131503570359500313600000000.1	x^16 + 13x^14 - 241x^12 - 3503x^10 - 7311x^8 + 32422x^6 + 83317x^4 + 49010x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2]$ (GRH)
16.12.2131503570359500313600000000.2	x^16 - 28x^14 + 212x^12 + 293x^10 - 8257x^8 + 22243x^6 + 377x^4 - 14703x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	Trivial (GRH)
16.4.2131503570359500313600000000.2	x^16 + 28x^14 + 134x^12 - 1677x^10 - 16242x^8 - 47879x^6 - 49764x^4 - 4901x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2]$ (GRH)
16.8.2131503570359500313600000000.5	x^16 - 11x^14 - 160x^12 + 946x^10 + 9904x^8 - 2639x^6 - 107445x^4 - 78416x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	Trivial (GRH)
16.8.2131503570359500313600000000.6	x^16 + 11x^14 - 127x^12 - 746x^10 + 6638x^8 - 7917x^6 - 14703x^4 + 14703x^2 + 4901	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2]$ (GRH)
16.16.35789621892199165414211328125.1	x^16 - 57x^14 - 26x^13 + 1311x^12 + 1074x^11 - 15461x^10 - 16935x^9 + 98370x^8 + 126777x^7 - 324977x^6 - 449307x^5 + 497217x^4 + 638886x^3 - 336979x^2 - 267154x + 81089	\( 5^{8}\cdot 13^{6}\cdot 29^{7}\cdot 1049^{2} \)	16T1558	Trivial (GRH)
16.0.545664914012032080281600000000.1	x^16 - 4x^14 - 340x^12 + 4274x^10 + 21474x^8 - 417716x^6 + 567385x^4 + 14046266x^2 + 4709861	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2, 4]$ (GRH)
16.4.545664914012032080281600000000.1	x^16 - 6x^15 + 16x^14 - 116x^13 - 96x^12 + 222x^11 - 828x^10 + 8092x^9 + 48234x^8 - 34630x^7 - 385816x^6 - 218166x^5 + 750695x^4 + 686428x^3 + 299738x^2 + 555822x + 153781	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[4]$ (GRH)
16.8.545664914012032080281600000000.1	x^16 + 4x^14 - 340x^12 - 4274x^10 + 21474x^8 + 417716x^6 + 567385x^4 - 14046266x^2 + 4709861	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2, 2]$ (GRH)
16.0.545664914012032080281600000000.2	x^16 - 4x^15 + 42x^14 - 230x^13 + 1266x^12 - 4418x^11 + 14360x^10 - 41668x^9 + 124109x^8 - 286190x^7 + 453076x^6 - 383612x^5 - 42224x^4 + 413450x^3 - 222246x^2 - 123442x + 250591	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[2, 4]$ (GRH)
16.4.545664914012032080281600000000.2	x^16 - 6x^15 + 62x^13 - 422x^12 + 2942x^11 - 15204x^10 + 64178x^9 - 227924x^8 + 739742x^7 - 2032096x^6 + 4655210x^5 - 9192746x^4 + 15503434x^3 - 20821468x^2 + 17185382x - 5372621	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[4]$ (GRH)
16.8.545664914012032080281600000000.2	x^16 - 4x^15 - 36x^14 + 88x^13 + 1143x^12 - 3082x^11 - 14066x^10 + 47012x^9 + 69843x^8 - 294992x^7 - 174982x^6 + 856700x^5 + 436787x^4 - 1275944x^3 - 877846x^2 + 805466x + 703921	\( 2^{24}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7} \)	16T1558	$[4]$ (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)
16.16.1022187390863100363395289742578125.1	x^16 - 3x^15 - 246x^14 + 946x^13 + 20060x^12 - 88305x^11 - 734082x^10 + 3680393x^9 + 12415935x^8 - 75326536x^7 - 73978895x^6 + 716474892x^5 - 173717859x^4 - 2428250331x^3 + 1392532762x^2 + 1942920230x - 120710321	\( 5^{8}\cdot 13^{10}\cdot 29^{7}\cdot 1049^{2} \)	16T1558	$[2]$ (GRH)
16.0.2345508660327164504585753600000000.1	x^16 + 260x^14 + 26620x^12 + 1377210x^10 + 38263662x^8 + 559128700x^6 + 3928831985x^4 + 10745001410x^2 + 5393065301	\( 2^{16}\cdot 5^{8}\cdot 13^{6}\cdot 29^{7}\cdot 1049^{2} \)	16T1558	$[2, 2, 2, 99742]$ (GRH)