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 29 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.11291175054931640625.1	x^16 - 5x^15 + 12x^14 - 15x^13 - 7x^12 + 60x^11 - 91x^10 + 25x^9 + 105x^8 - 160x^7 + 59x^6 + 75x^5 - 97x^4 + 30x^3 + 12x^2 - 10x + 1	\( 3^{12}\cdot 5^{14}\cdot 59^{2} \)	16T1162	Trivial
16.4.11291175054931640625.2	x^16 - 3x^15 + 6x^14 - 12x^13 + x^12 - 9x^11 - 21x^10 + 24x^9 - 33x^8 + 24x^7 - 21x^6 - 9x^5 + x^4 - 12x^3 + 6x^2 - 3x + 1	\( 3^{12}\cdot 5^{14}\cdot 59^{2} \)	16T1162	Trivial
16.8.9463398400000000000000.1	x^16 - 8x^15 + 16x^14 + 8x^13 - 29x^12 - 4x^11 - 16x^10 + 4x^9 + 37x^8 + 4x^7 - 16x^6 - 4x^5 - 29x^4 + 8x^3 + 16x^2 - 8x + 1	\( 2^{32}\cdot 5^{14}\cdot 19^{2} \)	16T1162	Trivial
16.8.9463398400000000000000.2	x^16 - 4x^15 - 6x^14 + 36x^13 - 4x^12 - 152x^11 + 176x^10 + 448x^9 - 543x^8 - 588x^7 + 506x^6 + 12x^5 - 314x^4 + 104x^3 + 44x^2 - 16x - 4	\( 2^{32}\cdot 5^{14}\cdot 19^{2} \)	16T1162	Trivial (GRH)
16.12.151414374400000000000000.1	x^16 - 8x^15 + 6x^14 + 88x^13 - 144x^12 - 404x^11 + 704x^10 + 1104x^9 - 1438x^8 - 1936x^7 + 1084x^6 + 1816x^5 + 156x^4 - 472x^3 - 224x^2 - 48x - 4	\( 2^{36}\cdot 5^{14}\cdot 19^{2} \)	16T1162	Trivial (GRH)
16.8.178776752400000000000000.1	x^16 - 8x^15 + 25x^14 - 20x^13 - 115x^12 + 406x^11 - 353x^10 - 760x^9 + 2035x^8 - 930x^7 - 2168x^6 + 2484x^5 + 280x^4 - 800x^3 - 200x^2 + 48x + 16	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 29^{2} \)	16T1162	Trivial (GRH)
16.8.178776752400000000000000.2	x^16 - 2x^15 - 10x^14 + 20x^13 - 10x^12 - 76x^11 + 42x^10 - 240x^9 - 260x^8 + 90x^7 - 288x^6 + 236x^5 + 95x^4 - 10x^3 + 110x^2 + 22x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 29^{2} \)	16T1162	Trivial (GRH)
16.0.790996784400000000000000.1	x^16 + 21x^14 + 112x^12 - 12x^10 - 330x^8 + 822x^6 + 5137x^4 + 7869x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	$[4]$
16.4.790996784400000000000000.1	x^16 - 11x^14 + 47x^12 - 38x^10 - 365x^8 + 1238x^6 - 613x^4 - 2989x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	Trivial
16.8.790996784400000000000000.1	x^16 - 21x^14 + 112x^12 + 12x^10 - 330x^8 - 822x^6 + 5137x^4 - 7869x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	Trivial (GRH)
16.0.790996784400000000000000.2	x^16 + 14x^14 + 62x^12 + 77x^10 - 95x^8 - 197x^6 + 482x^4 + 2806x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	$[4]$
16.4.790996784400000000000000.2	x^16 - 21x^14 + 172x^12 - 708x^10 + 1500x^8 - 927x^6 - 2963x^4 + 7686x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	Trivial
16.8.790996784400000000000000.2	x^16 - 14x^14 + 62x^12 - 77x^10 - 95x^8 + 197x^6 + 482x^4 - 2806x^2 + 3721	\( 2^{16}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2} \)	16T1162	Trivial (GRH)
16.12.1717986918400000000000000.1	x^16 - 12x^14 + 48x^12 - 64x^10 - 25x^8 + 116x^6 - 72x^4 + 8x^2 + 1	\( 2^{48}\cdot 5^{14} \)	16T1162	Trivial (GRH)
16.4.1717986918400000000000000.1	x^16 + 4x^14 - 8x^12 - 48x^10 - 30x^8 + 68x^6 + 72x^4 + 16x^2 + 1	\( 2^{48}\cdot 5^{14} \)	16T1162	Trivial
16.4.1717986918400000000000000.2	x^16 + 12x^14 + 48x^12 + 64x^10 - 25x^8 - 116x^6 - 72x^4 - 8x^2 + 1	\( 2^{48}\cdot 5^{14} \)	16T1162	Trivial (GRH)
16.0.48557483622400000000000000.1	x^16 - 4x^15 + 20x^14 - 60x^13 + 185x^12 - 392x^11 + 858x^10 - 1520x^9 + 2270x^8 - 2200x^7 + 2938x^6 - 852x^5 + 1110x^4 + 180x^3 + 390x^2 + 56x + 61	\( 2^{32}\cdot 5^{14}\cdot 1361^{2} \)	16T1162	$[4]$ (GRH)
16.8.48557483622400000000000000.1	x^16 - 2x^14 - 57x^12 - 60x^11 - 74x^10 + 260x^9 + 1200x^8 - 1540x^7 - 1004x^6 + 3820x^5 - 2217x^4 - 4480x^3 + 3608x^2 + 2240x - 1619	\( 2^{32}\cdot 5^{14}\cdot 1361^{2} \)	16T1162	Trivial (GRH)
16.0.68457752166400000000000000.1	x^16 + 8x^14 - 20x^13 + 8x^12 - 40x^11 - 504x^10 + 1300x^9 + 2745x^8 - 6000x^7 - 7324x^6 + 10820x^5 + 16798x^4 - 8600x^3 - 29092x^2 + 2760x + 24341	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	$[4]$ (GRH)
16.12.68457752166400000000000000.1	x^16 - 16x^14 - 60x^13 - 248x^12 - 440x^11 - 108x^10 + 260x^9 + 4625x^8 + 11360x^7 - 5192x^6 - 25620x^5 - 3858x^4 + 13240x^3 + 1096x^2 - 1880x + 181	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	Trivial (GRH)
16.4.68457752166400000000000000.1	x^16 - 4x^15 + 28x^14 - 88x^13 + 396x^12 - 1064x^11 + 3220x^10 - 6884x^9 + 15489x^8 - 26848x^7 + 40380x^6 - 39932x^5 + 11046x^4 + 17444x^3 - 21568x^2 + 6628x - 439	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	Trivial (GRH)
16.0.68457752166400000000000000.2	x^16 - 16x^14 - 20x^13 + 122x^12 + 320x^11 - 668x^10 - 2020x^9 + 2025x^8 + 10640x^7 - 4332x^6 - 43980x^5 + 17132x^4 + 90400x^3 + 45836x^2 - 326000x + 224401	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	$[4]$ (GRH)
16.12.68457752166400000000000000.2	x^16 - 4x^15 - 28x^14 + 128x^13 + 260x^12 - 1568x^11 - 708x^10 + 9644x^9 - 3239x^8 - 31920x^7 + 26700x^6 + 54700x^5 - 67690x^4 - 39060x^3 + 68840x^2 + 2180x - 18295	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	Trivial (GRH)
16.4.68457752166400000000000000.2	x^16 - 4x^14 - 20x^13 - 218x^12 + 320x^11 + 1408x^10 - 2020x^9 - 4290x^8 + 2320x^7 + 4852x^6 + 8740x^5 - 9518x^4 - 14720x^3 + 34384x^2 - 23420x + 6821	\( 2^{40}\cdot 5^{14}\cdot 101^{2} \)	16T1162	Trivial (GRH)
16.0.399539332710400000000000000.1	x^16 - 8x^14 + 38x^12 - 156x^10 + 555x^8 - 1356x^6 + 2558x^4 - 4148x^2 + 3721	\( 2^{44}\cdot 5^{14}\cdot 61^{2} \)	16T1162	$[2, 2]$ (GRH)
16.8.12430715807334400000000000000.1	x^16 - 4x^15 - 4x^14 + 144x^13 - 682x^12 + 436x^11 + 6644x^10 - 33008x^9 + 74193x^8 + 7916x^7 - 501424x^6 + 1471192x^5 - 2949992x^4 + 5180512x^3 - 6557196x^2 + 4631752x - 1330079	\( 2^{40}\cdot 5^{14}\cdot 1361^{2} \)	16T1162	$[2]$ (GRH)
16.16.668819629644740011880603666543017984.1	x^16 - 208x^14 - 144x^13 + 16476x^12 + 18000x^11 - 616768x^10 - 682112x^9 + 11326242x^8 + 7284512x^7 - 101458480x^6 + 10037264x^5 + 359939588x^4 - 260086032x^3 - 289818592x^2 + 347099232x - 87713567	\( 2^{62}\cdot 449^{4}\cdot 1889^{2} \)	16T1162	$[2]$ (GRH)
16.16.1186139225426340374118400000000000000.1	x^16 - 8x^15 - 308x^14 + 2296x^13 + 38866x^12 - 263408x^11 - 2607840x^10 + 15509448x^9 + 101165629x^8 - 500712216x^7 - 2314815140x^6 + 8765075664x^5 + 30570952056x^4 - 76367046112x^3 - 215062276912x^2 + 254794977984x + 624192924176	\( 2^{32}\cdot 5^{14}\cdot 199^{2}\cdot 421^{2}\cdot 2539^{2} \)	16T1162	$[2]$ (GRH)
16.0.23462097005834430807696998400000000000000.1	x^16 - 8x^15 + 412x^14 - 1764x^13 + 63806x^12 - 47388x^11 + 4670180x^10 + 16709548x^9 + 173831769x^8 + 1709712244x^7 + 5006084840x^6 + 60097040484x^5 + 247939978456x^4 + 656088145268x^3 + 8329269294588x^2 - 1393015120376x + 75558851901361	\( 2^{40}\cdot 3^{8}\cdot 5^{14}\cdot 41^{2}\cdot 563021^{2} \)	16T1162	$[2, 2, 4, 31435684]$ (GRH)