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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.30037248999755776.1	x^16 - 2x^14 + 2x^12 - 3x^10 + 7x^8 - 8x^6 + 5x^4 - 2x^2 + 1	\( 2^{12}\cdot 41^{2}\cdot 257^{4} \)	16T1538	Trivial
16.0.36859674750877696.1	x^16 - 3x^14 + 4x^12 + 2x^10 - 8x^8 + x^6 + 10x^4 - 6x^2 + 1	\( 2^{20}\cdot 433^{4} \)	16T1538	Trivial
16.0.73190108211183616.2	x^16 - 2x^15 - x^14 - 2x^13 + 14x^12 - 6x^11 - 27x^10 + 26x^9 + 34x^8 - 26x^7 - 27x^6 + 6x^5 + 14x^4 + 2x^3 - x^2 + 2x + 1	\( 2^{24}\cdot 257^{4} \)	16T1538	Trivial
16.0.83387253522694144.1	x^16 + x^12 - x^10 + 2x^8 - x^6 + x^4 + 1	\( 2^{18}\cdot 751^{4} \)	16T1538	Trivial
16.0.107613222848167936.1	x^16 - 2x^15 - 6x^14 + 12x^13 + 13x^12 - 18x^11 - 24x^10 - 12x^9 + 67x^8 + 16x^7 - 54x^6 - 30x^5 + 45x^4 + 4x^3 - 24x^2 + 6x + 7	\( 2^{24}\cdot 283^{4} \)	16T1538	Trivial
16.4.107613222848167936.1	x^16 - 2x^15 + 4x^12 - 24x^11 + 58x^10 - 100x^9 + 130x^8 - 138x^7 + 130x^6 - 108x^5 + 93x^4 - 74x^3 + 38x^2 - 10x + 1	\( 2^{24}\cdot 283^{4} \)	16T1538	Trivial
16.4.107613222848167936.2	x^16 - 2x^15 + 2x^14 - 10x^13 + 9x^12 + 16x^11 - 24x^10 + 2x^9 + 6x^8 + 12x^7 + 6x^6 - 36x^5 + 4x^4 + 20x^3 - 6x^2 - 2x + 1	\( 2^{24}\cdot 283^{4} \)	16T1538	Trivial
16.0.121485239855939584.1	x^16 + x^14 + 2x^12 + 3x^10 + 3x^8 + 3x^6 + 2x^4 + x^2 + 1	\( 2^{16}\cdot 17^{2}\cdot 283^{4} \)	16T1538	Trivial
16.0.121485239855939584.2	x^16 - x^14 + 2x^12 - 3x^10 + 3x^8 - 3x^6 + 2x^4 - x^2 + 1	\( 2^{16}\cdot 17^{2}\cdot 283^{4} \)	16T1538	Trivial
16.0.132947020994904064.1	x^16 + 2x^14 + 2x^12 + x^10 + x^8 + x^6 + 2x^4 + 2x^2 + 1	\( 2^{16}\cdot 13^{2}\cdot 331^{4} \)	16T1538	Trivial
16.0.3897476000608485376.1	x^16 + x^14 + 9x^10 + 23x^8 + 16x^6 + 5x^4 + 8x^2 + 4	\( 2^{16}\cdot 2777^{4} \)	16T1538	Trivial
16.4.3897476000608485376.1	x^16 + 7x^14 + 22x^12 + 36x^10 + 30x^8 - 16x^6 - 15x^4 - 8x^2 + 4	\( 2^{16}\cdot 2777^{4} \)	16T1538	Trivial
16.0.3897476000608485376.2	x^16 - 7x^14 + 22x^12 - 36x^10 + 30x^8 + 16x^6 - 15x^4 + 8x^2 + 4	\( 2^{16}\cdot 2777^{4} \)	16T1538	Trivial
16.4.3897476000608485376.2	x^16 - x^14 - 9x^10 + 23x^8 - 16x^6 + 5x^4 - 8x^2 + 4	\( 2^{16}\cdot 2777^{4} \)	16T1538	Trivial
16.8.15336535719789789184.1	x^16 + x^14 - 2x^12 - 2x^10 + 6x^8 - 21x^6 + 24x^4 - 9x^2 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1538	Trivial
16.0.15589904002433941504.1	x^16 + 5x^14 + 5x^12 + 2x^10 + 6x^8 + 2x^6 + 5x^4 + 5x^2 + 1	\( 2^{18}\cdot 2777^{4} \)	16T1538	Trivial
16.4.15589904002433941504.1	x^16 + 5x^14 - x^12 - 14x^10 + 9x^8 + 35x^6 - 16x^4 - 36x^2 + 1	\( 2^{18}\cdot 2777^{4} \)	16T1538	Trivial
16.4.15589904002433941504.2	x^16 - 4x^14 - x^12 + 4x^10 - 14x^8 + 27x^6 - 61x^4 + 63x^2 + 1	\( 2^{18}\cdot 2777^{4} \)	16T1538	Trivial
16.8.17464833213656006656.1	x^16 - 2x^14 - 9x^12 + 13x^10 + 9x^8 - 29x^6 + 28x^4 - 11x^2 + 1	\( 2^{16}\cdot 149^{2}\cdot 331^{4} \)	16T1538	Trivial
16.8.62359616009735766016.1	x^16 - 5x^14 + 5x^12 - 2x^10 + 6x^8 - 2x^6 + 5x^4 - 5x^2 + 1	\( 2^{20}\cdot 2777^{4} \)	16T1538	Trivial
16.8.98346354593429979136.2	x^16 - 8x^14 + 36x^12 - 104x^10 + 188x^8 - 208x^6 + 132x^4 - 40x^2 + 4	\( 2^{32}\cdot 389^{4} \)	16T1538	Trivial
16.8.128860300270118047744.1	x^16 - 7x^14 - x^12 + 43x^10 + 49x^8 + 43x^6 - x^4 - 7x^2 + 1	\( 2^{12}\cdot 23^{2}\cdot 2777^{4} \)	16T1538	Trivial
16.0.411517823199348326400.1	x^16 + 8x^14 + 20x^12 + 21x^10 + 25x^8 + 21x^6 + 20x^4 + 8x^2 + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{2}\cdot 1327^{4} \)	16T1538	Trivial
16.8.411517823199348326400.1	x^16 - 8x^14 + 20x^12 - 21x^10 + 25x^8 - 21x^6 + 20x^4 - 8x^2 + 1	\( 2^{16}\cdot 3^{4}\cdot 5^{2}\cdot 1327^{4} \)	16T1538	Trivial
16.0.439325380186051710976.1	x^16 - x^14 + 10x^12 - 32x^10 + 121x^8 - 168x^6 + 258x^4 - 157x^2 + 49	\( 2^{12}\cdot 18097^{4} \)	16T1538	$[2]$
16.0.439325380186051710976.2	x^16 + 6x^14 - 3x^12 + 2x^10 + 4x^8 + 2x^6 - 3x^4 + 6x^2 + 1	\( 2^{12}\cdot 18097^{4} \)	16T1538	$[2]$
16.12.921365448100612734976.1	x^16 - 10x^14 + 35x^12 - 55x^10 + 54x^8 - 55x^6 + 35x^4 - 10x^2 + 1	\( 2^{16}\cdot 10889^{4} \)	16T1538	Trivial (GRH)
16.4.921365448100612734976.1	x^16 - 3x^14 + 2x^12 - 2x^10 - 2x^6 + 2x^4 - 3x^2 + 1	\( 2^{16}\cdot 10889^{4} \)	16T1538	$[2]$
16.4.1700324243277261705216.1	x^16 - 4x^14 - 4x^10 + 32x^8 - 16x^6 - 256x^2 + 256	\( 2^{12}\cdot 3^{4}\cdot 8461^{4} \)	16T1538	Trivial
16.12.3685461792402450939904.1	x^16 - 13x^14 + 42x^12 + 13x^10 - 150x^8 + 13x^6 + 42x^4 - 13x^2 + 1	\( 2^{18}\cdot 10889^{4} \)	16T1538	Trivial
16.8.3953928421674465398784.1	x^16 - 7x^15 + 10x^14 + 29x^13 - 79x^12 - 25x^11 + 184x^10 - 5x^9 - 236x^8 + 5x^7 + 184x^6 + 25x^5 - 79x^4 - 29x^3 + 10x^2 + 7x + 1	\( 2^{12}\cdot 3^{2}\cdot 18097^{4} \)	16T1538	Trivial
16.8.3953928421674465398784.2	x^16 - x^15 - 6x^14 + 28x^13 - 30x^12 - 79x^11 + 218x^10 - 239x^9 + 145x^8 + 55x^7 - 170x^6 + 67x^5 + 44x^4 + 4x^3 - 12x^2 - 7x - 1	\( 2^{12}\cdot 3^{2}\cdot 18097^{4} \)	16T1538	Trivial
16.0.359456226794218697261056.1	x^16 + x^14 - 16x^12 - x^10 + 206x^8 - 9x^6 - 1296x^4 + 729x^2 + 6561	\( 2^{20}\cdot 24197^{4} \)	16T1538	$[10]$
16.16.359456226794218697261056.1	x^16 - 20x^14 + 145x^12 - 501x^10 + 891x^8 - 813x^6 + 353x^4 - 64x^2 + 4	\( 2^{20}\cdot 24197^{4} \)	16T1538	Trivial (GRH)
16.0.1065611167477530053204224.1	x^16 - 2x^15 + 9x^14 - 24x^13 + 72x^12 - 198x^11 + 464x^10 - 886x^9 + 1700x^8 - 2548x^7 + 3521x^6 - 4306x^5 + 4692x^4 - 4164x^3 + 3406x^2 - 1696x + 743	\( 2^{8}\cdot 197^{2}\cdot 18097^{4} \)	16T1538	$[2, 8]$
16.0.1437824907176874789044224.1	x^16 + 20x^14 + 145x^12 + 501x^10 + 891x^8 + 813x^6 + 353x^4 + 64x^2 + 4	\( 2^{22}\cdot 24197^{4} \)	16T1538	$[2, 8]$
16.16.1437824907176874789044224.1	x^16 - 31x^14 + 260x^12 - 987x^10 + 1941x^8 - 2020x^6 + 1064x^4 - 248x^2 + 16	\( 2^{22}\cdot 24197^{4} \)	16T1538	Trivial (GRH)
16.0.1585306957994745552935449.1	x^16 - 3x^15 + 6x^14 - 5x^13 + 110x^12 + 27x^11 + 432x^10 - 153x^9 + 1928x^8 - 29x^7 + 1494x^6 - 3245x^5 + 542x^4 - 1231x^3 + 881x^2 + 196x + 16	\( 997^{2}\cdot 35537^{4} \)	16T1538	Trivial
16.0.6493417299946477784823599104.1	x^16 - x^15 - 14x^14 - 75x^13 + 281x^12 + 1240x^11 + 407x^10 - 12353x^9 - 27279x^8 + 28070x^7 + 153512x^6 + 337912x^5 + 722669x^4 + 790635x^3 + 535039x^2 + 1184076x + 1245456	\( 2^{12}\cdot 997^{2}\cdot 35537^{4} \)	16T1538	$[2]$ (GRH)
16.0.196070675502739156742348734464.1	x^16 + 26x^14 - 162x^13 + 508x^12 - 2962x^11 + 13584x^10 - 43238x^9 + 137070x^8 - 449230x^7 + 1204442x^6 - 2277300x^5 + 5564157x^4 - 14652992x^3 + 9205006x^2 + 9782862x + 16075687	\( 2^{24}\cdot 3^{2}\cdot 19^{4}\cdot 97^{4}\cdot 103^{4} \)	16T1538	$[2, 2, 44]$ (GRH)