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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3692461181640625.1	x^16 - 2x^15 - 2x^14 + 9x^13 - 3x^12 - 15x^11 + 17x^10 + 8x^9 - 25x^8 + 8x^7 + 17x^6 - 15x^5 - 3x^4 + 9x^3 - 2x^2 - 2x + 1	\( 5^{12}\cdot 3889^{2} \)	16T1497	Trivial
16.0.6472705322265625.1	x^16 - x^15 + x^14 + x^13 + 3x^12 + 4x^11 + 4x^10 + 8x^9 + 8x^8 + 9x^7 + 6x^6 + 8x^5 + 8x^4 + 3x^3 + 4x^2 + 3x + 1	\( 5^{12}\cdot 19^{2}\cdot 271^{2} \)	16T1497	Trivial
16.0.6741949462890625.1	x^16 + x^14 - 5x^13 + 2x^12 - 5x^11 + 13x^10 - 10x^9 + 15x^8 - 20x^7 + 17x^6 - 20x^5 + 17x^4 - 10x^3 + 9x^2 - 5x + 1	\( 5^{14}\cdot 1051^{2} \)	16T1497	Trivial
16.0.11610062500000000.1	x^16 - 5x^15 + 15x^14 - 30x^13 + 43x^12 - 40x^11 + 15x^10 + 20x^9 - 36x^8 + 20x^7 + 15x^6 - 35x^5 + 27x^4 - 15x^3 + 10x^2 - 5x + 1	\( 2^{8}\cdot 5^{12}\cdot 431^{2} \)	16T1497	Trivial
16.0.14584336181640625.1	x^16 - 2x^15 + 3x^14 - 2x^13 - 2x^12 + 2x^11 + 2x^10 - 12x^9 + 19x^8 - 15x^7 + 5x^6 + 6x^5 - 8x^4 + 5x^3 - 2x + 1	\( 5^{12}\cdot 59^{2}\cdot 131^{2} \)	16T1497	Trivial
16.0.15010078369140625.1	x^16 - x^15 + 3x^14 - 6x^13 + 9x^12 - 14x^11 + 21x^10 - 24x^9 + 29x^8 - 32x^7 + 33x^6 - 25x^5 + 22x^4 - 17x^3 + 9x^2 - 4x + 1	\( 5^{12}\cdot 7841^{2} \)	16T1497	Trivial
16.0.24068613525390625.1	x^16 - 2x^15 + 4x^14 - 9x^13 + 11x^12 - 16x^11 + 20x^10 - 15x^9 + 17x^8 - 10x^7 - 2x^5 - 4x^4 + 3x^3 + x^2 + x + 1	\( 5^{12}\cdot 9929^{2} \)	16T1497	Trivial
16.0.28323838134765625.1	x^16 - 2x^15 - x^14 + 5x^13 - 2x^12 - 5x^11 + 6x^10 + 2x^9 - 7x^8 + 2x^7 + 6x^6 - 5x^5 - 2x^4 + 5x^3 - x^2 - 2x + 1	\( 5^{12}\cdot 10771^{2} \)	16T1497	Trivial
16.0.31334531494140625.1	x^16 - 2x^15 + 5x^14 - 3x^13 + 4x^12 + 4x^11 + 4x^10 - x^9 + 21x^8 - 13x^7 + 26x^6 - 7x^5 + 14x^4 + x^3 + 5x^2 + x + 1	\( 5^{12}\cdot 11329^{2} \)	16T1497	Trivial
16.0.119878242431640625.1	x^16 - x^15 - 2x^14 - x^13 + 2x^12 + 5x^11 + 2x^10 - 3x^9 - 5x^8 - 3x^7 + 2x^6 + 5x^5 + 2x^4 - x^3 - 2x^2 - x + 1	\( 5^{12}\cdot 22159^{2} \)	16T1497	Trivial
16.4.11427674609619140625.1	x^16 - 3x^15 + x^14 + 6x^12 + x^11 - 20x^10 + 16x^9 + 12x^8 + 2x^7 - 40x^6 - 7x^5 + 51x^4 - 20x^3 + 4x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 2671^{2} \)	16T1497	Trivial
16.4.13284369631075780561.1	x^16 - 2x^15 - x^14 + x^13 + x^12 + 3x^11 - 6x^10 - 5x^9 + 6x^8 + 5x^7 - 6x^6 - 3x^5 + x^4 - x^3 - x^2 + 2x + 1	\( 17^{12}\cdot 151^{2} \)	16T1497	Trivial
16.8.24126669511962890625.1	x^16 - 4x^15 + 16x^13 - 9x^12 - 28x^11 + 28x^10 + 11x^9 - 60x^8 + 126x^7 - 102x^6 - 20x^5 + 69x^4 - 57x^3 + 43x^2 - 14x + 1	\( 3^{8}\cdot 5^{12}\cdot 3881^{2} \)	16T1497	Trivial
16.8.35459233648681640625.1	x^16 - 4x^14 - 8x^12 + 13x^10 + 30x^8 - 58x^6 + 37x^4 - 11x^2 + 1	\( 3^{8}\cdot 5^{14}\cdot 941^{2} \)	16T1497	Trivial
16.0.73286708086181640625.1	x^16 - 7x^15 + 24x^14 - 54x^13 + 84x^12 - 73x^11 - 34x^10 + 243x^9 - 457x^8 + 486x^7 - 136x^6 - 584x^5 + 1344x^4 - 1728x^3 + 1536x^2 - 896x + 256	\( 5^{12}\cdot 547889^{2} \)	16T1497	Trivial
16.8.82373776000000000000.1	x^16 - 6x^15 + 15x^14 - 26x^13 + 34x^12 - 18x^11 - 24x^10 + 78x^9 - 119x^8 + 96x^7 - 31x^6 - 34x^5 + 69x^4 - 52x^3 + 25x^2 - 8x + 1	\( 2^{16}\cdot 5^{12}\cdot 2269^{2} \)	16T1497	Trivial
16.0.93619230963134765625.1	x^16 - 3x^15 + 5x^14 - 5x^13 + 6x^11 + 2x^10 + 2x^6 - 6x^5 + 5x^3 + 5x^2 + 3x + 1	\( 3^{8}\cdot 5^{14}\cdot 11^{2}\cdot 139^{2} \)	16T1497	$[2]$
16.0.112072358202091503616.1	x^16 - 4x^15 + 14x^14 - 44x^13 + 93x^12 - 168x^11 + 252x^10 - 304x^9 + 329x^8 - 276x^7 + 246x^6 - 140x^5 + 95x^4 - 48x^3 + 24x^2 - 8x + 2	\( 2^{48}\cdot 631^{2} \)	16T1497	Trivial
16.0.273503893564697265625.1	x^16 - 3x^15 + 7x^14 - 9x^13 + 19x^12 - 16x^11 + 49x^10 - 32x^9 + 98x^8 - 110x^7 + 145x^6 - 40x^5 + 52x^4 + 24x^3 + 19x^2 + 6x + 1	\( 5^{12}\cdot 439^{2}\cdot 2411^{2} \)	16T1497	$[3]$
16.8.688282603613525390625.1	x^16 - 3x^15 - x^14 + 5x^13 + 8x^12 + 10x^11 - 59x^10 - 12x^9 + 103x^8 - 12x^7 - 59x^6 + 10x^5 + 8x^4 + 5x^3 - x^2 - 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 19^{2}\cdot 1091^{2} \)	16T1497	Trivial
16.12.2877678736000000000000.1	x^16 - 4x^15 - 4x^14 + 34x^13 - 30x^12 - 70x^11 + 155x^10 - 18x^9 - 203x^8 + 232x^7 + 23x^6 - 340x^5 + 27x^4 + 142x^3 - 9x^2 - 16x + 1	\( 2^{16}\cdot 5^{12}\cdot 13411^{2} \)	16T1497	Trivial (GRH)
16.12.46132166656000000000000.1	x^16 - 18x^14 - 14x^13 + 82x^12 + 114x^11 + 26x^10 + 8x^9 - 243x^8 - 466x^7 - 82x^6 - 36x^5 - 244x^4 + 138x^3 + 260x^2 + 18x - 19	\( 2^{28}\cdot 5^{12}\cdot 839^{2} \)	16T1497	Trivial (GRH)
16.16.896545605373974853515625.1	x^16 - x^15 - 26x^14 + 26x^13 + 251x^12 - 243x^11 - 1134x^10 + 1021x^9 + 2526x^8 - 1934x^7 - 2850x^6 + 1554x^5 + 1607x^4 - 412x^3 - 370x^2 - 11x + 11	\( 5^{12}\cdot 11^{8}\cdot 4139^{2} \)	16T1497	Trivial (GRH)
16.16.4802917701136000000000000.1	x^16 - 26x^14 + 241x^12 - 1011x^10 + 2196x^8 - 2565x^6 + 1540x^4 - 400x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 547889^{2} \)	16T1497	Trivial (GRH)