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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.91137949462890625.1	x^16 - x^15 - 2x^14 + 2x^13 + x^12 - 4x^11 + 2x^10 + 5x^9 - 2x^7 - 2x^6 - 2x^5 - x^4 + x^2 + 2x + 1	\( 5^{12}\cdot 139^{4} \)	16T1027	Trivial
16.0.382870898681640625.1	x^16 - 4x^15 + 8x^14 - 7x^13 - 2x^12 + 13x^11 - 9x^10 - 11x^9 + 33x^8 - 33x^7 + 19x^6 - 4x^5 + 3x^4 - x^3 + 2x^2 + 2x + 1	\( 5^{12}\cdot 199^{4} \)	16T1027	Trivial
16.0.2085136000000000000.2	x^16 - 2x^15 + 2x^14 + 6x^13 - 9x^12 - 18x^11 + 68x^10 - 120x^9 + 125x^8 - 104x^7 + 92x^6 - 76x^5 + 59x^4 - 30x^3 + 14x^2 - 4x + 1	\( 2^{16}\cdot 5^{12}\cdot 19^{4} \)	16T1027	Trivial
16.0.533794816000000000000.3	x^16 + 2x^14 - 6x^13 - 8x^12 - 4x^11 - 34x^10 - 28x^9 + 22x^8 + 176x^7 + 148x^6 + 76x^5 + 436x^4 + 192x^3 - 320x^2 - 88x + 76	\( 2^{24}\cdot 5^{12}\cdot 19^{4} \)	16T1027	$[2]$
16.0.832756208047119140625.1	x^16 - 2x^15 + 10x^14 - 13x^13 + 32x^12 - 38x^11 + 41x^10 - 34x^9 + 25x^8 + 38x^7 + 26x^6 + 70x^5 + 53x^4 + 35x^3 + 22x^2 + 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 151^{4} \)	16T1027	$[2]$
16.8.832756208047119140625.1	x^16 - x^15 - 6x^14 + 15x^13 + 12x^12 - 65x^11 + 14x^10 + 120x^9 - 124x^8 - 118x^7 + 246x^6 + 107x^5 - 203x^4 - 90x^3 + 57x^2 + 29x + 1	\( 3^{8}\cdot 5^{12}\cdot 151^{4} \)	16T1027	Trivial (GRH)
16.0.1980016038014925930496.1	x^16 + 12x^12 + 8x^10 + 52x^8 + 16x^6 + 40x^4 + 64x^2 + 64	\( 2^{44}\cdot 103^{4} \)	16T1027	Trivial
16.8.5677660175062500000000.2	x^16 - x^15 - 2x^14 - 6x^13 + 5x^12 + 24x^11 - 17x^10 + 33x^9 - 181x^8 + 227x^7 + 112x^6 - 441x^5 + 406x^4 - 91x^3 - 237x^2 + 108x + 61	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 61^{4} \)	16T1027	Trivial (GRH)
16.0.31713911056000000000000.1	x^16 - 2x^15 + 12x^14 - 4x^13 + 83x^12 + 44x^11 + 534x^10 + 18x^9 + 2558x^8 - 914x^7 + 7356x^6 - 2518x^5 + 12178x^4 - 2118x^3 + 12298x^2 - 386x + 7621	\( 2^{16}\cdot 5^{12}\cdot 211^{4} \)	16T1027	$[2]$ (GRH)
16.0.330123790096000000000000.1	x^16 + 2x^14 - 2x^13 + 67x^12 - 108x^11 + 574x^10 - 596x^9 + 2115x^8 - 1864x^7 + 3302x^6 - 2816x^5 + 2647x^4 - 1528x^3 + 522x^2 - 36x + 1	\( 2^{16}\cdot 5^{12}\cdot 379^{4} \)	16T1027	$[2, 6]$ (GRH)
16.16.8110145691709136611311616.1	x^16 - 32x^14 - 8x^13 + 376x^12 + 272x^11 - 2064x^10 - 2672x^9 + 4642x^8 + 10224x^7 + 568x^6 - 12280x^5 - 11424x^4 - 3600x^3 + 80x^2 + 240x + 31	\( 2^{56}\cdot 103^{4} \)	16T1027	Trivial (GRH)
16.16.24464657022976000000000000.1	x^16 - 4x^15 - 22x^14 + 116x^13 + 74x^12 - 1016x^11 + 776x^10 + 2984x^9 - 4196x^8 - 2808x^7 + 6508x^6 - 280x^5 - 3108x^4 + 712x^3 + 264x^2 - 16x - 4	\( 2^{28}\cdot 5^{12}\cdot 139^{4} \)	16T1027	Trivial (GRH)