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 matches 1-50 of 54)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.122961997275390625.1	x^16 - 2x^15 + 8x^14 - 15x^13 + 31x^12 - 48x^11 + 68x^10 - 85x^9 + 89x^8 - 85x^7 + 68x^6 - 48x^5 + 31x^4 - 15x^3 + 8x^2 - 2x + 1	\( 5^{10}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial
16.4.122961997275390625.1	x^16 - x^15 - 5x^14 + x^13 + 11x^12 - x^11 - 15x^10 + x^9 + 15x^8 + x^7 - 15x^6 - x^5 + 11x^4 + x^3 - 5x^2 - x + 1	\( 5^{10}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial
16.0.1159787648056640625.1	x^16 - 2x^15 - 3x^14 + 7x^13 + 5x^12 - 20x^11 + 19x^10 + 4x^9 - 35x^8 + 19x^7 + 44x^6 - 89x^5 + 93x^4 - 58x^3 + 25x^2 - 6x + 1	\( 3^{4}\cdot 5^{10}\cdot 11^{2}\cdot 59^{4} \)	16T1174	Trivial
16.0.1159787648056640625.2	x^16 - x^15 + 9x^14 - 9x^13 + 34x^12 - 36x^11 + 76x^10 - 81x^9 + 114x^8 - 104x^7 + 104x^6 - 61x^5 + 51x^4 - x^3 + 19x^2 + 5x + 5	\( 3^{4}\cdot 5^{10}\cdot 11^{2}\cdot 59^{4} \)	16T1174	Trivial
16.4.3074049931884765625.1	x^16 - 4x^15 + 7x^14 - 2x^13 - 16x^12 + 40x^11 - 53x^10 + 64x^9 - 53x^8 + 6x^7 + 15x^6 - 23x^5 + 25x^4 - 9x^3 + x^2 - 5x + 1	\( 5^{12}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial
16.8.3074049931884765625.1	x^16 - 5x^14 + 4x^12 + 15x^10 - 49x^8 + 60x^6 - 26x^4 + 1	\( 5^{12}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial
16.0.5941162502500000000.1	x^16 - 4x^15 - x^14 + 26x^13 - 32x^12 - 28x^11 + 87x^10 - 82x^9 + 86x^8 - 112x^7 + 92x^6 - 56x^5 + 48x^4 - 34x^3 + 15x^2 - 6x + 4	\( 2^{8}\cdot 5^{10}\cdot 29^{2}\cdot 41^{4} \)	16T1174	Trivial
16.0.5941162502500000000.2	x^16 - 3x^15 + 5x^14 - 6x^12 + 17x^11 + 12x^10 + 10x^9 + 49x^8 + 10x^7 + 12x^6 + 17x^5 - 6x^4 + 5x^2 - 3x + 1	\( 2^{8}\cdot 5^{10}\cdot 29^{2}\cdot 41^{4} \)	16T1174	Trivial
16.4.8455691280628842496.1	x^16 - 8x^14 + 16x^12 + 3x^10 - 78x^8 + 94x^6 - 36x^4 + 3x^2 + 1	\( 2^{22}\cdot 17^{10} \)	16T1174	Trivial
16.4.8455691280628842496.2	x^16 - 7x^14 + 7x^12 + 39x^10 - 88x^8 + 39x^6 + 7x^4 - 7x^2 + 1	\( 2^{22}\cdot 17^{10} \)	16T1174	Trivial
16.0.14878401670322265625.1	x^16 + 8x^14 + 22x^12 + 36x^10 + 39x^8 + 19x^6 + 12x^4 + 7x^2 + 1	\( 5^{10}\cdot 11^{4}\cdot 101^{4} \)	16T1174	$[2]$
16.8.37072534071103515625.1	x^16 - 4x^15 - 3x^14 + 21x^13 + 5x^12 - 42x^11 - 27x^10 + 55x^9 + 78x^8 - 65x^7 - 93x^6 + 51x^5 + 50x^4 - 17x^3 - 12x^2 + 2x + 1	\( 5^{10}\cdot 101^{4}\cdot 191^{2} \)	16T1174	Trivial
16.0.44818117324422774784.1	x^16 + 2x^14 + x^12 + 6x^10 + 40x^8 + 34x^6 + x^4 + 6x^2 + 1	\( 2^{38}\cdot 113^{4} \)	16T1174	Trivial
16.4.44818117324422774784.1	x^16 - 2x^14 - 7x^12 + 6x^10 - 12x^8 + 6x^6 - 7x^4 - 2x^2 + 1	\( 2^{38}\cdot 113^{4} \)	16T1174	Trivial
16.0.70143975040000000000.1	x^16 - 3x^12 - 10x^10 + 46x^8 - 35x^6 - 5x^4 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.0.70143975040000000000.2	x^16 - 4x^14 + 7x^12 + 9x^10 - 14x^8 - 20x^6 + 35x^4 + 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.0.70143975040000000000.3	x^16 - 5x^14 + 8x^12 + 5x^10 - 4x^8 - 15x^6 + 30x^4 + 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.0.70143975040000000000.4	x^16 + 5x^14 + 8x^12 - 5x^10 - 4x^8 + 15x^6 + 30x^4 - 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.0.717089877190764396544.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 80x^12 - 116x^11 + 178x^10 - 208x^9 + 172x^8 - 144x^7 + 136x^6 - 84x^5 + 33x^4 - 24x^3 + 12x^2 + 2	\( 2^{42}\cdot 113^{4} \)	16T1174	Trivial
16.4.717089877190764396544.1	x^16 - 2x^12 + 16x^10 + 112x^8 - 192x^6 - 8x^4 - 64x^2 + 16	\( 2^{42}\cdot 113^{4} \)	16T1174	Trivial
16.8.717089877190764396544.1	x^16 - 14x^14 - 4x^13 + 73x^12 + 32x^11 - 168x^10 - 92x^9 + 187x^8 + 104x^7 - 128x^6 - 80x^5 + 42x^4 + 40x^3 - 8x - 2	\( 2^{42}\cdot 113^{4} \)	16T1174	Trivial
16.0.717089877190764396544.2	x^16 + 4x^14 - 8x^12 - 12x^10 + 14x^8 + 172x^6 - 72x^4 + 28x^2 + 1	\( 2^{42}\cdot 113^{4} \)	16T1174	$[2]$
16.4.717089877190764396544.2	x^16 - 2x^14 + 7x^12 - 6x^10 + 12x^8 + 38x^6 - 57x^4 + 2x^2 + 1	\( 2^{42}\cdot 113^{4} \)	16T1174	Trivial
16.8.717089877190764396544.2	x^16 - 8x^14 + 22x^12 - 52x^10 + 133x^8 - 68x^6 - 96x^4 + 56x^2 + 4	\( 2^{42}\cdot 113^{4} \)	16T1174	Trivial
16.8.1753599376000000000000.1	x^16 - 5x^14 + 24x^12 - 65x^10 + 81x^8 - 60x^6 + 34x^4 - 10x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.8.1753599376000000000000.2	x^16 - 8x^14 + 22x^12 - 25x^10 + 16x^8 - 25x^6 + 33x^4 - 14x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 19^{4}\cdot 29^{2} \)	16T1174	Trivial
16.4.2017375191040000000000.1	x^16 - 8x^14 - 8x^12 + 34x^10 - 6x^8 - 44x^6 - 3x^4 - 22x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 11^{4}\cdot 29^{2} \)	16T1174	$[2]$
16.4.2017375191040000000000.2	x^16 - 8x^14 + 34x^12 - 112x^10 + 259x^8 - 352x^6 + 82x^4 + 40x^2 + 1	\( 2^{24}\cdot 5^{10}\cdot 11^{4}\cdot 29^{2} \)	16T1174	$[2]$
16.0.2868359508763057586176.1	x^16 - 2x^12 - 16x^10 + 112x^8 + 192x^6 - 8x^4 + 64x^2 + 16	\( 2^{44}\cdot 113^{4} \)	16T1174	$[2]$
16.12.2868359508763057586176.1	x^16 - 14x^14 + 63x^12 - 118x^10 + 120x^8 - 118x^6 + 63x^4 - 14x^2 + 1	\( 2^{44}\cdot 113^{4} \)	16T1174	Trivial
16.4.2868359508763057586176.1	x^16 - 4x^14 + 4x^12 - 40x^10 + 72x^8 - 688x^6 - 240x^4 - 224x^2 + 16	\( 2^{44}\cdot 113^{4} \)	16T1174	Trivial
16.8.6439535368599619140625.1	x^16 - 4x^15 + x^14 + 24x^13 - 56x^12 + 48x^11 - 5x^10 - 123x^9 + 337x^8 - 335x^7 + 283x^6 - 506x^5 + 639x^4 - 585x^3 + 405x^2 - 130x + 5	\( 5^{10}\cdot 29^{2}\cdot 941^{4} \)	16T1174	Trivial
16.8.6439535368599619140625.2	x^16 - 8x^15 + 26x^14 - 42x^13 + 28x^12 + 14x^11 - 2x^10 - 166x^9 + 456x^8 - 674x^7 + 448x^6 + 182x^5 - 402x^4 + 112x^3 + 40x^2 - 13x - 1	\( 5^{10}\cdot 29^{2}\cdot 941^{4} \)	16T1174	Trivial
16.12.8058437453440000000000.1	x^16 - 9x^14 + 32x^12 - 96x^10 + 281x^8 - 500x^6 + 440x^4 - 175x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 11^{2}\cdot 101^{4} \)	16T1174	Trivial (GRH)
16.8.12952435906758181912576.1	x^16 - 4x^15 - 2x^14 + 40x^13 - 70x^12 - 80x^11 + 334x^10 - 212x^9 - 236x^8 + 568x^7 - 502x^6 - 72x^5 + 265x^4 + 144x^3 - 236x^2 + 72x - 2	\( 2^{38}\cdot 17^{2}\cdot 113^{4} \)	16T1174	Trivial
16.8.51809743627032727650304.1	x^16 - 10x^14 + 25x^12 + 24x^10 - 160x^8 + 96x^6 + 400x^4 - 640x^2 + 256	\( 2^{40}\cdot 17^{2}\cdot 113^{4} \)	16T1174	Trivial
16.8.56009470234240000000000.1	x^16 - 12x^14 + 66x^12 - 216x^10 + 451x^8 - 600x^6 + 479x^4 - 195x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{2}\cdot 101^{4} \)	16T1174	Trivial (GRH)
16.0.144796946017701263835136.1	x^16 - 8x^15 + 42x^14 - 136x^13 + 347x^12 - 744x^11 + 1540x^10 - 2640x^9 + 3081x^8 - 2152x^7 + 938x^6 - 744x^5 + 1093x^4 - 952x^3 + 448x^2 - 112x + 14	\( 2^{42}\cdot 7^{6}\cdot 23^{4} \)	16T1174	$[2, 2]$
16.0.160988384214990478515625.1	x^16 - x^15 - 8x^14 + 5x^13 + 85x^12 + 51x^11 - 284x^10 - 405x^9 + 454x^8 + 650x^7 - 231x^6 - 107x^5 + 290x^4 + 65x^3 - 12x^2 - 3x + 1	\( 5^{12}\cdot 29^{2}\cdot 941^{4} \)	16T1174	$[2, 2]$
16.8.527527959245440000000000.1	x^16 - 5x^14 - 18x^12 + 85x^10 + 151x^8 - 1015x^6 + 1680x^4 - 1175x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 89^{2}\cdot 101^{4} \)	16T1174	Trivial (GRH)
16.8.527527959245440000000000.2	x^16 - 9x^14 + 2x^12 + 44x^10 + 191x^8 - 360x^6 - 630x^4 + 125x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 89^{2}\cdot 101^{4} \)	16T1174	$[2]$ (GRH)
16.8.1400236755856000000000000.1	x^16 - 22x^14 + 114x^12 + 2x^10 - 144x^8 - 120x^6 + 15x^4 + 50x^2 + 25	\( 2^{16}\cdot 5^{12}\cdot 29^{2}\cdot 101^{4} \)	16T1174	Trivial (GRH)
16.16.3492500152858240000000000.1	x^16 - 30x^14 + 312x^12 - 1445x^10 + 3236x^8 - 3495x^6 + 1685x^4 - 350x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 101^{4}\cdot 229^{2} \)	16T1174	Trivial (GRH)
16.16.3492500152858240000000000.2	x^16 - 26x^14 + 262x^12 - 1339x^10 + 3856x^8 - 6475x^6 + 6220x^4 - 3125x^2 + 625	\( 2^{16}\cdot 5^{10}\cdot 101^{4}\cdot 229^{2} \)	16T1174	Trivial (GRH)
16.0.9180891080439666416015625.1	x^16 - x^15 + x^14 + 8x^13 + 72x^11 + 139x^10 - 365x^9 - 576x^8 - 115x^7 + 376x^6 + 1595x^5 + 565x^4 - 627x^3 + 421x^2 - 40x + 5	\( 3^{4}\cdot 5^{10}\cdot 41^{2}\cdot 1621^{4} \)	16T1174	$[2]$
16.0.22802876945601640000000000.1	x^16 + 3x^14 + 18x^12 + 343x^10 + 2366x^8 + 12615x^6 + 37745x^4 + 37000x^2 + 10000	\( 2^{12}\cdot 5^{10}\cdot 19^{6}\cdot 59^{4} \)	16T1174	$[2, 6]$
16.0.47103964466995840000000000.1	x^16 - 8x^15 + 20x^14 + 26x^12 - 520x^11 + 1214x^10 - 350x^9 - 1051x^8 - 1132x^7 + 10610x^6 - 21798x^5 + 21611x^4 - 11294x^3 + 11511x^2 - 8840x + 59105	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 101^{4} \)	16T1174	$[2, 20]$ (GRH)
16.0.219880372985150440000000000.1	x^16 - 2x^15 + 8x^14 - 6x^13 + 18x^12 + 94x^11 - 349x^10 + 141x^9 + 1585x^8 - 722x^7 + 9689x^6 + 5625x^5 + 54426x^4 - 3854x^3 + 147729x^2 - 4659x + 156301	\( 2^{12}\cdot 5^{10}\cdot 19^{4}\cdot 59^{6} \)	16T1174	$[2, 6]$ (GRH)
16.0.219880372985150440000000000.2	x^16 + 19x^14 + 74x^12 + 951x^10 + 3734x^8 + 4759x^6 + 5049x^4 + 5256x^2 + 1936	\( 2^{12}\cdot 5^{10}\cdot 19^{4}\cdot 59^{6} \)	16T1174	$[2, 2]$ (GRH)
16.0.422021389916544640000000000.1	x^16 + 30x^14 + 312x^12 + 1375x^10 + 2956x^8 + 3285x^6 + 1845x^4 + 450x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{2}\cdot 941^{4} \)	16T1174	$[96]$ (GRH)