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 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.48546204325249024.1	x^16 - 2x^14 + 5x^12 - 2x^10 + 12x^8 - 2x^6 + 5x^4 - 2x^2 + 1	\( 2^{34}\cdot 41^{4} \)	16T969	Trivial
16.0.100387585600000000.1	x^16 - 3x^15 + 6x^14 - 7x^13 + 3x^12 + 3x^11 - 6x^10 + 7x^9 - 4x^8 + 7x^7 - 6x^6 + 3x^5 + 3x^4 - 7x^3 + 6x^2 - 3x + 1	\( 2^{12}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.0.194184817300996096.1	x^16 - 4x^14 + 5x^12 + 4x^10 - 8x^8 - 4x^6 + 5x^4 + 4x^2 + 1	\( 2^{36}\cdot 41^{4} \)	16T969	Trivial
16.0.1606201369600000000.1	x^16 - 2x^15 + 2x^14 - 6x^13 + 8x^12 - 4x^11 + 6x^10 - 8x^9 + 17x^8 - 34x^7 + 24x^6 - 8x^5 + 13x^4 - 18x^3 + 13x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.0.1606201369600000000.2	x^16 - 8x^15 + 36x^14 - 112x^13 + 273x^12 - 546x^11 + 931x^10 - 1366x^9 + 1735x^8 - 1890x^7 + 1751x^6 - 1354x^5 + 855x^4 - 424x^3 + 154x^2 - 36x + 4	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.0.1606201369600000000.3	x^16 - 4x^15 + 10x^14 - 18x^13 + 32x^12 - 48x^11 + 62x^10 - 68x^9 + 73x^8 - 64x^7 + 48x^6 - 26x^5 + 17x^4 - 4x^3 + 5x^2 + 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.4.1606201369600000000.3	x^16 - 3x^14 - 3x^12 + 3x^10 - 12x^8 + 3x^6 - 3x^4 - 3x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.4.1606201369600000000.4	x^16 + 3x^14 - 3x^12 - 3x^10 - 12x^8 - 3x^6 - 3x^4 + 3x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 89^{4} \)	16T969	Trivial
16.8.4635236761600000000.2	x^16 - 2x^15 - 8x^14 + 26x^13 - 19x^12 - 4x^11 + 4x^10 - 16x^9 + 53x^8 - 56x^7 + 6x^6 + 54x^5 - 53x^4 + 6x^3 + 16x^2 - 8x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.8.4635236761600000000.3	x^16 - 6x^15 + 14x^14 - 14x^13 - 17x^12 + 94x^11 - 184x^10 + 222x^9 - 167x^8 + 34x^7 + 74x^6 - 112x^5 + 135x^4 - 116x^3 + 54x^2 - 12x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.0.4635236761600000000.4	x^16 - 2x^14 + 11x^12 - 16x^10 + 73x^8 - 52x^6 + 19x^4 - 6x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial
16.0.4635236761600000000.5	x^16 + 6x^14 + 13x^12 + 6x^10 + 8x^8 + 54x^6 + 73x^4 + 14x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial
16.0.38999408308687890625.1	x^16 - 2x^15 + 9x^14 - 14x^13 + 53x^12 - 64x^11 + 115x^10 - 135x^9 + 209x^8 - 186x^7 + 204x^6 - 149x^5 + 121x^4 - 63x^3 + 28x^2 - 7x + 1	\( 5^{8}\cdot 29^{4}\cdot 109^{4} \)	16T969	$[2]$
16.8.38999408308687890625.1	x^16 - 2x^15 - 2x^14 + 10x^12 + 23x^11 - 40x^10 - 45x^9 + 2x^8 + 120x^7 + 71x^6 - 216x^5 + 26x^4 + 73x^3 - 14x^2 - 7x + 1	\( 5^{8}\cdot 29^{4}\cdot 109^{4} \)	16T969	Trivial (GRH)
16.0.38999408308687890625.2	x^16 - 4x^15 + x^14 + 14x^13 - 11x^12 - 12x^11 - 2x^10 - 3x^9 + 56x^8 - 43x^7 + 41x^6 - 75x^5 + 44x^4 - 26x^3 + 30x^2 - x + 1	\( 5^{8}\cdot 29^{4}\cdot 109^{4} \)	16T969	Trivial
16.0.38999408308687890625.3	x^16 - 4x^15 + x^14 + 14x^13 - 8x^12 - 26x^11 + 19x^10 + 37x^9 - 49x^8 - 7x^7 + 41x^6 - 10x^5 + 5x^4 - 57x^3 + 77x^2 - 42x + 9	\( 5^{8}\cdot 29^{4}\cdot 109^{4} \)	16T969	Trivial
16.8.74163788185600000000.1	x^16 - 4x^15 - 6x^14 + 32x^13 + 20x^12 - 96x^11 - 76x^10 + 120x^9 + 162x^8 + 4x^7 - 120x^6 - 72x^5 + 28x^4 - 64x^3 - 64x^2 + 4	\( 2^{28}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.8.74163788185600000000.2	x^16 - 4x^15 - 6x^14 + 36x^13 + 16x^12 - 148x^11 - 28x^10 + 320x^9 + 50x^8 - 332x^7 - 16x^6 + 176x^5 - 68x^4 - 160x^3 - 80x^2 - 24x - 4	\( 2^{28}\cdot 5^{8}\cdot 29^{4} \)	16T969	Trivial (GRH)
16.0.136174910946750390625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 68x^12 - 44x^11 - 2x^10 + 32x^9 - 6x^8 - 80x^7 + 106x^6 - 2x^5 - 54x^4 + 4x^3 + 18x^2 - 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T969	Trivial
16.4.136174910946750390625.1	x^16 - 2x^15 - x^14 + 16x^13 - 30x^12 + 46x^10 - 2x^9 - 101x^8 + 84x^7 + 49x^6 - 80x^5 - 25x^4 + 28x^3 + 21x^2 + 6x + 1	\( 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T969	Trivial
16.0.136174910946750390625.2	x^16 - 4x^15 + 3x^14 + 2x^13 + 12x^12 - 52x^11 + 63x^10 + 31x^9 - 113x^8 + 23x^7 + 83x^6 - 38x^5 - 11x^4 + 19x^3 + x^2 - 2x + 1	\( 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T969	Trivial
16.4.136174910946750390625.2	x^16 - 2x^15 - 2x^14 - 10x^13 - 16x^12 - 19x^11 - 60x^10 - 125x^9 - 195x^8 - 235x^7 - 240x^6 - 187x^5 - 116x^4 - 55x^3 - 18x^2 - x + 1	\( 5^{8}\cdot 29^{4}\cdot 149^{4} \)	16T969	Trivial
16.0.44133664812763327950625.1	x^16 + 11x^14 + 78x^12 + 304x^10 + 313x^8 - 412x^6 - 78x^4 + 303x^2 + 1	\( 5^{4}\cdot 29^{8}\cdot 109^{4} \)	16T969	Trivial (GRH)
16.0.44133664812763327950625.2	x^16 - 8x^15 + 38x^14 - 126x^13 + 312x^12 - 598x^11 + 931x^10 - 1223x^9 + 1526x^8 - 1912x^7 + 2134x^6 - 1854x^5 + 1843x^4 - 1861x^3 + 1892x^2 - 1095x + 1205	\( 5^{4}\cdot 29^{8}\cdot 109^{4} \)	16T969	Trivial (GRH)
16.0.216625969799691187890625.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 246x^12 - 566x^11 + 1142x^10 - 1904x^9 + 2832x^8 - 3842x^7 + 4638x^6 - 4622x^5 + 4216x^4 - 3314x^3 + 1646x^2 - 401x + 41	\( 5^{8}\cdot 29^{4}\cdot 941^{4} \)	16T969	$[2]$ (GRH)
16.0.216625969799691187890625.2	x^16 + x^14 - 17x^12 - 38x^10 + 99x^8 + 190x^6 + 450x^4 + 500x^2 + 625	\( 5^{8}\cdot 29^{4}\cdot 941^{4} \)	16T969	$[5]$ (GRH)
16.0.448112381530677314584576.1	x^16 - 4x^15 + 2x^14 + 20x^13 - 21x^12 - 24x^11 + 54x^10 + 52x^9 + 29x^8 + 44x^7 + 360x^6 + 328x^5 - 318x^4 - 288x^3 + 192x^2 - 128x + 92	\( 2^{40}\cdot 17^{4}\cdot 47^{4} \)	16T969	$[2]$ (GRH)
16.8.448112381530677314584576.1	x^16 - 22x^14 - 12x^13 + 215x^12 + 196x^11 - 1146x^10 - 1268x^9 + 3422x^8 + 4016x^7 - 5586x^6 - 6132x^5 + 5083x^4 + 3820x^3 - 3326x^2 - 1004x + 959	\( 2^{40}\cdot 17^{4}\cdot 47^{4} \)	16T969	Trivial (GRH)
16.8.14879702148671516050456576.1	x^16 + 12x^14 - 104x^12 - 1092x^10 + 126x^8 + 948x^6 + 152x^4 - 60x^2 + 1	\( 2^{44}\cdot 7^{4}\cdot 137^{4} \)	16T969	$[2]$ (GRH)
16.8.34888832870078427770650624.1	x^16 - 10x^14 + x^12 - 16x^10 + 1084x^8 - 3616x^6 + 4528x^4 - 2560x^2 + 576	\( 2^{34}\cdot 7^{8}\cdot 137^{4} \)	16T969	Trivial (GRH)
16.16.135391231124806992431640625.1	x^16 - 5x^15 - 19x^14 + 121x^13 + 31x^12 - 748x^11 + 237x^10 + 2043x^9 - 886x^8 - 2900x^7 + 1146x^6 + 2214x^5 - 629x^4 - 855x^3 + 115x^2 + 130x + 5	\( 5^{12}\cdot 29^{4}\cdot 941^{4} \)	16T969	Trivial (GRH)
16.16.135391231124806992431640625.2	x^16 - 2x^15 - 28x^14 + 61x^13 + 247x^12 - 627x^11 - 739x^10 + 2629x^9 - 17x^8 - 4118x^7 + 2126x^6 + 1932x^5 - 1594x^4 - 115x^3 + 285x^2 - 35x - 5	\( 5^{12}\cdot 29^{4}\cdot 941^{4} \)	16T969	Trivial (GRH)
16.0.238075234378744256807305216.1	x^16 - 4x^14 + 106x^12 - 732x^10 + 1657x^8 - 688x^6 - 1424x^4 + 3456x^2 + 5184	\( 2^{48}\cdot 7^{4}\cdot 137^{4} \)	16T969	$[32]$ (GRH)
16.0.238075234378744256807305216.2	x^16 - 4x^14 + 26x^12 - 216x^10 + 499x^8 - 1320x^6 + 11642x^4 + 5780x^2 + 83521	\( 2^{48}\cdot 7^{4}\cdot 137^{4} \)	16T969	$[8]$ (GRH)
16.8.14196799556792561689600000000.1	x^16 - 12x^14 - 39x^12 + 522x^10 - 119x^8 - 3253x^6 + 231x^4 + 5133x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{4} \)	16T969	Trivial (GRH)
16.8.14196799556792561689600000000.2	x^16 - 9x^14 - 91x^12 + 901x^10 - 1064x^8 - 3266x^6 + 1739x^4 + 3799x^2 + 841	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 941^{4} \)	16T969	Trivial (GRH)
16.0.1732569100827059303563569135616.1	x^16 - 2x^15 - 7x^14 - 4x^13 + 52x^12 + 132x^11 - 384x^10 - 340x^9 + 515x^8 + 4238x^7 + 14227x^6 - 10064x^5 - 14400x^4 + 56344x^3 + 29980x^2 - 25440x + 15584	\( 2^{28}\cdot 17^{4}\cdot 16673^{4} \)	16T969	$[2, 198]$ (GRH)
16.0.16065802539724479719011164160000.1	x^16 + 56x^14 + 1242x^12 + 14240x^10 + 93479x^8 + 363358x^6 + 821169x^4 + 987745x^2 + 483025	\( 2^{16}\cdot 5^{4}\cdot 29^{8}\cdot 941^{4} \)	16T969	$[2, 874]$ (GRH)