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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.688731938571157504.1	x^16 - 4x^15 + 14x^14 - 34x^13 + 66x^12 - 100x^11 + 112x^10 - 76x^9 + 22x^8 - 36x^7 + 144x^6 - 248x^5 + 246x^4 - 156x^3 + 64x^2 - 16x + 2	\( 2^{28}\cdot 37^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.0.946199974038715881.1	x^16 - 2x^15 - 2x^14 + 6x^13 + 2x^12 - 12x^11 + 10x^9 + 11x^8 - 8x^7 - 18x^6 + 2x^5 + 29x^4 - 20x^3 + 7x^2 - 30x + 25	\( 3^{8}\cdot 229^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.4.10172948830228578304.1	x^16 - 2x^14 - 4x^13 - 8x^12 + 16x^11 + 6x^10 - 36x^9 + 27x^8 + 20x^7 - 62x^6 - 4x^5 + 32x^4 - 8x^3 - 4x^2 + 4x - 1	\( 2^{36}\cdot 23^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.4.27487790694400000000.1	x^16 - 4x^15 + 10x^14 - 16x^13 + 23x^12 - 40x^11 + 70x^10 - 68x^9 - 29x^8 + 192x^7 - 276x^6 + 192x^5 - 32x^4 - 56x^3 + 48x^2 - 16x + 2	\( 2^{46}\cdot 5^{8} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.0.56334303438328515625.1	x^16 - x^15 + 7x^14 - 6x^13 + 20x^12 - 21x^11 + 32x^10 - 58x^9 + 61x^8 - 122x^7 + 126x^6 - 145x^5 + 158x^4 - 76x^3 + 105x^2 - 11x + 29	\( 5^{8}\cdot 229^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial (GRH)
16.0.1298528369092716162129.1	x^16 - 5x^15 + 14x^14 - 22x^13 + 32x^12 - 85x^11 + 252x^10 - 513x^9 + 763x^8 - 1077x^7 + 1776x^6 - 2557x^5 + 3134x^4 - 3628x^3 + 3602x^2 - 2279x + 619	\( 3^{12}\cdot 367^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.0.2419539909105613275136.1	x^16 - 4x^15 - 4x^14 + 24x^13 + 21x^12 - 42x^11 + 24x^10 + 48x^9 - 48x^8 + 22x^7 + 114x^6 - 62x^5 - 19x^4 + 40x^3 + 22x^2 + 6x + 1	\( 2^{24}\cdot 229^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial
16.0.4518770248965364383744.1	x^16 - 2x^15 - 2x^13 + 12x^12 - 20x^11 + 72x^10 + 48x^9 + 252x^8 + 236x^7 + 420x^6 + 412x^5 + 354x^4 + 284x^3 + 140x^2 + 64x + 22	\( 2^{28}\cdot 3^{8}\cdot 37^{6} \)	$\GL(2,Z/4)$ (as 16T186)	$[2]$
16.0.4518770248965364383744.2	x^16 - 2x^15 + 8x^14 - 16x^13 + 34x^12 - 50x^11 + 108x^10 - 4x^9 + 378x^8 + 414x^7 + 764x^6 + 728x^5 + 612x^4 + 342x^3 + 104x^2 + 16x + 1	\( 2^{28}\cdot 3^{8}\cdot 37^{6} \)	$\GL(2,Z/4)$ (as 16T186)	$[2]$
16.0.52268213136063490228224.1	x^16 - 2x^15 + 7x^14 - 36x^13 + 62x^12 - 158x^11 + 399x^10 - 538x^9 + 991x^8 - 1436x^7 + 1350x^6 - 1828x^5 + 1373x^4 - 486x^3 + 394x^2 + 20x + 100	\( 2^{16}\cdot 3^{12}\cdot 107^{6} \)	$\GL(2,Z/4)$ (as 16T186)	$[2]$ (GRH)
16.0.4276439742589131330420736.1	x^16 - 8x^15 + 36x^14 - 96x^13 + 172x^12 - 128x^11 - 88x^10 + 432x^9 - 108x^8 - 288x^7 + 1060x^6 - 1544x^5 + 1244x^4 - 536x^3 + 352x^2 - 600x + 1511	\( 2^{44}\cdot 79^{6} \)	$\GL(2,Z/4)$ (as 16T186)	$[2, 16]$ (GRH)
16.16.4276439742589131330420736.1	x^16 - 4x^15 - 16x^14 + 76x^13 + 36x^12 - 408x^11 + 144x^10 + 932x^9 - 695x^8 - 920x^7 + 1000x^6 + 236x^5 - 518x^4 + 108x^3 + 36x^2 - 8x - 1	\( 2^{44}\cdot 79^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial (GRH)
16.16.15874601343641928698167296.1	x^16 - 4x^15 - 22x^14 + 112x^13 + 64x^12 - 878x^11 + 744x^10 + 1936x^9 - 3210x^8 - 184x^7 + 2870x^6 - 1370x^5 - 401x^4 + 430x^3 - 88x^2 + 1	\( 2^{24}\cdot 3^{8}\cdot 229^{6} \)	$\GL(2,Z/4)$ (as 16T186)	Trivial (GRH)
16.0.79202442563427805645766656.1	x^16 - 4x^15 + 10x^14 - 44x^13 + 72x^12 + 80x^11 + 284x^10 + 1236x^9 + 652x^8 + 228x^7 + 7152x^6 - 9200x^5 + 15216x^4 - 11896x^3 + 8812x^2 - 3368x + 866	\( 2^{38}\cdot 257^{6} \)	$\GL(2,Z/4)$ (as 16T186)	$[2, 24]$ (GRH)