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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.26987918400000000.1	x^16 - x^15 + x^14 - 5x^13 + 4x^12 + 5x^11 - 4x^10 - 9x^8 + 12x^7 + 2x^6 - 9x^5 + 8x^4 - 7x^3 + x^2 + x + 1	\( 2^{12}\cdot 3^{2}\cdot 5^{8}\cdot 37^{4} \)	16T1046	Trivial
16.0.31673320900000000.1	x^16 - 2x^15 + 2x^14 - 8x^13 + 14x^12 - 10x^11 + 20x^10 - 34x^9 + 20x^8 - 12x^7 + 20x^6 - 10x^5 - x^4 - 4x^3 + 8x^2 - 4x + 1	\( 2^{8}\cdot 5^{8}\cdot 13^{2}\cdot 37^{4} \)	16T1046	Trivial
16.0.515165452956073984.1	x^16 - 2x^14 - 2x^10 + 6x^8 + 2x^6 + 2x^2 + 1	\( 2^{38}\cdot 37^{4} \)	16T1046	Trivial
16.0.515165452956073984.2	x^16 - 2x^14 + 4x^12 - 2x^10 - 2x^8 + 2x^6 + 4x^4 + 2x^2 + 1	\( 2^{38}\cdot 37^{4} \)	16T1046	Trivial
16.4.620175937656250000.2	x^16 - 2x^15 - x^14 + 8x^13 - 11x^12 + 4x^11 + 3x^10 - 6x^9 + 17x^8 - 15x^7 - 14x^6 + 23x^5 + 4x^4 - 15x^3 + 2x^2 + 4x - 1	\( 2^{4}\cdot 5^{10}\cdot 251^{4} \)	16T1046	Trivial
16.4.777663683605037056.1	x^16 + 4x^14 - 6x^12 - 4x^10 - 21x^8 + 52x^6 - 26x^4 + 1	\( 2^{40}\cdot 29^{4} \)	16T1046	Trivial
16.12.157633109816006250000.1	x^16 - 11x^14 + 41x^12 - 49x^10 - 37x^8 + 103x^6 - 16x^4 - 37x^2 + 1	\( 2^{4}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	16T1046	Trivial (GRH)
16.8.495266247521728515625.1	x^16 - 2x^15 - 14x^14 + 29x^13 + 75x^12 - 167x^11 - 185x^10 + 485x^9 + 175x^8 - 742x^7 + 67x^6 + 567x^5 - 215x^4 - 193x^3 + 113x^2 + 20x - 19	\( 5^{12}\cdot 13^{2}\cdot 331^{4} \)	16T1046	Trivial (GRH)
16.8.4398833596213134765625.1	x^16 - 3x^15 - 14x^14 + 50x^13 + 66x^12 - 319x^11 - 105x^10 + 986x^9 + 17x^8 - 1603x^7 - 275x^6 + 1653x^5 + 1156x^4 - 1655x^3 - 901x^2 + 1146x - 199	\( 5^{12}\cdot 53^{2}\cdot 283^{4} \)	16T1046	Trivial (GRH)
16.0.10464242526589378625536.1	x^16 - 4x^15 + 16x^14 - 64x^13 + 192x^12 - 496x^11 + 1188x^10 - 2520x^9 + 4598x^8 - 7496x^7 + 11112x^6 - 14368x^5 + 16076x^4 - 16000x^3 + 12728x^2 - 7424x + 3548	\( 2^{44}\cdot 29^{6} \)	16T1046	Trivial
16.4.12768281895096506250000.1	x^16 - 3x^15 - x^14 + 25x^13 - 50x^12 + 26x^11 + 80x^10 - 251x^9 + 397x^8 - 400x^7 + 305x^6 - 245x^5 + 211x^4 - 139x^3 + 56x^2 - 12x + 1	\( 2^{4}\cdot 3^{16}\cdot 5^{8}\cdot 83^{4} \)	16T1046	$[2]$ (GRH)
16.12.32228928287404541015625.1	x^16 - 16x^14 - x^13 + 105x^12 + 17x^11 - 363x^10 - 111x^9 + 701x^8 + 352x^7 - 721x^6 - 557x^5 + 303x^4 + 391x^3 + 25x^2 - 76x - 19	\( 3^{2}\cdot 5^{12}\cdot 19^{4}\cdot 103^{4} \)	16T1046	Trivial (GRH)
16.0.39071704248281406250000.1	x^16 - 2x^15 + 8x^14 - 14x^13 + 44x^12 + 4x^11 - 42x^10 + 443x^9 - 983x^8 + 2481x^7 - 2558x^6 - 2254x^5 + 18332x^4 - 34763x^3 + 38418x^2 - 20125x + 4331	\( 2^{4}\cdot 5^{10}\cdot 251^{6} \)	16T1046	$[2, 4]$
16.4.40354076112897600000000.1	x^16 + 11x^14 + 41x^12 + 49x^10 - 37x^8 - 103x^6 - 16x^4 + 37x^2 + 1	\( 2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	16T1046	$[2]$ (GRH)
16.8.1579217486082822509765625.1	x^16 - x^15 - 14x^14 + 14x^13 + 82x^12 - 77x^11 - 257x^10 + 206x^9 + 481x^8 - 273x^7 - 739x^6 + 335x^5 + 1236x^4 - 829x^3 - 1205x^2 + 670x + 521	\( 3^{2}\cdot 5^{12}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4} \)	16T1046	Trivial (GRH)
16.16.33693554028465480712890625.1	x^16 - 4x^15 - 26x^14 + 117x^13 + 247x^12 - 1360x^11 - 947x^10 + 7974x^9 + 339x^8 - 24679x^7 + 6954x^6 + 38359x^5 - 15462x^4 - 25337x^3 + 9109x^2 + 3515x - 149	\( 5^{12}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4} \)	16T1046	Trivial (GRH)
16.8.33693554028465480712890625.1	x^16 + 2x^14 - 4x^13 - 57x^12 - 106x^11 - 10x^10 + 85x^9 + 486x^8 + 1356x^7 + 1405x^6 + 2538x^5 - 7870x^4 - 16285x^3 + 8878x^2 + 12041x - 569	\( 5^{12}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4} \)	16T1046	Trivial (GRH)
16.0.17537439366439787736572265625.1	x^16 + 26x^14 - x^13 + 319x^12 + 13x^11 + 2533x^10 + 441x^9 + 15227x^8 + 4072x^7 + 67729x^6 + 18493x^5 + 205353x^4 + 34975x^3 + 410887x^2 + 9972x + 520451	\( 5^{12}\cdot 19^{4}\cdot 103^{4}\cdot 2213^{2} \)	16T1046	$[1490]$ (GRH)
16.0.43292507018833059260009765625.1	x^16 - x^15 + 50x^14 - 52x^13 + 952x^12 - 636x^11 + 9390x^10 - 834x^9 + 54241x^8 + 29331x^7 + 235141x^6 + 169817x^5 + 728516x^4 + 496341x^3 + 1103694x^2 + 605979x + 705681	\( 3^{2}\cdot 5^{12}\cdot 19^{6}\cdot 61^{2}\cdot 103^{4} \)	16T1046	$[2, 2, 2, 2, 178]$ (GRH)
16.16.84720885663538576000000000000.1	x^16 - 55x^14 + 1220x^12 - 14125x^10 + 92375x^8 - 344375x^6 + 698250x^4 - 676875x^2 + 225625	\( 2^{16}\cdot 5^{12}\cdot 19^{6}\cdot 103^{4} \)	16T1046	Trivial (GRH)