Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.239685200591389196288.1	x^16 - 2x^14 - 2x^12 + 9x^10 - 3x^8 - 14x^6 + 10x^4 - 2x^2 + 2	\( 2^{35}\cdot 17^{8} \)	16T1642	Trivial (GRH)
16.0.239685200591389196288.2	x^16 + 2x^14 - 2x^12 - 9x^10 - 3x^8 + 14x^6 + 10x^4 + 2x^2 + 2	\( 2^{35}\cdot 17^{8} \)	16T1642	Trivial
16.4.239685200591389196288.2	x^16 - 9x^14 + 31x^12 - 53x^10 + 47x^8 - 20x^6 + 4x^4 - 2x^2 + 2	\( 2^{35}\cdot 17^{8} \)	16T1642	Trivial (GRH)
16.0.239685200591389196288.3	x^16 + 9x^14 + 31x^12 + 53x^10 + 47x^8 + 20x^6 + 4x^4 + 2x^2 + 2	\( 2^{35}\cdot 17^{8} \)	16T1642	Trivial
16.2.3834963209462227140608.1	x^16 + 2x^14 - 23x^12 + 42x^10 + 9x^8 - 24x^6 - 52x^4 - 20x^2 - 2	\( -\,2^{39}\cdot 17^{8} \)	16T1642	Trivial
16.6.3834963209462227140608.1	x^16 - 8x^12 + 16x^10 - 49x^8 - 64x^6 + 18x^4 + 24x^2 - 2	\( -\,2^{39}\cdot 17^{8} \)	16T1642	Trivial (GRH)
16.2.3834963209462227140608.2	x^16 - 8x^12 - 16x^10 - 49x^8 + 64x^6 + 18x^4 - 24x^2 - 2	\( -\,2^{39}\cdot 17^{8} \)	16T1642	Trivial
16.6.3834963209462227140608.2	x^16 - 2x^14 - 23x^12 - 42x^10 + 9x^8 + 24x^6 - 52x^4 + 20x^2 - 2	\( -\,2^{39}\cdot 17^{8} \)	16T1642	Trivial (GRH)
16.0.216103714323709222887358464.1	x^16 - 56x^12 + 312x^10 + 6400x^8 + 27360x^6 + 39768x^4 + 3360x^2 + 1776	\( 2^{44}\cdot 3^{11}\cdot 37^{5} \)	16T1642	Trivial (GRH)
16.0.216103714323709222887358464.2	x^16 - 56x^12 - 312x^10 + 6400x^8 - 27360x^6 + 39768x^4 - 3360x^2 + 1776	\( 2^{44}\cdot 3^{11}\cdot 37^{5} \)	16T1642	Trivial (GRH)
16.0.3231121441418329318400000000.1	x^16 + 40x^14 + 656x^12 + 5740x^10 + 29063x^8 + 85785x^6 + 139592x^4 + 106485x^2 + 23129	\( 2^{16}\cdot 5^{8}\cdot 101^{5}\cdot 229^{3} \)	16T1642	$[2, 426]$ (GRH)
16.16.3231121441418329318400000000.1	x^16 - 40x^14 + 656x^12 - 5740x^10 + 29063x^8 - 85785x^6 + 139592x^4 - 106485x^2 + 23129	\( 2^{16}\cdot 5^{8}\cdot 101^{5}\cdot 229^{3} \)	16T1642	Trivial (GRH)
16.8.41402800270917370540087890625.1	x^16 - 6x^15 - 19x^14 + 158x^13 + 23x^12 - 1290x^11 + 757x^10 + 4830x^9 - 4578x^8 - 9234x^7 + 12626x^6 + 5114x^5 - 16581x^4 + 9834x^3 + 2593x^2 - 8428x + 4111	\( 5^{11}\cdot 29^{3}\cdot 101^{5}\cdot 149^{3} \)	16T1642	Trivial (GRH)
16.0.80778036035458232960000000000.1	x^16 + 66x^14 + 1741x^12 + 24271x^10 + 195396x^8 + 917220x^6 + 2360880x^4 + 2730825x^2 + 578225	\( 2^{16}\cdot 5^{10}\cdot 101^{5}\cdot 229^{3} \)	16T1642	$[2, 2, 2526]$ (GRH)
16.16.80778036035458232960000000000.1	x^16 - 60x^14 + 1451x^12 - 18245x^10 + 128929x^8 - 519955x^6 + 1160940x^4 - 1311025x^2 + 578225	\( 2^{16}\cdot 5^{10}\cdot 101^{5}\cdot 229^{3} \)	16T1642	Trivial (GRH)
16.0.4181682827362654424548876953125.1	x^16 - 49x^14 + 1090x^12 - 14352x^10 + 122309x^8 - 691280x^6 + 2534880x^4 - 5530880x^2 + 5530880	\( 5^{11}\cdot 29^{3}\cdot 101^{6}\cdot 149^{3} \)	16T1642	$[2, 4, 12]$ (GRH)
16.8.422349965563628096879436572265625.1	x^16 - 4x^15 + 102x^14 - 332x^13 + 3382x^12 - 8514x^11 + 35444x^10 - 66076x^9 - 6105x^8 - 112204x^7 - 516604x^6 + 1051474x^5 + 1695667x^4 - 459358x^3 - 861001x^2 + 46166x + 120371	\( 5^{11}\cdot 29^{3}\cdot 101^{7}\cdot 149^{3} \)	16T1642	$[2]$ (GRH)
16.0.42657346521926437784823093798828125.1	x^16 + 136x^14 - 58x^13 + 7596x^12 - 6354x^11 + 225107x^10 - 262273x^9 + 3807771x^8 - 5085440x^7 + 36338415x^6 - 45893065x^5 + 174591890x^4 - 139729010x^3 + 343797955x^2 - 127293585x + 222521795	\( 5^{11}\cdot 29^{3}\cdot 101^{8}\cdot 149^{3} \)	16T1642	$[2, 2, 4, 12]$ (GRH)