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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.5258930030792146944.1	x^16 - 4x^14 + 4x^12 - 16x^10 - 20x^8 + 8x^6 + 16x^4 - 16x^2 + 4	\( 2^{40}\cdot 3^{14} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial
16.0.5258930030792146944.3	x^16 + 4x^14 + 4x^12 + 16x^10 - 20x^8 - 8x^6 + 16x^4 + 16x^2 + 4	\( 2^{40}\cdot 3^{14} \)	$C_2\times SD_{16}$ (as 16T48)	$[2]$
16.0.33115249535031967744.4	x^16 + 8x^12 + 34x^8 + 72x^4 + 49	\( 2^{48}\cdot 7^{6} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial
16.0.472769874482845188096.3	x^16 - 2x^12 + 5x^8 + 2x^4 + 1	\( 2^{56}\cdot 3^{8} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial (GRH)
16.4.1622647227216566419456.2	x^16 - 30x^8 + 1	\( 2^{48}\cdot 7^{8} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial (GRH)
16.4.1891079497931380752384.7	x^16 - 28x^12 - 190x^8 + 28x^4 + 1	\( 2^{58}\cdot 3^{8} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial (GRH)
16.0.11017296355467800346624.2	x^16 - 8x^15 + 32x^14 - 60x^13 + 68x^12 - 112x^11 + 520x^10 - 936x^9 + 844x^8 - 144x^7 + 1216x^6 - 2120x^5 + 1808x^4 + 240x^3 + 32x^2 - 16x + 4	\( 2^{32}\cdot 3^{12}\cdot 13^{6} \)	$C_2\times SD_{16}$ (as 16T48)	$[2]$
16.0.86162309624498535530496.1	x^16 - 12x^14 + 114x^12 - 312x^10 + 606x^8 - 576x^6 + 396x^4 - 144x^2 + 36	\( 2^{54}\cdot 3^{14} \)	$C_2\times SD_{16}$ (as 16T48)	$[3]$ (GRH)
16.0.2820427866999756888735744.1	x^16 + 20x^14 + 172x^12 + 740x^10 + 1714x^8 + 1892x^6 + 2476x^4 + 452x^2 + 1369	\( 2^{40}\cdot 3^{12}\cdot 13^{6} \)	$C_2\times SD_{16}$ (as 16T48)	$[2, 2, 6]$ (GRH)
16.16.2820427866999756888735744.1	x^16 - 28x^14 + 292x^12 - 1456x^10 + 3724x^8 - 4744x^6 + 2512x^4 - 208x^2 + 4	\( 2^{40}\cdot 3^{12}\cdot 13^{6} \)	$C_2\times SD_{16}$ (as 16T48)	Trivial (GRH)
16.0.476652309522958914196340736.1	x^16 - 4x^15 + 4x^13 + 174x^12 - 912x^11 + 2260x^10 - 2780x^9 + 3636x^8 - 17008x^7 + 40276x^6 - 40584x^5 + 28872x^4 - 45184x^3 + 74220x^2 - 42872x + 14278	\( 2^{40}\cdot 3^{12}\cdot 13^{8} \)	$C_2\times SD_{16}$ (as 16T48)	$[2, 2, 12]$ (GRH)
16.16.476652309522958914196340736.1	x^16 - 8x^15 - 12x^14 + 200x^13 - 42x^12 - 1872x^11 + 760x^10 + 8396x^9 - 756x^8 - 17840x^7 - 8336x^6 + 11760x^5 + 13038x^4 + 4744x^3 + 696x^2 + 44x + 1	\( 2^{40}\cdot 3^{12}\cdot 13^{8} \)	$C_2\times SD_{16}$ (as 16T48)	$[2]$ (GRH)