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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.42286532693852160000.2	x^16 - 4x^15 + 6x^14 - 8x^13 - 8x^12 + 96x^11 - 170x^10 + 60x^9 + 169x^8 - 624x^7 + 1082x^6 - 92x^5 - 1824x^4 + 1596x^3 + 388x^2 - 1020x + 433	\( 2^{32}\cdot 3^{8}\cdot 5^{4}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial
16.0.42286532693852160000.3	x^16 - 8x^15 + 32x^14 - 68x^13 + 71x^12 + 20x^11 - 120x^10 + 116x^9 + 57x^8 - 140x^7 + 128x^6 + 44x^5 - 69x^4 + 112x^3 + 49	\( 2^{32}\cdot 3^{8}\cdot 5^{4}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2]$
16.0.326284974489600000000.1	x^16 + 6x^14 + 3x^12 + 24x^10 + 273x^8 + 648x^6 + 667x^4 + 378x^2 + 81	\( 2^{32}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2]$
16.0.503017767708917760000.1	x^16 - 8x^15 + 32x^14 - 60x^13 + 86x^12 - 180x^11 + 488x^10 - 668x^9 + 613x^8 - 924x^7 + 2088x^6 - 1944x^5 + 1152x^4 - 1512x^3 + 2592x^2 - 1296x + 324	\( 2^{32}\cdot 3^{8}\cdot 5^{4}\cdot 13^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial
16.0.676584523101634560000.1	x^16 + 28x^14 + 324x^12 + 2008x^10 + 7212x^8 + 15160x^6 + 17936x^4 + 10800x^2 + 2500	\( 2^{36}\cdot 3^{8}\cdot 5^{4}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2]$
16.0.5220559591833600000000.1	x^16 - 4x^15 + 6x^14 + 4x^13 - 30x^12 + 12x^11 + 170x^10 - 536x^9 + 1343x^8 - 2944x^7 + 4898x^6 - 6384x^5 + 7104x^4 - 6760x^3 + 5472x^2 - 3224x + 961	\( 2^{36}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2, 2]$
16.8.26429082933657600000000.1	x^16 - 8x^15 + 20x^14 - 112x^12 + 308x^11 - 450x^10 + 380x^9 - 231x^8 + 316x^7 - 678x^6 + 956x^5 - 704x^4 + 196x^3 + 18x^2 - 12x + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial (GRH)
16.8.26429082933657600000000.2	x^16 - 4x^15 + 6x^14 + 4x^13 - 25x^12 + 20x^11 + 14x^10 + 52x^9 - 481x^8 + 1228x^7 - 1646x^6 + 1120x^5 + 75x^4 - 644x^3 + 316x^2 - 36x + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial (GRH)
16.0.4602926960641415577600000000.1	x^16 + 20x^14 + 217x^12 + 1468x^10 + 7248x^8 + 23708x^6 + 57433x^4 + 75508x^2 + 58081	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 11^{4}\cdot 13^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2, 6, 72]$ (GRH)
16.16.4602926960641415577600000000.1	x^16 - 36x^14 + 497x^12 - 3412x^10 + 12408x^8 - 23356x^6 + 20673x^4 - 6412x^2 + 121	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 11^{4}\cdot 13^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial (GRH)
16.0.6191171251706894745600000000.1	x^16 + 44x^14 + 818x^12 + 8172x^10 + 48275x^8 + 174324x^6 + 401870x^4 + 546296x^2 + 421201	\( 2^{36}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4}\cdot 11^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	$[2, 2, 2, 156]$ (GRH)
16.16.6191171251706894745600000000.1	x^16 - 52x^14 + 1058x^12 - 10932x^10 + 61883x^8 - 191292x^6 + 298022x^4 - 188200x^2 + 32761	\( 2^{36}\cdot 3^{8}\cdot 5^{8}\cdot 7^{4}\cdot 11^{4} \)	$C_2\times Q_8:C_2^2$ (as 16T69)	Trivial (GRH)