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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.8817149082834027.1	x^14 - x^13 + 4x^12 + x^11 + 6x^10 + 4x^9 + 10x^8 + 12x^6 - 5x^5 + 4x^4 - 7x^3 + 2x^2 - x + 1	\( -\,3^{7}\cdot 13^{4}\cdot 109^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.0.8817149082834027.2	x^14 - 2x^13 + 5x^12 - 6x^11 + 9x^10 - 7x^9 + 8x^8 - 3x^7 + 7x^6 + 7x^5 + 5x^4 + 3x^3 + 4x^2 - x + 1	\( -\,3^{7}\cdot 13^{4}\cdot 109^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.6.8857465265197237.1	x^14 - x^13 - 5x^12 + 6x^11 + 6x^10 - 9x^9 - x^8 + 7x^7 + x^6 - 9x^5 - 6x^4 + 6x^3 + 5x^2 - x - 1	\( 13^{7}\cdot 109^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.6.8857465265197237.2	x^14 - 6x^12 - 3x^11 + 9x^10 + 16x^9 + 8x^8 - 23x^7 - 31x^6 - 14x^5 - x^4 + 12x^3 + 10x^2 + 4x + 1	\( 13^{7}\cdot 109^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.0.28745771808565755904.1	x^14 + 16x^12 + 94x^10 + 256x^8 + 337x^6 + 204x^4 + 52x^2 + 4	\( -\,2^{26}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	$[2]$
14.0.28745771808565755904.2	x^14 + 17x^12 + 108x^10 + 328x^8 + 492x^6 + 328x^4 + 68x^2 + 4	\( -\,2^{26}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	$[2]$
14.14.919864697874104188928.1	x^14 - 24x^12 + 219x^10 - 978x^8 + 2263x^6 - 2628x^4 + 1357x^2 - 242	\( 2^{31}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.14.919864697874104188928.2	x^14 - 20x^12 + 144x^10 - 466x^8 + 740x^6 - 568x^4 + 176x^2 - 8	\( 2^{31}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial