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 4 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.22146577948554513666070757969641536.1	x^9 - 20307x^7 - 643055x^6 + 138412512x^5 + 8796667488x^4 - 176694943488x^3 - 30297960822528x^2 - 967845661396992x - 10323499378798592	\( -\,2^{6}\cdot 3^{12}\cdot 7^{7}\cdot 967^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 7801212]$ (GRH)
9.3.61074718905675065984760751816603136.1	x^9 - 2x^8 - 12783x^7 - 655523x^6 - 8351247x^5 - 109011858x^4 - 648630606x^3 - 3516028401x^2 - 9062063283x - 22186138127	\( -\,2^{9}\cdot 7^{7}\cdot 43^{7}\cdot 127^{7} \)	$S_3\times C_3$ (as 9T4)	$[6, 6, 6, 6, 78876]$ (GRH)
9.3.145301052590257268777341611415271616.1	x^9 - 9507x^7 - 205985x^6 + 30431907x^5 + 1325408898x^4 - 18341132568x^3 - 2154460739013x^2 - 47277836420067x - 346690767098467	\( -\,2^{6}\cdot 3^{12}\cdot 11^{3}\cdot 3169^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 93510522]$ (GRH)
9.3.936731787215569280121379977620891136.1	x^9 - 25761x^7 - 918809x^6 + 222575040x^5 + 15926171508x^4 - 359711868708x^3 - 69450114770892x^2 - 2496333846718440x - 29955576128950872	\( -\,2^{9}\cdot 3^{12}\cdot 31^{7}\cdot 277^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 3, 3, 1036659]$ (GRH)