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 21 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.79082438656.1	x^9 - 3x^8 + 12x^6 - 14x^5 - 2x^4 + 12x^2 + x + 1	\( 2^{14}\cdot 13^{6} \)	$\PSL(2,8)$ (as 9T27)	Trivial
9.1.1450463739904.1	x^9 - x^8 + 12x^6 - 12x^5 - 28x^4 + 48x^3 - 20x^2 + 5x - 1	\( 2^{14}\cdot 97^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.2312735309824.1	x^9 - x^8 - 16x^6 + 36x^5 - 12x^4 - 8x^3 - 3x - 1	\( 2^{14}\cdot 109^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.2671367962624.1	x^9 + 4x^7 - 10x^5 - 12x^4 + 12x^2 + 10x + 4	\( 2^{14}\cdot 113^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.4169931445681.1	x^9 + x^7 - 4x^6 - 12x^4 - x^3 - 7x^2 - x - 1	\( 1429^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.4262209798144.1	x^9 - x^8 + 8x^7 - 18x^6 + 28x^5 - 56x^4 + 68x^3 - 56x^2 + 26x - 6	\( 2^{14}\cdot 127^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.6029426229121.1	x^9 - 2x^8 + 10x^7 - 25x^6 + 34x^5 - 40x^4 + 52x^3 - 45x^2 + 20x - 4	\( 1567^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.6116164255744.1	x^9 + 8x^7 - 16x^6 + 30x^5 - 64x^4 + 80x^3 - 56x^2 + 22x - 4	\( 2^{14}\cdot 139^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.6347497291776.1	x^9 - 6x^6 + 18x^5 - 18x^4 + 36x^3 + 18x^2 + 27x + 22	\( 2^{14}\cdot 3^{18} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.6769201929361.1	x^9 - 2x^8 + 6x^6 - 8x^5 - 12x^4 + 12x^3 + 12x^2 - x + 1	\( 1613^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.8075418025984.1	x^9 - 4x^8 + 10x^5 + 20x^4 - 72x^3 - 8x^2 + 161x - 128	\( 2^{14}\cdot 149^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.8215383330001.1	x^9 - 18x^7 - 2x^6 + 85x^5 + 24x^4 - 8x^3 + 19x^2 + 5x - 14	\( 1693^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.8517805686784.1	x^9 - 2x^8 + 2x^7 + 10x^6 - 18x^5 + 30x^4 + 66x^3 - 42x^2 + 71x + 152	\( 2^{14}\cdot 151^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.15904215784081.1	x^9 - 3x^8 + 4x^6 + 5x^5 - 18x^4 + 23x^3 - 25x^2 + 16x - 4	\( 1997^{4} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.114290809913344.1	x^9 + 34x^5 - 136x^4 + 272x^3 - 340x^2 + 238x - 68	\( 2^{14}\cdot 17^{8} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.514147280633856.1	x^9 - 12x^6 - 18x^5 + 36x^2 - 27x - 128	\( 2^{14}\cdot 3^{22} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.41645929731342336.1	x^9 - 36x^6 - 54x^5 + 432x^3 + 324x^2 - 243x - 1152	\( 2^{14}\cdot 3^{26} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.41645929731342336.2	x^9 - 36x^6 - 54x^5 - 324x^4 - 216x^3 - 972x^2 - 243x - 2124	\( 2^{14}\cdot 3^{26} \)	$\PSL(2,8)$ (as 9T27)	$[7]$
9.1.1805931759515773661624549376.1	x^9 - 444x^6 - 4662x^5 - 27972x^4 - 151848x^3 - 693972x^2 - 1299699x - 26643404	\( 2^{14}\cdot 3^{22}\cdot 37^{8} \)	$\PSL(2,8)$ (as 9T27)	$[63]$ (GRH)
9.9.16339134383250936197651486708561524809.1	x^9 - 3x^8 - 12000x^7 - 295072x^6 + 27805575x^5 + 1157871573x^4 + 7683210630x^3 - 82305140040x^2 - 848281897593x - 1186350537195	\( 3^{4}\cdot 37^{6}\cdot 2977717^{4} \)	$\PSL(2,8)$ (as 9T27)	$[21]$ (GRH)
9.9.823197013411488700177278327969031167198339136.1	x^9 - x^8 - 46044x^7 + 2290792x^6 + 604538774x^5 - 54192964154x^4 - 1082243626268x^3 + 258358461584640x^2 - 8789861772156959x + 75454628055435091	\( 2^{6}\cdot 7^{10}\cdot 37^{8}\cdot 263^{4}\cdot 1283^{4} \)	$\PSL(2,8)$ (as 9T27)	$[9]$ (GRH)