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 matches 1-50 of 1146)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.22663495936.1	x^9 - 4x^8 + 10x^7 - 16x^6 + 20x^5 - 22x^4 + 22x^3 - 16x^2 + 8x - 2	\( 2^{8}\cdot 97^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.56013635584.1	x^9 - x^8 - 6x^7 + 6x^6 + 8x^5 + 4x^4 - 10x^3 - 6x^2 + 5x + 3	\( 2^{14}\cdot 43^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.69257922561.1	x^9 - 3x^8 + 3x^7 + 2x^6 - 3x^5 - 3x^4 + 8x^3 - 3x^2 + 1	\( 3^{12}\cdot 19^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.72313663744.1	x^9 - x^8 - 4x^7 + 28x^3 + 26x^2 + 9x + 1	\( 2^{8}\cdot 7^{10} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.139314069504.1	x^9 - 3x^8 + 12x^7 - 20x^6 + 36x^5 - 36x^4 + 40x^3 - 24x^2 + 12x - 4	\( 2^{18}\cdot 3^{12} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.326653399296.1	x^9 - 3x^8 + 6x^7 - 10x^6 + 12x^5 - 12x^4 + 8x^3 - 12x^2 - 4	\( 2^{8}\cdot 3^{12}\cdot 7^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.557256278016.1	x^9 - 4x^6 + 18x^5 - 12x^4 - 24x^3 + 36x^2 + 45x + 12	\( 2^{20}\cdot 3^{12} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.557256278016.2	x^9 - 12x^5 - 24x^4 + 16x^3 + 48x^2 + 12x + 16	\( 2^{20}\cdot 3^{12} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1075850221824.1	x^9 - 3x^8 + 4x^7 + 6x^2 + 3x + 3	\( 2^{8}\cdot 3^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1511207993344.1	x^9 - 3x^8 + 4x^7 - 8x^2 - 4x - 4	\( 2^{18}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1511207993344.2	x^9 - 4x^8 + 4x^7 - 14x^5 + 56x^4 - 84x^3 + 80x^2 - 47x + 12	\( 2^{18}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1511207993344.3	x^9 - 3x^8 + 4x^7 + 4x^2 + 2x + 2	\( 2^{18}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1586874322944.1	x^9 - 6x^6 - 12x^3 - 36x^2 - 18x - 4	\( 2^{12}\cdot 3^{18} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.1912622616576.1	x^9 - x^8 + 2x^7 - 14x^4 - 14x^3 + 16x^2 + 33x - 3	\( 2^{12}\cdot 3^{4}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.2125764000000.1	x^9 - 3x^8 + 6x^7 + 8x^6 - 24x^5 + 42x^4 + 6x^3 + 30	\( 2^{8}\cdot 3^{12}\cdot 5^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.2624400000000.2	x^9 - x^8 - 4x^7 - 6x^6 + 16x^5 + 16x^4 + 4x^3 - 44x^2 + 4x - 4	\( 2^{10}\cdot 3^{8}\cdot 5^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.3070176804864.1	x^9 - 12x^6 + 6x^5 + 24x^4 + 64x^3 + 36x^2 - 3x - 8	\( 2^{14}\cdot 3^{8}\cdot 13^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.3689472640000.1	x^9 - 3x^8 + 4x^7 - 32x^2 - 16x - 16	\( 2^{10}\cdot 5^{4}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.4001504141376.1	x^9 - 6x^7 - 6x^6 + 12x^5 + 24x^4 + 4x^3 - 24x^2 + 39x - 8	\( 2^{6}\cdot 3^{12}\cdot 7^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	$[3]$
9.1.4303400887296.1	x^9 - x^8 + 2x^7 + 48x^2 + 36x + 12	\( 2^{10}\cdot 3^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.4628074479616.1	x^9 - x^8 + 2x^7 - 8x^2 - 6x - 2	\( 2^{14}\cdot 7^{10} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.6044831973376.1	x^9 - 3x^8 + 4x^7 + 16x^2 + 8x + 8	\( 2^{20}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	$[3]$
9.1.7529536000000.1	x^9 - 2x^8 + 2x^7 - 6x^6 + 48x^5 + 22x^4 + 6x^3 - 26x^2 - 17x - 4	\( 2^{12}\cdot 5^{6}\cdot 7^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.8033551259904.1	x^9 - 6x^6 - 18x^5 - 54x^4 - 90x^3 - 90x^2 - 54x - 16	\( 2^{8}\cdot 3^{22} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.11284439629824.1	x^9 - 3x^8 - 24x^6 + 18x^5 + 18x^4 - 24x^3 + 9x - 3	\( 2^{18}\cdot 3^{16} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.11284439629824.2	x^9 - 3x^8 - 4x^6 + 12x^5 - 24x^4 - 16x^3 - 36x^2 + 6x - 26	\( 2^{18}\cdot 3^{16} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.11284439629824.3	x^9 - 3x^8 + 12x^7 - 4x^6 + 18x^5 + 18x^4 + 36x^3 + 36x^2 + 9x - 3	\( 2^{18}\cdot 3^{16} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.13286025000000.2	x^9 - 3x^8 - 6x^7 + 38x^6 - 24x^5 + 48x^4 - 84x^3 + 72x^2 - 36x + 8	\( 2^{6}\cdot 3^{12}\cdot 5^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.17213603549184.1	x^9 - 3x^8 + 4x^7 - 24x^2 - 12x - 12	\( 2^{12}\cdot 3^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.17213603549184.2	x^9 - 3x^8 + 4x^7 - 14x^6 + 14x^4 + 56x^3 + 54x^2 + 13x - 1	\( 2^{12}\cdot 3^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.17213603549184.3	x^9 - 2x^8 + 8x^7 + 72x^2 + 108x + 72	\( 2^{12}\cdot 3^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.20905817554944.1	x^9 - 12x^6 - 12x^5 - 24x^4 + 64x^3 + 96x^2 + 72x + 96	\( 2^{14}\cdot 3^{12}\cdot 7^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.21607027568896.1	x^9 - 2x^8 + 8x^7 - 14x^6 + 28x^5 - 56x^4 + 56x^3 - 72x^2 + 88x - 44	\( 2^{8}\cdot 7^{8}\cdot 11^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.21607027568896.2	x^9 - 3x^8 + 18x^7 - 28x^6 + 84x^5 - 42x^4 + 98x^3 + 88x^2 - 5x + 93	\( 2^{8}\cdot 7^{8}\cdot 11^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.21785966991936.1	x^9 + 42x^5 - 42x^4 - 126x^3 + 132x^2 + 21x + 28	\( 2^{6}\cdot 3^{10}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial (GRH)
9.1.22483074023424.1	x^9 - 3x^8 + 4x^7 + 24x^2 + 12x + 12	\( 2^{18}\cdot 3^{6}\cdot 7^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.23059204000000.1	x^9 - x^8 + 2x^7 + 28x^5 - 28x^4 + 28x^3 + 24x^2 + 200x - 204	\( 2^{8}\cdot 5^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	$[3]$
9.1.23059204000000.2	x^9 - 3x^8 + 4x^7 - 10x^2 - 5x - 5	\( 2^{8}\cdot 5^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.23059204000000.3	x^9 - 3x^8 + 4x^7 + 10x^2 + 5x + 5	\( 2^{8}\cdot 5^{6}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.25389989167104.10	x^9 + 12x^3 - 36x^2 - 18x + 48	\( 2^{16}\cdot 3^{18} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.26458925342976.4	x^9 - 3x^8 + 3x^7 + 11x^6 + 18x^5 + 3x^3 + 9x^2 - 12	\( 2^{8}\cdot 3^{16}\cdot 7^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial (GRH)
9.1.27549901440000.1	x^9 - 3x^8 + 12x^7 - 28x^6 + 72x^5 - 108x^4 + 108x^3 - 72x^2 + 36x - 12	\( 2^{10}\cdot 3^{16}\cdot 5^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.30601961865216.2	x^9 - 4x^8 + 4x^7 + 14x^5 - 28x^4 - 4x^2 + 51x - 16	\( 2^{16}\cdot 3^{4}\cdot 7^{8} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.31870270181376.4	x^9 - 8x^6 + 30x^5 + 90x^4 + 44x^3 + 84x^2 + 27x + 26	\( 2^{12}\cdot 3^{12}\cdot 11^{4} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial (GRH)
9.1.32134205039616.1	x^9 - 24x^6 + 48x^3 + 216x^2 - 108x - 296	\( 2^{10}\cdot 3^{22} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	$[3]$
9.1.32428742501376.1	x^9 - x^8 + 6x^7 - 6x^6 + 16x^5 + 18x^4 + 54x^3 + 80x^2 + 66x + 34	\( 2^{10}\cdot 3^{8}\cdot 13^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	$[3]$
9.1.34012224000000.8	x^9 + 12x^7 - 2x^6 + 48x^5 - 6x^4 + 72x^3 + 18x^2 + 27x + 6	\( 2^{12}\cdot 3^{12}\cdot 5^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial (GRH)
9.1.45137758519296.1	x^9 - 48x^3 + 216x - 160	\( 2^{20}\cdot 3^{16} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial (GRH)
9.1.47469233803264.3	x^9 - 3x^8 + 4x^7 - 12x^6 + 16x^5 + 72x^4 - 336x^3 + 560x^2 - 400x + 112	\( 2^{12}\cdot 7^{4}\cdot 13^{6} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial
9.1.52716660869376.1	x^9 - x^8 + 4x^7 - 42x^5 + 42x^4 - 84x^3 + 36x^2 + 573x - 633	\( 2^{8}\cdot 3^{6}\cdot 7^{10} \)	$\mathrm{P}\Gamma\mathrm{L}(2,8)$ (as 9T32)	Trivial