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 matches 1-50 of 636)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.92371321.1	x^9 - 2x^8 + 5x^7 - 7x^6 + 8x^5 - 9x^4 + 7x^3 - 4x^2 + 3x - 1	\( 7^{2}\cdot 1373^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.132043081.1	x^9 + 2x^7 - 3x^6 + 3x^5 - 4x^4 + 3x^3 - 4x^2 + 2x - 1	\( 11491^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.613107121.1	x^9 - 2x^8 + 5x^6 - 7x^5 + 2x^4 + 6x^3 - 7x^2 + 4x - 1	\( 11^{2}\cdot 2251^{2} \)	$A_9$ (as 9T33)	Trivial
9.5.3200504329.1	x^9 - x^8 - x^7 - 2x^5 + 4x^4 - 5x^2 + 1	\( 11^{2}\cdot 37^{2}\cdot 139^{2} \)	$A_9$ (as 9T33)	Trivial
9.5.4781860801.1	x^9 - 3x^8 + x^7 + 4x^6 - x^5 - 5x^4 - 3x^3 + 4x^2 + 2x - 1	\( 69151^{2} \)	$A_9$ (as 9T33)	Trivial
9.5.22253180625.1	x^9 - 2x^8 - x^6 + 6x^4 + x^3 - 2x^2 - 3x - 1	\( 3^{6}\cdot 5^{4}\cdot 13^{2}\cdot 17^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.22992263424.1	x^9 - 3x^8 + 9x^7 - 21x^6 + 39x^5 - 51x^4 + 45x^3 - 27x^2 + 9x - 3	\( 2^{8}\cdot 3^{12}\cdot 13^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.117062516736.1	x^9 - 3x^8 + 12x^7 - 24x^6 + 36x^5 - 24x^4 + 6x^3 + 6x^2 - 3x + 1	\( 2^{14}\cdot 3^{10}\cdot 11^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.774400000000.1	x^9 - x^8 - 4x^7 + 4x^6 + 6x^5 - 14x^4 + 34x^3 - 34x^2 + 4x - 4	\( 2^{14}\cdot 5^{8}\cdot 11^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.1479901446144.1	x^9 - 3x^8 + 4x^7 + 12x^6 - 56x^5 + 56x^4 + 60x^3 - 188x^2 + 193x - 83	\( 2^{24}\cdot 3^{6}\cdot 11^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.2624400000000.1	x^9 - 2x^8 - 4x^6 + 14x^5 - 12x^4 - 6x^3 + 30x^2 - 27x + 12	\( 2^{10}\cdot 3^{8}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.3321506250000.1	x^9 - 6x^7 - 4x^6 + 27x^5 + 12x^4 - 80x^3 + 18x^2 + 87x - 56	\( 2^{4}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.1	x^9 - 20x^6 - 45x^5 - 102x^4 - 120x^3 - 120x^2 - 60x - 20	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.2	x^9 - 6x^7 - 15x^6 + 9x^5 + 21x^4 - 21x^2 - 1	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.3	x^9 - 6x^7 - 6x^6 + 18x^5 + 42x^4 - 30x^3 - 162x^2 - 162x - 54	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.4	x^9 - 3x^8 + 6x^7 - 10x^6 + 18x^5 - 12x^4 + 16x^3 - 42x^2 + 45x + 9	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.5	x^9 - 3x^8 + 9x^7 - 27x^6 + 6x^5 + 18x^4 - 39x^3 - 3x^2 + 9x - 7	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.6	x^9 - 3x^8 + 12x^7 - 34x^6 + 84x^5 - 150x^4 + 250x^3 - 300x^2 + 225x - 75	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.5904900000000.7	x^9 - 2x^8 + 4x^7 - 8x^6 + 16x^5 + 22x^4 - 44x^3 + 178x^2 - 221x + 432	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.7836416409600.1	x^9 - 3x^8 + 12x^7 - 12x^6 + 42x^5 - 6x^4 + 132x^3 + 60x^2 + 165x + 185	\( 2^{16}\cdot 3^{14}\cdot 5^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.9042800765625.1	x^9 + 6x^7 - 11x^6 - 3x^5 - 69x^4 - 15x^3 - 99x^2 + 99x - 33	\( 3^{14}\cdot 5^{6}\cdot 11^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.9226406250000.1	x^9 - 2x^8 + 9x^7 - 18x^6 + 26x^5 - 15x^4 - 5x^3 + 20x^2 - 15x + 5	\( 2^{4}\cdot 3^{10}\cdot 5^{10} \)	$A_9$ (as 9T33)	$[2]$
9.9.11729467378561.1	x^9 - 16x^7 - 8x^6 + 69x^5 + 57x^4 - 61x^3 - 61x^2 - 8x + 1	\( 37^{2}\cdot 151^{2}\cdot 613^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.13286025000000.1	x^9 - 3x^8 + 9x^7 - 12x^6 + 6x^5 + 18x^4 - 59x^3 + 87x^2 - 81x + 48	\( 2^{6}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.21785966991936.2	x^9 - 3x^8 - 3x^7 + 14x^6 - 21x^5 + 84x^4 - 91x^3 + 180x^2 - 78x + 55	\( 2^{6}\cdot 3^{10}\cdot 7^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.23619600000000.1	x^9 - 3x^8 + 4x^7 - 12x^6 - 9x^5 + 93x^4 - 54x^3 - 108x^2 + 99x - 27	\( 2^{10}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.26040609000000.1	x^9 - 6x^7 - 3x^6 - 36x^5 + 36x^4 + 60x^3 + 189x^2 + 357x + 224	\( 2^{6}\cdot 3^{12}\cdot 5^{6}\cdot 7^{2} \)	$A_9$ (as 9T33)	Trivial
9.9.27468531727849.1	x^9 - 2x^8 - 12x^7 + 17x^6 + 37x^5 - 39x^4 - 26x^3 + 27x^2 - x - 1	\( 5241043^{2} \)	$A_9$ (as 9T33)	Trivial
9.9.29682796068864.1	x^9 - x^8 - 16x^7 + 24x^6 + 48x^5 - 72x^4 - 32x^3 + 32x^2 + 3x - 3	\( 2^{18}\cdot 3^{2}\cdot 3547^{2} \)	$A_9$ (as 9T33)	Trivial
9.1.41990400000000.1	x^9 - 2x^8 + 4x^7 - 8x^6 + 16x^5 - 8x^4 + 16x^3 - 32x^2 + 4x + 72	\( 2^{14}\cdot 3^{8}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.45137758519296.2	x^9 - 3x^8 + 32x^6 - 24x^5 - 24x^4 + 32x^3 - 12x + 4	\( 2^{20}\cdot 3^{16} \)	$A_9$ (as 9T33)	Trivial
9.1.53144100000000.3	x^9 - 3x^8 - 6x^7 + 18x^6 + 3x^5 - 75x^4 - 120x^3 + 60x^2 + 120x - 380	\( 2^{8}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.53144100000000.6	x^9 - 3x^7 - 9x^5 - 114x^4 + 195x^3 - 468x^2 + 240x - 74	\( 2^{8}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.53144100000000.12	x^9 - 3x^8 - 6x^7 + 8x^6 + 36x^5 - 50x^3 + 15x + 5	\( 2^{8}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.53144100000000.13	x^9 - 15x^6 + 81x^4 - 60x^3 + 10	\( 2^{8}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.53144100000000.14	x^9 - 3x^8 - 6x^7 + 38x^6 - 84x^5 + 120x^4 - 110x^3 + 90x^2 - 45x + 15	\( 2^{8}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.94478400000000.2	x^9 - 4x^8 - 4x^7 + 16x^6 + 26x^5 + 32x^4 + 52x^3 + 32x^2 + 17x + 12	\( 2^{12}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.94478400000000.6	x^9 - 2x^8 + 46x^6 - 156x^5 + 360x^4 - 480x^3 + 480x^2 - 270x + 120	\( 2^{12}\cdot 3^{10}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial
9.1.119191893590016.2	x^9 - 3x^8 + 48x^3 - 144x^2 + 144x - 48	\( 2^{14}\cdot 3^{16}\cdot 13^{2} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.119574225000000.6	x^9 - 3x^8 - 9x^7 + x^6 + 24x^5 + 9x^4 - 37x^3 - 81x^2 - 81x - 34	\( 2^{6}\cdot 3^{14}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.151336128515625.4	x^9 - 9x^7 + 45x^5 - 18x^4 - 90x^3 + 27x^2 + 45x - 25	\( 3^{18}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.212576400000000.1	x^9 + 15x^5 - 84x^4 + 180x^3 - 270x^2 + 450x - 150	\( 2^{10}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.212576400000000.2	x^9 - 3x^8 - 3x^7 + 6x^6 + 33x^5 - 45x^4 - 45x^3 + 60x^2 + 30x - 10	\( 2^{10}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.212576400000000.3	x^9 - 3x^8 + 12x^7 - 24x^6 + 84x^5 - 24x^4 + 72x^3 + 132x^2 - 9x + 199	\( 2^{10}\cdot 3^{12}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.289340100000000.1	x^9 - 2x^8 - 6x^7 + 12x^6 + 21x^5 - 18x^4 - 24x^3 + 48x^2 + 144x - 288	\( 2^{8}\cdot 3^{10}\cdot 5^{8}\cdot 7^{2} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.306110016000000.8	x^9 + 12x^7 - 8x^6 + 51x^5 - 36x^4 + 102x^3 + 54x + 84	\( 2^{12}\cdot 3^{14}\cdot 5^{6} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.348575471870976.1	x^9 - 3x^8 - 3x^7 + 21x^6 - 21x^5 - 21x^4 - 21x^3 + 339x^2 - 324x + 96	\( 2^{10}\cdot 3^{10}\cdot 7^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.478296900000000.14	x^9 - 20x^6 + 12x^4 + 140x^3 - 90x^2 - 150x - 70	\( 2^{8}\cdot 3^{14}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.478296900000000.16	x^9 - 9x^4 - 10	\( 2^{8}\cdot 3^{14}\cdot 5^{8} \)	$A_9$ (as 9T33)	Trivial (GRH)
9.1.669698211446784.1	x^9 - 12x^3 + 9x - 16	\( 2^{26}\cdot 3^{10}\cdot 13^{2} \)	$A_9$ (as 9T33)	Trivial (GRH)