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 17974)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.449728821.1	x^9 - x^8 + 3x^7 + 3x^5 + 5x^4 + 6x^3 + x - 1	\( 3^{3}\cdot 23^{3}\cdot 37^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.827683353.1	x^9 - x^7 - x^6 + 4x^5 + 3x^4 - 3x^3 - 8x^2 - 5x - 1	\( 3^{4}\cdot 7^{3}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1008604096.1	x^9 - 3x^8 + 8x^7 - 10x^6 + 11x^5 - 3x^4 - x^3 + 7x^2 - 3x + 1	\( 2^{6}\cdot 23^{2}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1206078209.1	x^9 - x^8 - 3x^6 + 4x^5 + x^4 + 5x^3 - 2x^2 + 3x - 1	\( 7^{3}\cdot 17^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1543824900.1	x^9 - 2x^8 + 3x^7 - 3x^6 + x^5 + x + 1	\( 2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 83^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1554778368.1	x^9 - 3x^8 + 4x^7 - 6x^6 + 10x^5 - 8x^4 + 4x^3 - 6x^2 + x - 1	\( 2^{8}\cdot 3^{3}\cdot 11^{3}\cdot 13^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1602572337.1	x^9 - 3x^8 + 6x^7 - 7x^6 + 9x^4 - 11x^3 + 9x^2 - 3x + 1	\( 3^{3}\cdot 17^{2}\cdot 59^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.1947729861.1	x^9 - x^8 - 2x^6 + x^5 + x^4 + 7x^3 - 4x^2 + 4x - 8	\( 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.2710612928.1	x^9 - 3x^8 + 8x^7 - 7x^6 + x^5 + 19x^4 - 27x^3 + 26x^2 - 8x + 1	\( 2^{6}\cdot 23^{3}\cdot 59^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3010743296.1	x^9 - x^8 + x^7 - x^6 + 2x^5 + 4x^4 + 6x^3 + 4x^2 + 2x - 2	\( 2^{10}\cdot 11^{3}\cdot 47^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3295407616.1	x^9 - 3x^8 + 5x^7 - x^6 - 5x^5 + 9x^4 - 6x^2 + 7x + 1	\( 2^{9}\cdot 23^{5} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3295407616.2	x^9 - x^8 - x^7 - 2x^6 - 3x^5 + 10x^4 + 9x^3 - 10x^2 - 6x - 5	\( 2^{9}\cdot 23^{5} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3706477056.1	x^9 - 3x^8 - 2x^7 + 11x^6 + 3x^5 - 21x^4 - x^3 + 18x^2 - 4x + 1	\( 2^{9}\cdot 3^{5}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3761099541.1	x^9 - 3x^8 + 4x^6 + 6x^5 - 15x^4 + 15x^3 - 9x^2 - 6x - 1	\( 3^{3}\cdot 23^{3}\cdot 107^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3840162048.1	x^9 - 6x^6 + 10x^3 - 6	\( 2^{8}\cdot 3^{7}\cdot 19^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.3840162048.2	x^9 - 2x^6 + 4x^3 - 2	\( 2^{8}\cdot 3^{7}\cdot 19^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4000405725.1	x^9 - 4x^8 + 6x^7 - 3x^6 - 2x^5 + 8x^4 - 6x^3 + 4x - 1	\( 3^{8}\cdot 5^{2}\cdot 29^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4029274125.1	x^9 + x^7 - 3x^6 + x^5 - 2x^4 - 3x^3 - x^2 - 2x - 1	\( 3^{8}\cdot 5^{3}\cdot 17^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4169786688.2	x^9 - x^8 + 7x^7 + 12x^5 + 7x^4 + 13x^3 + 7x^2 + 4x + 1	\( 2^{6}\cdot 3^{7}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4211732416.1	x^9 - x^8 + 3x^7 - 2x^6 + 4x^5 - 3x^4 + 7x^3 - 9x^2 + 2x + 1	\( 2^{6}\cdot 31^{3}\cdot 47^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4286418453.1	x^9 - 3x^8 + 4x^7 - 8x^6 + 8x^5 + 4x^4 - x^3 - 7x^2 - 1	\( 3^{3}\cdot 31^{3}\cdot 73^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4344531525.1	x^9 - 2x^8 - 2x^7 + 4x^6 + x^3 - 2x^2 + 6x + 11	\( 3^{3}\cdot 5^{2}\cdot 23^{5} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4551303168.1	x^9 - x^8 + 4x^7 - 6x^5 + 2x^4 - 2x^3 - 6x^2 + 3x - 3	\( 2^{13}\cdot 3^{4}\cdot 19^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.4945971456.1	x^9 - 2x^6 - 2	\( 2^{8}\cdot 3^{5}\cdot 43^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5071514624.1	x^9 - x^8 + 4x^7 - 4x^6 + 6x^5 + 6x^4 + 2x^3 + 10x^2 + 3x + 1	\( 2^{10}\cdot 11^{3}\cdot 61^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5277386277.1	x^9 - 5x^6 + 12x^3 - 9	\( 3^{11}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5277386277.2	x^9 - 3x^6 + 4x^3 - 3	\( 3^{11}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5277386277.3	x^9 - 4x^6 + 5x^3 - 3	\( 3^{11}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5277386277.4	x^9 - 2x^6 - x^3 + 3	\( 3^{11}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5646663225.1	x^9 - 2x^8 + 3x^7 - 8x^6 + 13x^5 - 16x^4 + 19x^3 - 15x^2 + 5x + 1	\( 3^{3}\cdot 5^{2}\cdot 7^{3}\cdot 29^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5873448753.1	x^9 - 2x^6 + 2x^3 - 3	\( 3^{7}\cdot 139^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5987076525.1	x^9 - x^6 + 4x^3 - 5	\( 3^{9}\cdot 5^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5987076525.2	x^9 - 4x^6 + 7x^3 - 5	\( 3^{9}\cdot 5^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.5987076525.3	x^9 - x^6 - 4x^3 + 5	\( 3^{9}\cdot 5^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6076102464.1	x^9 - 3x^8 + 9x^7 - 20x^6 + 24x^5 - 33x^4 + 15x^3 - 15x^2 - 1	\( 2^{6}\cdot 3^{3}\cdot 17^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6088178133.1	x^9 - 4x^8 + 10x^7 - 16x^6 + 15x^5 - 9x^4 + 2x^3 + 13x^2 - 4x + 1	\( 3^{5}\cdot 29^{2}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6371311797.1	x^9 - x^8 + x^6 + 2x^5 - x^4 - x^3 - 12x^2 - 10x - 3	\( 3^{3}\cdot 31^{3}\cdot 89^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6460610112.1	x^9 - x^8 + 2x^7 - 3x^6 + 10x^5 - 5x^4 - 7x^3 + 4x^2 + 8x + 2	\( 2^{6}\cdot 3^{3}\cdot 11^{3}\cdot 53^{2} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6706706688.1	x^9 - 2x^6 + 2x^3 - 2	\( 2^{8}\cdot 3^{9}\cdot 11^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6706706688.2	x^9 - 4x^6 + 4x^3 - 2	\( 2^{8}\cdot 3^{9}\cdot 11^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6706706688.3	x^9 - 2x^6 + 2	\( 2^{8}\cdot 3^{9}\cdot 11^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.6956883693.1	x^9 - 4x^8 + 8x^7 - 8x^6 + 5x^5 - 10x^4 + 30x^3 - 39x^2 + 27x - 9	\( 3^{5}\cdot 31^{5} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.3.7232952991.1	x^9 - 3x^8 + 7x^6 - 5x^5 - 8x^4 + 12x^3 + 2x^2 - 12x - 1	\( -\,11^{2}\cdot 17^{3}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.7498065348.1	x^9 - 3x^8 + 2x^7 + 4x^6 - 2x^5 - x^3 + 2x^2 + 4x + 2	\( 2^{2}\cdot 3^{6}\cdot 137^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.7589871936.1	x^9 - 4x^8 + 13x^7 - 29x^6 + 51x^5 - 70x^4 + 78x^3 - 63x^2 + 41x - 17	\( 2^{6}\cdot 3^{3}\cdot 19^{2}\cdot 23^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.7591423977.1	x^9 + 5x^7 - 2x^6 + 9x^5 - 5x^4 + 10x^3 - 4x^2 + 5x - 2	\( 3^{3}\cdot 37^{2}\cdot 59^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.7883502957.1	x^9 - 3x^8 + 7x^6 - 6x^5 - 9x^4 + 15x^3 + 12x^2 + 6x + 1	\( 3^{7}\cdot 11^{2}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.7883502957.3	x^9 - 2x^6 - x^3 + 11	\( 3^{7}\cdot 11^{2}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.3.8037507123.1	x^9 - 3x^8 + x^7 + 6x^6 - 17x^5 + 26x^4 - 27x^3 + 16x^2 - 5x + 1	\( -\,3^{8}\cdot 107^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial
9.1.8068832768.1	x^9 - x^8 + x^6 + 8x^5 - 20x^4 + 16x^3 + 4x^2 - 16x + 8	\( 2^{9}\cdot 23^{2}\cdot 31^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	Trivial