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 883)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.31381059609.1	x^9 - 6x^6 + 12x^3 + 1	\( 3^{22} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.62523502209.1	x^9 + 3x^7 - 3x^6 + 3x^5 - 6x^4 - 3x^3 - 3x^2 + 3x - 1	\( 3^{12}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.99179645184.1	x^9 + 9x^5 - 21x^3 - 36x^2 - 18x - 4	\( 2^{8}\cdot 3^{18} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.148718980881.4	x^9 + 3x^7 - 4x^6 - 24x^4 - 20x^3 - 9x^2 + 24x - 11	\( 3^{12}\cdot 23^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.176319369216.3	x^9 - 3x^8 + 3x^7 - 3x^6 + 3x^5 - 3x^4 + 6x^2 + 3x + 1	\( 2^{12}\cdot 3^{16} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.242137805625.2	x^9 - 3x^6 + 27x^5 - 27x^4 + 33x^3 - 9x + 7	\( 3^{18}\cdot 5^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.243885847104.1	x^9 - 2x^8 + 8x^7 - 9x^6 + 18x^5 - 6x^4 + 3x^3 + 10x^2 - 6x + 1	\( 2^{6}\cdot 3^{4}\cdot 19^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.301181440000.1	x^9 - 2x^8 - 2x^7 + 6x^6 + 9x^5 - 3x^3 - 12x^2 - 11x - 6	\( 2^{12}\cdot 5^{4}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.375878121921.1	x^9 - 9x^7 - x^6 + 27x^5 + 6x^4 - 36x^3 - 9x^2 + 27x - 15	\( 3^{12}\cdot 29^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.404567235136.1	x^9 + 2x^7 - x^6 - 10x^5 + 8x^4 - 13x^3 + 18x^2 - 6x + 19	\( 2^{6}\cdot 43^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.444611571264.2	x^9 - 2x^6 + 20x^3 + 8	\( 2^{6}\cdot 3^{10}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.490796923761.2	x^9 - 9x^7 - x^6 + 27x^5 + 6x^4 - 52x^3 - 9x^2 + 75x - 47	\( 3^{12}\cdot 31^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.630247042161.1	x^9 - 3x^8 - 3x^7 + 18x^6 - 3x^5 - 48x^4 + 15x^3 + 78x^2 - 12x - 64	\( 3^{16}\cdot 11^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.797493650625.1	x^9 + 9x^7 - 6x^6 + 33x^5 - 27x^4 + 92x^3 - 12x^2 + 99x + 10	\( 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.797493650625.2	x^9 - 3x^8 - 3x^7 + 15x^6 + 3x^5 - 51x^4 + 75x^3 - 54x^2 + 24	\( 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.930196594089.1	x^9 - 9x^6 + 9x^5 - 9x^4 + 33x^3 - 72x^2 + 81x - 41	\( 3^{18}\cdot 7^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.1071483765625.1	x^9 - 3x^8 + 5x^7 - 11x^6 - 3x^5 - 17x^4 - 6x^3 - 28x^2 + 3x - 13	\( 5^{6}\cdot 7^{4}\cdot 13^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.1076561880625.1	x^9 - 3x^8 + 5x^7 - x^6 - 35x^5 + 99x^4 - 176x^3 + 222x^2 - 131x + 27	\( 5^{4}\cdot 7^{6}\cdot 11^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.1425299311881.3	x^9 - 8x^6 + 10x^3 + 27	\( 3^{10}\cdot 17^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.1586874322944.4	x^9 - 9x^7 + 27x^5 - 48x^3 + 63x - 38	\( 2^{12}\cdot 3^{18} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.1827904000000.1	x^9 - 4x^8 + x^7 + 12x^6 - 5x^5 - 16x^4 - 14x^3 - 12x^2 + 99x + 46	\( 2^{12}\cdot 5^{6}\cdot 13^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2008387814976.2	x^9 - 12x^6 + 48x^3 + 8	\( 2^{6}\cdot 3^{22} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.2008387814976.4	x^9 - 6x^6 + 12x^3 + 64	\( 2^{6}\cdot 3^{22} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.2075751918009.2	x^9 - x^8 + 6x^7 - 5x^6 + 17x^5 - 15x^4 + 19x^3 + 14x^2 + 27	\( 3^{10}\cdot 7^{4}\cdot 11^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2515497505024.1	x^9 - 2x^8 + 4x^7 + 4x^6 - 7x^5 + 32x^4 - x^3 + 90x^2 - 11x + 92	\( 2^{8}\cdot 7^{6}\cdot 17^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2565164201769.1	x^9 - 3x^8 + 6x^7 - 9x^6 - 3x^5 + 30x^4 + 15x^3 - 12x^2 + 36x - 112	\( 3^{12}\cdot 13^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2565164201769.2	x^9 - 3x^7 - 9x^6 + 15x^5 + 6x^4 + 6x^3 - 33x^2 + 33x - 19	\( 3^{12}\cdot 13^{6} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.2593262550321.1	x^9 - 11x^6 + 36x^5 - 9x^4 + 15x^3 + 12x^2 + 12x + 8	\( 3^{12}\cdot 47^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2778012227169.1	x^9 - 2x^6 + 14x^3 - 1	\( 3^{10}\cdot 19^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[9]$
9.1.2778012227169.2	x^9 - 10x^6 + 46x^3 + 27	\( 3^{10}\cdot 19^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.2966827112704.2	x^9 - x^7 - 14x^6 - 4x^5 + 70x^4 + 21x^3 + 140x^2 + 36x + 64	\( 2^{8}\cdot 7^{4}\cdot 13^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.3203498588224.1	x^9 - 2x^8 + 5x^7 + 2x^6 + 23x^5 + 46x^4 + 115x^3 - 254x^2 - 700x - 392	\( 2^{6}\cdot 11^{4}\cdot 43^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.3765342321601.2	x^9 - 4x^8 + 17x^7 - 28x^6 + 16x^5 + 28x^4 - 12x^3 - x^2 + 18x - 11	\( 7^{4}\cdot 199^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.4001504141376.2	x^9 - 6x^7 + 12x^5 + 48x^3 - 168x^2 + 168x - 56	\( 2^{6}\cdot 3^{12}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.4001504141376.3	x^9 - 10x^6 - 4x^3 - 8	\( 2^{6}\cdot 3^{12}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.4001504141376.4	x^9 - x^6 + 5x^3 + 1	\( 2^{6}\cdot 3^{12}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[9]$
9.1.4001504141376.5	x^9 - 6x^7 - 6x^6 + 12x^5 + 24x^4 + 60x^3 + 144x^2 + 144x + 48	\( 2^{6}\cdot 3^{12}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.4600819082304.1	x^9 - 3x^8 + 4x^7 - 9x^6 + 34x^5 - 31x^4 + 39x^3 + 70x^2 + 4x - 8	\( 2^{6}\cdot 3^{4}\cdot 31^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.5064403678929.1	x^9 - 3x^8 + 3x^7 - 15x^6 + 21x^5 - 21x^4 + 21x^3 - 84x^2 + 84x - 56	\( 3^{16}\cdot 7^{6} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.5226454388736.1	x^9 - 3x^8 - 3x^7 - x^6 + 30x^5 + 24x^4 - 11x^3 - 93x^2 - 90x - 26	\( 2^{12}\cdot 3^{12}\cdot 7^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.5226454388736.2	x^9 - 3x^8 + 6x^7 - 4x^6 + 15x^5 - 9x^4 + 39x^3 + 15x^2 + 3x + 1	\( 2^{12}\cdot 3^{12}\cdot 7^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.5534900853769.1	x^9 - 3x^8 + 11x^6 + 2x^5 - 107x^4 + 275x^3 - 419x^2 + 317x - 111	\( 7^{6}\cdot 19^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.5822911651041.2	x^9 - 4x^8 + 8x^7 + 4x^6 - 3x^5 - 6x^4 + 193x^3 - 34x^2 - 496x + 2344	\( 3^{8}\cdot 31^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.6108930140625.1	x^9 - 3x^8 + 8x^7 - 8x^6 + 29x^5 - 17x^4 + 53x^3 + 27x^2 + 5x + 1	\( 3^{4}\cdot 5^{6}\cdot 13^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.6160309108009.1	x^9 + 7x^7 - 6x^6 + 4x^5 - 28x^4 - 63x^3 - 8x^2 + 28x - 8	\( 7^{4}\cdot 37^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.6439662447201.1	x^9 - 8x^6 + 18x^5 - 45x^4 + 20x^3 + 9x^2 + 93x - 92	\( 3^{12}\cdot 59^{4} \)	$C_3^2 : C_6$ (as 9T11)	Trivial
9.1.6887475360000.1	x^9 - 3x^8 - 3x^7 + 9x^6 + 15x^5 - 21x^4 - 12x^3 + 6x^2 + 15x - 55	\( 2^{8}\cdot 3^{16}\cdot 5^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.7702667535424.1	x^9 - 4x^8 + 18x^7 - 69x^6 + 212x^5 - 518x^4 + 999x^3 - 1610x^2 + 1622x - 419	\( 2^{6}\cdot 19^{4}\cdot 31^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.8107185625344.1	x^9 - 2x^8 + 8x^7 + 8x^6 - 13x^5 + 124x^4 - 103x^3 + 272x^2 - 83x + 144	\( 2^{8}\cdot 3^{8}\cdot 13^{6} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$
9.1.8936757492481.1	x^9 - 3x^8 + 7x^7 + 3x^6 - 3x^5 + 27x^4 + 55x^3 + 46x^2 + 64x + 168	\( 7^{4}\cdot 13^{4}\cdot 19^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[3]$