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 657)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.2315685267.1	x^9 - x^6 - 2x^3 + 1	\( -\,3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.7529536000.2	x^9 - 2x^8 + 4x^7 - 11x^6 + 13x^5 - 13x^4 + 13x^3 - 8x^2 + 5x - 1	\( -\,2^{9}\cdot 5^{3}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.10460353203.1	x^9 - 3x^3 - 1	\( -\,3^{21} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.19573852375.1	x^9 - 4x^8 + 6x^7 - 6x^6 + x^5 + 6x^4 + x^3 - 8x^2 + 12x - 8	\( -\,5^{3}\cdot 7^{6}\cdot 11^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.22039921152.1	x^9 - 3x^8 + 3x^7 + 6x^6 - 6x^5 - 3x^4 + 9x^3 - 3x^2 - 6x + 1	\( -\,2^{9}\cdot 3^{16} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.22785532875.1	x^9 - 3x^8 + 3x^7 - 6x^6 + 6x^5 - 3x^4 - 7x^3 + 12x^2 - 12x + 8	\( -\,3^{12}\cdot 5^{3}\cdot 7^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.24794911296.1	x^9 - 3x^6 + 9x^5 + 9x^4 - 27x^3 + 18x^2 - 9x + 1	\( -\,2^{6}\cdot 3^{18} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.36992610368.2	x^9 - x^8 - 7x^7 + 4x^6 + 22x^5 - 3x^4 - 41x^3 - 19x^2 + 18x + 13	\( -\,2^{6}\cdot 7^{6}\cdot 17^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.55175798943.2	x^9 - 3x^8 - x^6 - 9x^5 - 3x^4 + x^3 - 12x^2 + 6x + 1	\( -\,3^{12}\cdot 47^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.57295185651.1	x^9 - 3x^8 + 6x^6 - 18x^4 + 27x^3 - 36x + 24	\( -\,3^{16}\cdot 11^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.81295282368.1	x^9 - x^8 - 5x^7 + 8x^6 + 12x^5 - 15x^4 - 17x^3 + 17x^2 + 24x + 7	\( -\,2^{6}\cdot 3^{3}\cdot 19^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.81452401875.1	x^9 - 2x^8 - 2x^7 - x^6 - 6x^5 + 10x^4 + 6x^3 - 6x^2 - 4x - 1	\( -\,3^{3}\cdot 5^{4}\cdot 13^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.90724673403.1	x^9 - 3x^8 + 10x^7 - 18x^6 + 13x^5 - 17x^4 + 10x^3 - 3x^2 + 7x - 1	\( -\,3^{3}\cdot 7^{6}\cdot 13^{4} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.93329542656.2	x^9 - 3x^7 - x^6 + 9x^5 - 6x^4 - 8x^3 - 3x^2 + 9x + 1	\( -\,2^{9}\cdot 3^{12}\cdot 7^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.95006081547.2	x^9 - x^6 - 4x^3 - 1	\( -\,3^{9}\cdot 13^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.132885227727.2	x^9 - 3x^6 - 9x^5 - 27x^4 - 9x^3 + 54x^2 + 99x + 57	\( -\,3^{18}\cdot 7^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.133159451283.1	x^9 - 3x^8 + 9x^7 - 20x^6 + 30x^5 - 45x^4 + 28x^3 + 18x - 9	\( -\,3^{13}\cdot 17^{4} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.145282683375.4	x^9 - 3x^6 - 9x^5 + 9x^4 + 9x^3 + 36x^2 + 27x + 3	\( -\,3^{19}\cdot 5^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.148203857088.3	x^9 - 2x^6 - 8x^3 + 8	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.148203857088.4	x^9 - 4x^6 - 4x^3 + 8	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.160900419519.2	x^9 - x^8 + 4x^7 - x^6 + 9x^5 - 9x^4 - 5x^3 + 20x^2 - 30x + 13	\( -\,3^{3}\cdot 7^{6}\cdot 37^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.207773767683.2	x^9 - 3x^8 + 9x^7 - 16x^6 + 3x^5 + 36x^4 - 65x^3 + 60x^2 - 27x + 3	\( -\,3^{13}\cdot 19^{4} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.215051077696.1	x^9 + 3x^7 - 5x^6 + 3x^5 + 18x^4 - 14x^3 + 23x^2 + 13x - 29	\( -\,2^{6}\cdot 7^{6}\cdot 13^{4} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.270588935232.1	x^9 - 4x^8 + 11x^7 - 17x^6 + x^5 + 30x^4 - 56x^3 + 65x^2 - 3x - 29	\( -\,2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 11^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.289460658375.5	x^9 + 6x^7 - x^6 - 9x^5 + 45x^4 - 57x^3 + 108x^2 - 123x + 43	\( -\,3^{9}\cdot 5^{3}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.344373768000.1	x^9 - 3x^8 + 6x^7 - 9x^6 + 15x^5 - 39x^4 + 51x^3 - 12x^2 - 12x - 1	\( -\,2^{6}\cdot 3^{16}\cdot 5^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.349955492823.3	x^9 - 3x^8 + 6x^7 - 9x^6 + 21x^5 - 33x^4 + 21x^3 - 12x^2 + 6x + 1	\( -\,3^{15}\cdot 29^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.383401590192.1	x^9 - 5x^6 - 2x^3 + 8	\( -\,2^{4}\cdot 3^{3}\cdot 31^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.437664515463.3	x^9 + 3x^7 - 6x^6 - 18x^5 - 12x^4 - 22x^3 - 27x^2 + 12x + 13	\( -\,3^{12}\cdot 7^{7} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.523749454407.1	x^9 - 3x^8 + 9x^7 - 21x^6 + 27x^5 - 9x^4 - 9x - 3	\( -\,3^{16}\cdot 23^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.595077871104.2	x^9 - 9x^6 + 9x^5 - 27x^4 - 3x^3 - 18x^2 - 9x - 1	\( -\,2^{9}\cdot 3^{19} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.640281040659.2	x^9 - 3x^8 + 12x^6 - 27x^5 + 42x^4 - 40x^3 + 21x^2 - 12x + 5	\( -\,3^{3}\cdot 13^{6}\cdot 17^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.669462604992.7	x^9 - 12x^3 - 8	\( -\,2^{6}\cdot 3^{21} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.669462604992.8	x^9 - 6x^6 + 8	\( -\,2^{6}\cdot 3^{21} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.727861062159.4	x^9 - 3x^8 - 19x^6 + 3x^5 - 15x^4 + 17x^3 + 18x^2 + 6x + 19	\( -\,3^{13}\cdot 7^{3}\cdot 11^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.872352628875.1	x^9 - 2x^8 - 5x^7 + 34x^6 - 73x^5 - x^4 + 170x^3 - 170x^2 + 76x - 43	\( -\,3^{3}\cdot 5^{3}\cdot 7^{6}\cdot 13^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.880044158287.2	x^9 - x^8 - 5x^7 + 3x^6 + 17x^5 + 7x^4 - 29x^3 - 12x^2 + 28x - 8	\( -\,7^{3}\cdot 37^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.926004075723.2	x^9 - 2x^6 - 5x^3 - 1	\( -\,3^{9}\cdot 19^{6} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.927144591751.6	x^9 - x^8 - 11x^7 - 7x^6 + 47x^5 + 33x^4 - 27x^3 + 70x^2 + 140x + 56	\( -\,7^{6}\cdot 199^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.1034747179375.1	x^9 - 7x^7 - 10x^6 + 12x^5 + 38x^4 + 50x^3 - x^2 - 20x + 1	\( -\,5^{4}\cdot 7^{3}\cdot 13^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1037426999616.2	x^9 + 3x^7 - 8x^6 - 18x^5 - 30x^4 - 15x^3 - 36x^2 + 12x + 8	\( -\,2^{6}\cdot 3^{9}\cdot 7^{7} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1185630856704.1	x^9 - 6x^7 - 14x^6 - 9x^5 + 42x^4 + 83x^3 - 84x - 56	\( -\,2^{9}\cdot 3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1185630856704.3	x^9 + 3x^7 - 4x^6 - 18x^5 - 36x^4 - 31x^3 - 18x^2 + 24x + 8	\( -\,2^{9}\cdot 3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1185630856704.4	x^9 - 3x^7 - 8x^6 - 18x^5 - 12x^4 + 39x^3 + 90x^2 + 72x + 8	\( -\,2^{9}\cdot 3^{9}\cdot 7^{6} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1235079060111.4	x^9 - 9x^7 - 7x^6 + 27x^5 + 42x^4 - 28x^3 - 63x^2 + 3x + 47	\( -\,3^{9}\cdot 13^{7} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1282404865311.2	x^9 - 3x^8 + 6x^7 + 3x^6 - 39x^5 + 69x^4 + 27x^3 - 66x^2 + 114x - 1	\( -\,3^{16}\cdot 31^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.1304676467983.2	x^9 - x^8 + 3x^7 - 15x^6 + x^5 + 21x^4 + 25x^3 + 8x^2 - 92x + 8	\( -\,7^{6}\cdot 223^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1458274104000.8	x^9 - 3x^8 - 9x^7 + 28x^6 + 30x^5 - 99x^4 - 47x^3 + 219x^2 + 6x - 289	\( -\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial
9.3.1458274104000.12	x^9 + 3x^7 - 13x^6 - 21x^5 - 54x^4 - 60x^3 - 27x^2 - 27x + 27	\( -\,2^{6}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3} \)	$C_3^2 : S_3 $ (as 9T13)	$[3]$
9.3.1517703207488.1	x^9 - 2x^8 + 19x^6 - 37x^5 + 29x^4 + 33x^3 - 54x^2 + 43x - 5	\( -\,2^{6}\cdot 13^{6}\cdot 17^{3} \)	$C_3^2 : S_3 $ (as 9T13)	Trivial