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 18961)

Label	Polynomial	Discriminant	Galois group	Class group
6.0.16807.1	x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( -\,7^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.19683.1	x^6 - x^3 + 1	\( -\,3^{9} \)	$C_6$ (as 6T1)	Trivial
6.0.64827.1	x^6 - x^5 + 3x^4 + 5x^2 - 2x + 1	\( -\,3^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.0.153664.1	x^6 + 5x^4 + 6x^2 + 1	\( -\,2^{6}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.300125.1	x^6 - x^5 - 7x^4 + 2x^3 + 7x^2 - 2x - 1	\( 5^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.371293.1	x^6 - x^5 - 5x^4 + 4x^3 + 6x^2 - 3x - 1	\( 13^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.419904.1	x^6 + 6x^4 + 9x^2 + 1	\( -\,2^{6}\cdot 3^{8} \)	$C_6$ (as 6T1)	Trivial
6.6.453789.1	x^6 - x^5 - 6x^4 + 6x^3 + 8x^2 - 8x + 1	\( 3^{3}\cdot 7^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.771147.1	x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1	\( -\,3^{3}\cdot 13^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.820125.1	x^6 - 9x^4 - 4x^3 + 9x^2 + 3x - 1	\( 3^{8}\cdot 5^{3} \)	$C_6$ (as 6T1)	Trivial
6.6.1075648.1	x^6 - 7x^4 + 14x^2 - 7	\( 2^{6}\cdot 7^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.1229312.1	x^6 + 10x^4 + 24x^2 + 8	\( -\,2^{9}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.1229312.1	x^6 - 10x^4 + 24x^2 - 8	\( 2^{9}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.1259712.1	x^6 - 6x^4 + 9x^2 - 3	\( 2^{6}\cdot 3^{9} \)	$C_6$ (as 6T1)	Trivial
6.0.1827904.1	x^6 + 9x^4 + 14x^2 + 1	\( -\,2^{6}\cdot 13^{4} \)	$C_6$ (as 6T1)	$[3]$
6.0.2100875.1	x^6 - x^5 + 8x^4 - 8x^3 + 22x^2 - 22x + 29	\( -\,5^{3}\cdot 7^{5} \)	$C_6$ (as 6T1)	$[2]$
6.0.2250423.1	x^6 + 9x^4 - 5x^3 + 36x^2 - 12x + 8	\( -\,3^{8}\cdot 7^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.2460375.1	x^6 + 6x^4 - 4x^3 + 9x^2 - 12x + 19	\( -\,3^{9}\cdot 5^{3} \)	$C_6$ (as 6T1)	$[2]$
6.0.2476099.1	x^6 - x^5 + 2x^4 + 8x^3 - x^2 - 5x + 7	\( -\,19^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.3195731.1	x^6 - x^5 + 4x^4 - 3x^3 + 29x^2 - 4x + 71	\( -\,7^{4}\cdot 11^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.3359232.1	x^6 + 12x^4 + 36x^2 + 8	\( -\,2^{9}\cdot 3^{8} \)	$C_6$ (as 6T1)	$[3]$
6.6.3359232.1	x^6 - 12x^4 + 36x^2 - 8	\( 2^{9}\cdot 3^{8} \)	$C_6$ (as 6T1)	Trivial
6.0.3518667.1	x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49	\( -\,3^{3}\cdot 19^{4} \)	$C_6$ (as 6T1)	$[3]$
6.6.3570125.1	x^6 - x^5 - 12x^4 + 13x^3 + 19x^2 - 10x - 5	\( 5^{3}\cdot 13^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.4148928.1	x^6 - 2x^5 - 12x^4 + 18x^3 + 23x^2 - 16x + 1	\( 2^{6}\cdot 3^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.5274997.1	x^6 - x^5 - 14x^4 + 9x^3 + 35x^2 - 16x - 1	\( 7^{4}\cdot 13^{3} \)	$C_6$ (as 6T1)	Trivial
6.6.6751269.1	x^6 - 12x^4 - 5x^3 + 36x^2 + 30x + 1	\( 3^{9}\cdot 7^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.8103375.1	x^6 - x^5 + 7x^4 - 5x^3 + 49x^2 - 9x + 139	\( -\,3^{3}\cdot 5^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	$[2]$
6.0.8340544.1	x^6 + 13x^4 + 50x^2 + 49	\( -\,2^{6}\cdot 19^{4} \)	$C_6$ (as 6T1)	Trivial
6.0.8605184.1	x^6 + 14x^4 + 56x^2 + 56	\( -\,2^{9}\cdot 7^{5} \)	$C_6$ (as 6T1)	$[4]$
6.6.8605184.1	x^6 - 14x^4 + 56x^2 - 56	\( 2^{9}\cdot 7^{5} \)	$C_6$ (as 6T1)	Trivial
6.0.8732691.1	x^6 - 3x^5 + 6x^4 - 5x^3 + 33x^2 - 54x + 111	\( -\,3^{8}\cdot 11^{3} \)	$C_6$ (as 6T1)	$[3]$
6.0.9796423.1	x^6 - x^5 - 3x^4 + 7x^3 + 25x^2 - 55x + 79	\( -\,7^{3}\cdot 13^{4} \)	$C_6$ (as 6T1)	Trivial
6.0.10024911.1	x^6 - x^5 + 8x^4 - 9x^3 + 6x^2 + 10x + 25	\( -\,3^{3}\cdot 13^{5} \)	$C_6$ (as 6T1)	$[4]$
6.0.10077696.1	x^6 + 12x^4 + 36x^2 + 24	\( -\,2^{9}\cdot 3^{9} \)	$C_6$ (as 6T1)	$[2]$
6.6.10077696.1	x^6 - 12x^4 + 36x^2 - 24	\( 2^{9}\cdot 3^{9} \)	$C_6$ (as 6T1)	Trivial
6.6.11796113.1	x^6 - x^5 - 17x^4 + 11x^3 + 57x^2 - 25x - 13	\( 7^{4}\cdot 17^{3} \)	$C_6$ (as 6T1)	Trivial
6.6.14414517.1	x^6 - 3x^5 - 12x^4 + 27x^3 + 21x^2 - 48x + 17	\( 3^{8}\cdot 13^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.14623232.1	x^6 - 2x^5 - x^4 - 2x^3 + 34x^2 + 28x + 73	\( -\,2^{9}\cdot 13^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.14623232.1	x^6 - 2x^5 - 13x^4 + 14x^3 + 26x^2 - 28x + 1	\( 2^{9}\cdot 13^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.16290125.1	x^6 - x^5 - 16x^4 + x^3 + 47x^2 + 10x - 11	\( 5^{3}\cdot 19^{4} \)	$C_6$ (as 6T1)	Trivial
6.0.16468459.1	x^6 - x^5 + 10x^4 - 7x^3 + 75x^2 - 16x + 239	\( -\,7^{4}\cdot 19^{3} \)	$C_6$ (as 6T1)	$[3]$
6.0.19208000.1	x^6 - 2x^5 + 12x^4 - 14x^3 + 87x^2 - 64x + 281	\( -\,2^{6}\cdot 5^{3}\cdot 7^{4} \)	$C_6$ (as 6T1)	$[6]$
6.6.22370117.1	x^6 - x^5 - 20x^4 + 20x^3 + 106x^2 - 106x - 83	\( 7^{5}\cdot 11^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.23762752.1	x^6 + 13x^4 + 26x^2 + 13	\( -\,2^{6}\cdot 13^{5} \)	$C_6$ (as 6T1)	$[2]$
6.0.24935067.1	x^6 - x^5 + 11x^4 - 6x^3 + 108x^2 - 80x + 64	\( -\,3^{3}\cdot 31^{4} \)	$C_6$ (as 6T1)	Trivial
6.6.26198073.1	x^6 - 18x^4 - 8x^3 + 81x^2 + 72x - 17	\( 3^{9}\cdot 11^{3} \)	$C_6$ (as 6T1)	Trivial
6.0.28629151.1	x^6 - x^5 + 3x^4 - 11x^3 + 44x^2 - 36x + 32	\( -\,31^{5} \)	$C_6$ (as 6T1)	$[9]$
6.0.29042496.1	x^6 + 21x^4 + 126x^2 + 189	\( -\,2^{6}\cdot 3^{3}\cdot 7^{5} \)	$C_6$ (as 6T1)	$[2, 2]$
6.0.29212967.1	x^6 - x^5 + 13x^4 - 9x^3 + 107x^2 - 25x + 377	\( -\,7^{4}\cdot 23^{3} \)	$C_6$ (as 6T1)	$[9]$