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 46108)

Label	Polynomial	Discriminant	Galois group	Class group
6.0.85184.1	x^6 - 2x^5 + 2x^4 - 4x^3 + 4x^2 - 2x + 2	\( -\,2^{6}\cdot 11^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.109744.1	x^6 - x^5 + 2x^4 + x^3 + 2x^2 + 3x + 1	\( -\,2^{4}\cdot 19^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.205379.2	x^6 - 2x^5 + 2x^4 + 2x^3 - 2x^2 + x + 2	\( -\,59^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.268119.1	x^6 + 4x^4 - 3x^3 + 8x^2 - 5x + 3	\( -\,3^{2}\cdot 31^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.304175.1	x^6 - 3x^5 + 7x^4 - 9x^3 + 13x^2 - 9x + 11	\( -\,5^{2}\cdot 23^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.596183.1	x^6 - 2x^5 + 3x^4 + 4x^3 + 2x^2 - 6x + 25	\( -\,7^{2}\cdot 23^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.658503.2	x^6 - 3x^5 + 5x^4 - 5x^3 + x^2 + x + 1	\( -\,3^{3}\cdot 29^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.686000.2	x^6 - x^5 + 2x^4 + 3x^3 + 2x^2 - x + 1	\( -\,2^{4}\cdot 5^{3}\cdot 7^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.778688.1	x^6 + 3x^4 + 8x^2 + 23	\( -\,2^{6}\cdot 23^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.778688.2	x^6 + x^4 + 23	\( -\,2^{6}\cdot 23^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.778688.3	x^6 + 8x^4 + 23x^2 + 23	\( -\,2^{6}\cdot 23^{3} \)	$S_4$ (as 6T8)	Trivial
6.2.810448.1	x^6 - 3x^5 + 6x^4 - 7x^3 + 2x^2 + x - 1	\( 2^{4}\cdot 37^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1043504.1	x^6 - x^5 + 2x^4 - 7x^3 + 4x^2 - 7x + 19	\( -\,2^{4}\cdot 7^{2}\cdot 11^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1080000.1	x^6 - 2x^5 + x^4 + 2x^3 + x^2 - 2x + 1	\( -\,2^{6}\cdot 3^{3}\cdot 5^{4} \)	$S_4$ (as 6T8)	Trivial
6.0.1225043.2	x^6 - 2x^5 + x^4 - 2x^3 + 5x^2 - 2x + 4	\( -\,107^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1272112.2	x^6 - x^5 + 2x^4 - 3x^3 + 10x^2 - 13x + 5	\( -\,2^{4}\cdot 43^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1280000.1	x^6 - x^4 + 2x^2 + 2	\( -\,2^{11}\cdot 5^{4} \)	$S_4$ (as 6T8)	Trivial
6.0.1362944.1	x^6 + 3x^4 + 11x^2 + 11	\( -\,2^{10}\cdot 11^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1362944.2	x^6 + 7x^4 + 15x^2 + 11	\( -\,2^{10}\cdot 11^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.1472207.1	x^6 - x^5 + 10x^4 - 13x^3 + 38x^2 - 32x + 40	\( -\,11^{2}\cdot 23^{3} \)	$S_4$ (as 6T8)	$[3]$
6.0.1906624.1	x^6 + 9x^4 + 28x^2 + 31	\( -\,2^{6}\cdot 31^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.1906624.2	x^6 - 3x^4 + 31	\( -\,2^{6}\cdot 31^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1906624.3	x^6 + x^4 + 31	\( -\,2^{6}\cdot 31^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.1929375.1	x^6 - 3x^5 + 4x^4 - 3x^3 + 8x^2 - 2x + 3	\( -\,3^{2}\cdot 5^{4}\cdot 7^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.2122416.2	x^6 - x^5 + 4x^4 - 5x^3 + 4x^2 - x + 1	\( -\,2^{4}\cdot 3^{3}\cdot 17^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.2239488.1	x^6 + 3x^4 + 3x^2 + 3	\( -\,2^{10}\cdot 3^{7} \)	$S_4$ (as 6T8)	$[2]$
6.0.2255067.1	x^6 - 3x^5 + 10x^4 - 15x^3 + 12x^2 - 5x + 2	\( -\,3^{3}\cdot 17^{4} \)	$S_4$ (as 6T8)	Trivial
6.0.2685619.2	x^6 - 3x^5 - 2x^4 + 9x^3 + x^2 - 6x + 4	\( -\,139^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.2744000.1	x^6 + 5x^4 - 2x^3 + 5x^2 + 1	\( -\,2^{6}\cdot 5^{3}\cdot 7^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.2744000.2	x^6 + 2x^4 - 6x^3 + 8x^2 - 6x + 2	\( -\,2^{6}\cdot 5^{3}\cdot 7^{3} \)	$S_4$ (as 6T8)	$[2]$
6.2.3241792.1	x^6 + x^4 - 4x^3 + 7x^2 - 2x - 5	\( 2^{6}\cdot 37^{3} \)	$S_4$ (as 6T8)	Trivial
6.2.3241792.2	x^6 + x^4 - 12x^3 - 9x^2 - 6x - 1	\( 2^{6}\cdot 37^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.3499200.4	x^6 - 6x^4 - 4x^3 + 12x^2 + 18x + 10	\( -\,2^{6}\cdot 3^{7}\cdot 5^{2} \)	$S_4$ (as 6T8)	$[2]$
6.0.3516263.1	x^6 - 3x^5 + 13x^4 - 15x^3 + 51x^2 - 43x + 133	\( -\,17^{2}\cdot 23^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.3599024.1	x^6 - x^5 + 2x^4 + 7x^3 + 4x^2 - 7x + 41	\( -\,2^{4}\cdot 11^{3}\cdot 13^{2} \)	$S_4$ (as 6T8)	Trivial
6.0.3604711.1	x^6 - x^5 + x^4 + x^3 + 29x^2 - 61x + 81	\( -\,11^{2}\cdot 31^{3} \)	$S_4$ (as 6T8)	$[4]$
6.0.3950784.1	x^6 + x^4 - 6x^3 + 5x^2 + 16x + 9	\( -\,2^{6}\cdot 3^{2}\cdot 19^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.3950784.2	x^6 + 3x^4 - 2x^3 + 9x^2 + 12x + 23	\( -\,2^{6}\cdot 3^{2}\cdot 19^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.4148928.2	x^6 - 2x^5 + 8x^4 - 18x^3 + 24x^2 - 18x + 6	\( -\,2^{6}\cdot 3^{3}\cdot 7^{4} \)	$S_4$ (as 6T8)	$[3]$
6.0.4174016.1	x^6 - 2x^5 + 12x^4 - 14x^3 + 36x^2 - 22x + 38	\( -\,2^{6}\cdot 7^{2}\cdot 11^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.4392287.1	x^6 - x^5 - x^4 - 7x^3 - 17x^2 + 77x + 121	\( -\,19^{2}\cdot 23^{3} \)	$S_4$ (as 6T8)	$[4]$
6.0.4478976.1	x^6 + 3x^4 + 6x^2 + 6	\( -\,2^{11}\cdot 3^{7} \)	$S_4$ (as 6T8)	$[2]$
6.0.4499456.1	x^6 - x^5 + 5x^4 - 6x^3 + 17x^2 + 5x + 1	\( -\,2^{11}\cdot 13^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.4499456.2	x^6 - x^5 - 7x^4 + 2x^3 + 25x^2 + 29x + 13	\( -\,2^{11}\cdot 13^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.4499456.3	x^6 + 4x^4 + 13x^2 + 26	\( -\,2^{11}\cdot 13^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.5034679.1	x^6 - x^5 + 12x^4 - 3x^3 + 48x^2 + 4x + 88	\( -\,13^{2}\cdot 31^{3} \)	$S_4$ (as 6T8)	Trivial
6.0.5088448.1	x^6 - 2x^5 + 4x^4 + 10x^3 - 2x + 10	\( -\,2^{6}\cdot 43^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.5088448.2	x^6 - 2x^5 + 2x^4 + 4x^3 - 4x^2 + 2x + 6	\( -\,2^{6}\cdot 43^{3} \)	$S_4$ (as 6T8)	$[2]$
6.0.5120000.1	x^6 + 4x^4 + 7x^2 + 2	\( -\,2^{13}\cdot 5^{4} \)	$S_4$ (as 6T8)	Trivial
6.0.5120000.2	x^6 - 4x^4 + 2x^2 + 8	\( -\,2^{13}\cdot 5^{4} \)	$S_4$ (as 6T8)	Trivial