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 2319)

Label	Polynomial	Discriminant	Galois group	Class group
6.2.525625.1	x^6 - x^5 + x^4 - x^3 - 4x^2 + 5	\( 5^{4}\cdot 29^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.600625.1	x^6 - x^5 + 4x^4 - 2x^3 + 6x^2 - 5x + 1	\( 5^{4}\cdot 31^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.802816.1	x^6 - 2x^5 - x^4 + 6x^2 - 4x + 2	\( 2^{14}\cdot 7^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.2175625.1	x^6 - x^5 + x^4 - 7x^3 - 6x^2 - 6x - 1	\( 5^{4}\cdot 59^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.2313441.1	x^6 - x^5 - 3x^4 + x^3 + 6x^2 - 3	\( 3^{4}\cdot 13^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.2325625.1	x^6 - x^5 + 6x^4 - 2x^3 + 4x^2 + 9x - 1	\( 5^{4}\cdot 61^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.4100625.1	x^6 - 6x^4 - x^3 + 9x^2 + 3x - 11	\( 3^{8}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.4100625.2	x^6 + 6x^4 - 3x^3 + 9x^2 - 9x + 1	\( 3^{8}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.4840000.2	x^6 - x^5 + x^4 - 12x^3 - 21x^2 - 11x - 1	\( 2^{6}\cdot 5^{4}\cdot 11^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.4950625.1	x^6 - x^5 + 4x^4 - 10x^3 + 15x - 5	\( 5^{4}\cdot 89^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.7290000.1	x^6 - 6x^4 - 4x^3 + 9x^2 + 12x - 16	\( 2^{4}\cdot 3^{6}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.7290000.2	x^6 + 6x^4 - 2x^3 + 9x^2 - 6x - 4	\( 2^{4}\cdot 3^{6}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.8254129.1	x^6 - 2x^5 + 4x^4 - 9x^3 + 5x^2 + 4x - 4	\( 13^{4}\cdot 17^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.11560000.1	x^6 - x^5 - 4x^4 - 7x^3 - 16x^2 - 21x - 11	\( 2^{6}\cdot 5^{4}\cdot 17^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.11560000.3	x^6 - 2x^5 + 4x^4 + 4x^3 - 6x^2 + 18x + 1	\( 2^{6}\cdot 5^{4}\cdot 17^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.11943936.1	x^6 + 6x^4 - 4x^3 + 9x^2 - 12x - 4	\( 2^{14}\cdot 3^{6} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.11943936.2	x^6 + 6x^4 - 4x^3 - 9x^2 + 12x - 4	\( 2^{14}\cdot 3^{6} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.12425625.1	x^6 - 3x^5 + 6x^4 - 15x^2 + 30x - 20	\( 3^{2}\cdot 5^{4}\cdot 47^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.12425625.2	x^6 - 3x^5 + 9x^4 - 9x^3 + 9x^2 + 12x + 1	\( 3^{2}\cdot 5^{4}\cdot 47^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.12780625.1	x^6 - 2x^5 - 6x^4 + 19x^3 - x^2 - 37x + 31	\( 5^{4}\cdot 11^{2}\cdot 13^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.13875625.1	x^6 - x^5 - x^4 + 5x^3 - 10x^2 - 30x - 5	\( 5^{4}\cdot 149^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.14250625.1	x^6 - x^5 + 9x^4 - 7x^3 + 16x^2 - 20x + 1	\( 5^{4}\cdot 151^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.14440000.2	x^6 - x^5 - x^4 - 12x^3 - 24x^2 - 20x - 4	\( 2^{6}\cdot 5^{4}\cdot 19^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.15108769.1	x^6 - 3x^5 + x^4 - x^3 + 11x^2 - 24x + 27	\( 13^{4}\cdot 23^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.16370116.1	x^6 - 2x^5 + 7x^4 + 2x^3 + x^2 + 24x - 1	\( 2^{2}\cdot 7^{2}\cdot 17^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.17682025.1	x^6 - 2x^5 + 5x^4 - 3x^3 + 3x^2 + 2x - 7	\( 5^{2}\cdot 29^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.18490000.1	x^6 - 2x^5 + 4x^4 - 6x^3 + 4x^2 - 12x - 9	\( 2^{4}\cdot 5^{4}\cdot 43^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.18490000.2	x^6 - 3x^5 + 11x^4 - 14x^3 + 21x^2 + 5x - 1	\( 2^{4}\cdot 5^{4}\cdot 43^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.20025625.1	x^6 - 3x^5 + 4x^4 - 2x^3 - 19x^2 + 30x + 20	\( 5^{4}\cdot 179^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.20475625.1	x^6 - x^5 - 9x^4 - 7x^3 + 29x^2 + 44x + 19	\( 5^{4}\cdot 181^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.21160000.3	x^6 - 2x^5 + x^4 - 20x^3 + 15x^2 + 30x + 55	\( 2^{6}\cdot 5^{4}\cdot 23^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.21160000.4	x^6 - x^5 + 5x^4 + 10x^3 - 10x^2 + 44x + 76	\( 2^{6}\cdot 5^{4}\cdot 23^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.21855625.2	x^6 - x^5 + 5x^4 + 15x^3 - 10x^2 + 54x + 61	\( 5^{4}\cdot 11^{2}\cdot 17^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.22325625.3	x^6 + 6x^4 - 7x^3 + 9x^2 - 21x + 11	\( 3^{6}\cdot 5^{4}\cdot 7^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.22325625.4	x^6 - 9x^4 - 13x^3 + 9x^2 + 36x + 31	\( 3^{6}\cdot 5^{4}\cdot 7^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.24920064.1	x^6 - 2x^5 + 11x^4 - 12x^3 + 25x^2 - 14x - 1	\( 2^{14}\cdot 3^{2}\cdot 13^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.24920064.2	x^6 - 2x^5 + 9x^4 - 4x^3 + 21x^2 + 10x + 1	\( 2^{14}\cdot 3^{2}\cdot 13^{2} \)	$C_3^2:C_4$ (as 6T10)	$[3]$
6.2.27541504.1	x^6 + 6x^4 - 8x^3 - 2x^2 - 32x + 4	\( 2^{14}\cdot 41^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.27825625.1	x^6 - x^5 + 11x^4 - 11x^3 + 26x^2 - 10x - 5	\( 5^{4}\cdot 211^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.29160000.2	x^6 - 6x^4 - 4x^3 + 9x^2 + 12x - 76	\( 2^{6}\cdot 3^{6}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.29160000.5	x^6 + 6x^4 - 8x^3 + 9x^2 - 24x - 4	\( 2^{6}\cdot 3^{6}\cdot 5^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.32490000.1	x^6 - 2x^5 + 10x^3 - 20x^2 - 72x - 81	\( 2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 19^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.33350625.1	x^6 - 3x^5 - 4x^4 + 10x^3 - 5x^2 + 10x - 20	\( 3^{2}\cdot 5^{4}\cdot 7^{2}\cdot 11^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.34656769.1	x^6 + x^4 - x^3 - 7x^2 + 14x - 7	\( 7^{2}\cdot 29^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.35700625.1	x^6 - 2x^5 + 6x^4 - 5x^3 - 25x^2 + 50x - 20	\( 5^{4}\cdot 239^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.36192256.1	x^6 - 2x^5 - 5x^4 - 16x^3 + 8x + 28	\( 2^{14}\cdot 47^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.36300625.1	x^6 - x^5 + 11x^4 - 21x^3 + 36x^2 - 110x + 95	\( 5^{4}\cdot 241^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.37015056.2	x^6 + 6x^4 - 6x^3 + 9x^2 - 18x - 4	\( 2^{4}\cdot 3^{4}\cdot 13^{4} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.38130625.1	x^6 - x^5 - 4x^4 - 2x^3 - 16x^2 - x + 59	\( 5^{4}\cdot 13^{2}\cdot 19^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial
6.2.38440000.1	x^6 - 2x^5 - 6x^4 + 12x^3 - 4x^2 - 70x - 55	\( 2^{6}\cdot 5^{4}\cdot 31^{2} \)	$C_3^2:C_4$ (as 6T10)	Trivial