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 5261)

Label	Polynomial	Discriminant	Galois group	Class group
6.2.153664.1	x^6 + x^4 - 2x^2 - 1	\( 2^{6}\cdot 7^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.405769.1	x^6 - x^5 - 2x^4 + x^3 - 7	\( 7^{4}\cdot 13^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.419904.1	x^6 - 3x^2 - 1	\( 2^{6}\cdot 3^{8} \)	$A_4$ (as 6T4)	Trivial
6.2.714025.1	x^6 - x^5 - x^4 - 3x^3 - x^2 - x + 1	\( 5^{2}\cdot 13^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.1827904.1	x^6 - x^4 - 4x^2 - 1	\( 2^{6}\cdot 13^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.1896129.1	x^6 - 7x^3 - 6x^2 - 9x - 3	\( 3^{8}\cdot 17^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.2019241.1	x^6 - x^5 + 3x^4 + 7x^3 - 9x^2 + 19x - 13	\( 7^{4}\cdot 29^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.2368521.1	x^6 - 3x^4 - 10x^3 - 18x^2 - 18x - 9	\( 3^{8}\cdot 19^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.4036081.1	x^6 - 2x^5 + 8x^4 + 3x^3 - 4x^2 + 31x - 29	\( 7^{4}\cdot 41^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.4439449.1	x^6 - 2x^5 - x^4 + x^3 - 14x^2 + 28x - 56	\( 7^{4}\cdot 43^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.6385729.1	x^6 - 2x^5 + 5x^3 + 5x - 1	\( 7^{2}\cdot 19^{4} \)	$A_4$ (as 6T4)	$[2]$
6.2.8340544.2	x^6 - 2x^4 - 5x^2 - 1	\( 2^{6}\cdot 19^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.8982009.1	x^6 + 3x^4 - 5x^3 - 12x^2 - 36x - 24	\( 3^{8}\cdot 37^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.12103441.1	x^6 - 3x^5 + 3x^4 - x^3 - 49x^2 + 49x - 91	\( 7^{4}\cdot 71^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.14776336.1	x^6 + 4x^4 - 5x^2 - 16	\( 2^{4}\cdot 31^{4} \)	$A_4$ (as 6T4)	$[2]$
6.2.15768841.1	x^6 - x^5 - x^4 - 9x^3 + 11x^2 - 7x - 1	\( 11^{2}\cdot 19^{4} \)	$A_4$ (as 6T4)	$[2]$
6.2.16540489.1	x^6 - x^5 + 10x^4 + 7x^3 - 2x^2 + 96x - 104	\( 7^{4}\cdot 83^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.18429849.1	x^6 - 3x^5 + 9x^4 - 13x^3 - 21x^2 + 27x - 51	\( 3^{8}\cdot 53^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.22591009.1	x^6 - 3x^5 - x^4 + 7x^3 - 85x^2 + 81x - 167	\( 7^{4}\cdot 97^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.25969216.1	x^6 + x^4 - 65x^2 - 169	\( 2^{6}\cdot 7^{4}\cdot 13^{2} \)	$A_4$ (as 6T4)	$[2]$
6.6.25969216.1	x^6 - 19x^4 + 104x^2 - 169	\( 2^{6}\cdot 7^{4}\cdot 13^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.25969216.2	x^6 + 4x^4 - 39x^2 - 169	\( 2^{6}\cdot 7^{4}\cdot 13^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.27447121.1	x^6 - 2x^5 + 5x^4 - 23x^3 + 22x^2 - 20x - 8	\( 13^{4}\cdot 31^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.30658369.1	x^6 - 2x^5 - 2x^4 + 28x^3 - 109x^2 + 146x - 251	\( 7^{4}\cdot 113^{2} \)	$A_4$ (as 6T4)	Trivial
6.6.33074001.1	x^6 - 18x^4 - 16x^3 + 57x^2 + 36x - 57	\( 3^{8}\cdot 71^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.34963569.1	x^6 - 3x^5 + 6x^4 + 9x^3 - 60x^2 + 132x - 136	\( 3^{8}\cdot 73^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.38725729.1	x^6 - x^5 + 10x^4 - 21x^3 - 16x^2 - 142x - 223	\( 7^{4}\cdot 127^{2} \)	$A_4$ (as 6T4)	$[4]$
6.2.45697600.1	x^6 + x^4 - 30x^2 - 25	\( 2^{6}\cdot 5^{2}\cdot 13^{4} \)	$A_4$ (as 6T4)	$[2]$
6.6.45697600.1	x^6 - 12x^4 + 35x^2 - 25	\( 2^{6}\cdot 5^{2}\cdot 13^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.45697600.2	x^6 - 4x^4 - 25x^2 - 25	\( 2^{6}\cdot 5^{2}\cdot 13^{4} \)	$A_4$ (as 6T4)	$[2]$
6.2.46389721.1	x^6 - 2x^5 + x^4 - 32x^3 - 88x^2 - 32x - 281	\( 7^{4}\cdot 139^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.51969681.1	x^6 - 3x^5 + 9x^4 + x^3 - 27x^2 - 9x - 153	\( 3^{8}\cdot 89^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.54700816.2	x^6 + 4x^4 - 9x^2 - 4	\( 2^{4}\cdot 43^{4} \)	$A_4$ (as 6T4)	$[2]$
6.6.59105344.1	x^6 - 11x^4 + 30x^2 - 16	\( 2^{6}\cdot 31^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.59105344.3	x^6 - x^5 - 9x^3 + 31x^2 - 18x - 2	\( 2^{6}\cdot 31^{4} \)	$A_4$ (as 6T4)	Trivial
6.6.63091249.1	x^6 - 2x^5 - 16x^4 + 5x^3 + 52x^2 + 13x - 13	\( 13^{4}\cdot 47^{2} \)	$A_4$ (as 6T4)	Trivial
6.6.66961489.1	x^6 - x^5 - 26x^4 + 17x^3 + 194x^2 - 64x - 344	\( 7^{4}\cdot 167^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.75116889.1	x^6 + 12x^4 - 14x^3 + 15x^2 - 144x - 159	\( 3^{8}\cdot 107^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.77951241.1	x^6 - 3x^5 + 15x^4 - 9x^3 - 33x^2 - 93x - 199	\( 3^{8}\cdot 109^{2} \)	$A_4$ (as 6T4)	Trivial
6.6.78659161.1	x^6 - x^5 - 26x^4 + 17x^3 + 194x^2 - 64x - 449	\( 7^{4}\cdot 181^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.80227849.1	x^6 - 2x^5 + 7x^4 + 9x^3 - 20x^2 + 76x - 40	\( 13^{4}\cdot 53^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.93180409.1	x^6 - 2x^5 + 5x^4 - 14x^3 - 102x^2 + 216x - 783	\( 7^{4}\cdot 197^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.105822369.1	x^6 - 3x^5 + 15x^4 + 9x^3 - 87x^2 + 213x - 307	\( 3^{8}\cdot 127^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.106894921.1	x^6 - 2x^5 + 6x^4 - 34x^3 - 105x^2 - 196x - 637	\( 7^{4}\cdot 211^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.119399329.1	x^6 - x^5 + 2x^4 + 31x^3 - 170x^2 + 314x - 841	\( 7^{4}\cdot 223^{2} \)	$A_4$ (as 6T4)	$[2]$
6.2.119946304.2	x^6 - 4x^4 - 7x^2 - 1	\( 2^{6}\cdot 37^{4} \)	$A_4$ (as 6T4)	Trivial
6.2.121352256.1	x^6 + 9x^4 - 102x^2 - 289	\( 2^{6}\cdot 3^{8}\cdot 17^{2} \)	$A_4$ (as 6T4)	$[2]$
6.6.121352256.1	x^6 - 24x^4 + 153x^2 - 289	\( 2^{6}\cdot 3^{8}\cdot 17^{2} \)	$A_4$ (as 6T4)	Trivial
6.2.121352256.2	x^6 + 18x^4 + 51x^2 - 289	\( 2^{6}\cdot 3^{8}\cdot 17^{2} \)	$A_4$ (as 6T4)	$[4]$
6.6.124612569.1	x^6 - 2x^5 - 12x^4 + 22x^3 + 33x^2 - 38x - 37	\( 3^{2}\cdot 61^{4} \)	$A_4$ (as 6T4)	Trivial