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 3933)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.1614110976.1	x^8 - 2x^7 - 2x^6 + 8x^5 + 14x^4 - 40x^3 + 40x^2 - 20x + 4	\( 2^{8}\cdot 3^{8}\cdot 31^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.1693157904.1	x^8 - 3x^7 - 3x^6 + 16x^5 - 36x^3 + x^2 + 39x + 21	\( 2^{4}\cdot 3^{8}\cdot 127^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.2385638649.1	x^8 + 9x^6 - 2x^5 + 21x^4 - 12x^3 + 13x^2 - 12x + 3	\( 3^{12}\cdot 67^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.2485221904.1	x^8 - x^7 + 2x^6 + 3x^5 + x^3 + 10x^2 - 7x + 3	\( 2^{4}\cdot 11^{4}\cdot 103^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.3105609984.2	x^8 - 4x^7 + 16x^6 - 26x^5 + 35x^4 - 2x^3 - 2x^2 + 32x + 13	\( 2^{8}\cdot 3^{8}\cdot 43^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.3838050304.3	x^8 - 4x^7 + 4x^6 + 5x^4 - 16x^3 + 28x^2 - 16x + 8	\( 2^{18}\cdot 11^{4} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.4145685769.1	x^8 - x^7 + 2x^6 - 3x^5 + 8x^4 + 20x^3 + 21x^2 + 12x + 4	\( 31^{4}\cdot 67^{2} \)	$V_4^2:S_3$ (as 8T34)	$[3]$
8.0.4705960000.1	x^8 - 4x^7 + 5x^6 - x^5 + x^4 + 2x^3 - x^2 - 3x + 2	\( 2^{6}\cdot 5^{4}\cdot 7^{6} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.4787532864.2	x^8 - 3x^7 + 5x^6 - 4x^5 + 6x^4 - 7x^3 + 9x^2 - 4x + 1	\( 2^{6}\cdot 3^{4}\cdot 31^{4} \)	$V_4^2:S_3$ (as 8T34)	$[6]$
8.0.5505046416.1	x^8 - 2x^7 - 8x^6 + 22x^5 + 19x^4 - 50x^3 + 40x^2 + 46x + 13	\( 2^{4}\cdot 3^{8}\cdot 229^{2} \)	$V_4^2:S_3$ (as 8T34)	$[4]$
8.0.6561000000.1	x^8 - x^7 + 4x^6 - 7x^5 + 4x^4 - 4x^3 + 16x^2 - 28x + 16	\( 2^{6}\cdot 3^{8}\cdot 5^{6} \)	$V_4^2:S_3$ (as 8T34)	$[4]$
8.0.6879707136.2	x^8 + 6x^6 - 4x^5 + 24x^4 - 24x^3 + 44x^2 - 24x + 18	\( 2^{20}\cdot 3^{8} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.7779240000.5	x^8 - x^7 - 5x^6 + x^5 + 9x^4 + 11x^3 - 5x^2 - 11x + 16	\( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 7^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.8279544064.2	x^8 - 4x^7 + 8x^6 + 2x^5 - 33x^4 + 54x^3 + 2x^2 - 74x + 75	\( 2^{8}\cdot 11^{4}\cdot 47^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.9474296896.1	x^8 - 4x^7 + 3x^6 + 5x^5 + 4x^4 + 2x^3 + 6x^2 + 6x + 4	\( 2^{6}\cdot 23^{6} \)	$V_4^2:S_3$ (as 8T34)	$[3]$
8.0.9980010000.2	x^8 - 3x^7 + 2x^6 - 15x^5 + 30x^4 + 9x^3 + 17x^2 - 60x + 28	\( 2^{4}\cdot 3^{6}\cdot 5^{4}\cdot 37^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.10528401664.3	x^8 - 4x^7 + 10x^6 - 10x^5 + 11x^4 - 50x^3 + 118x^2 - 104x + 31	\( 2^{8}\cdot 11^{4}\cdot 53^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.11193640000.3	x^8 - x^7 + 2x^6 - x^5 - 2x^4 + 4x^3 - 6x + 4	\( 2^{6}\cdot 5^{4}\cdot 23^{4} \)	$V_4^2:S_3$ (as 8T34)	$[6]$
8.0.13064490000.2	x^8 - 2x^7 + 4x^6 - 2x^5 + 9x^4 - 10x^3 + 22x^2 - 10x + 19	\( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 127^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.13916213089.1	x^8 - 3x^7 + 11x^5 - 4x^4 - 50x^3 + 115x^2 - 110x + 48	\( 23^{4}\cdot 223^{2} \)	$V_4^2:S_3$ (as 8T34)	$[3]$
8.0.15650010000.4	x^8 - 2x^7 - 13x^6 + 10x^5 + 55x^4 + 26x^3 + 17x^2 + 50x + 28	\( 2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 139^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.17133762816.1	x^8 - 2x^7 - 4x^6 + 14x^5 + 5x^4 - 38x^3 - 4x^2 + 56x + 37	\( 2^{8}\cdot 3^{8}\cdot 101^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.17180655625.2	x^8 - x^7 - 5x^6 + x^5 + 16x^4 + 18x^3 + 9x^2 + 3x + 2	\( 5^{4}\cdot 7^{4}\cdot 107^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.17648591104.3	x^8 - 4x^7 + 16x^6 - 30x^5 + 47x^4 - 34x^3 + 22x^2 - 16x + 5	\( 2^{8}\cdot 19^{4}\cdot 23^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.17742240000.9	x^8 - 2x^7 + 4x^6 + 10x^5 - 45x^4 + 50x^3 + 100x^2 - 250x + 175	\( 2^{8}\cdot 3^{4}\cdot 5^{4}\cdot 37^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.18339659776.10	x^8 - 4x^7 - 2x^6 + 20x^5 - 2x^4 - 16x^3 - 32x^2 - 16x + 104	\( 2^{16}\cdot 23^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.19955517696.4	x^8 - 2x^7 - 2x^6 + 8x^5 - 16x^4 - 16x^3 + 184x^2 - 320x + 172	\( 2^{8}\cdot 3^{8}\cdot 109^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.4.20880250000.1	x^8 - x^7 - 6x^6 + 13x^5 - 6x^4 + x^3 - 14x^2 + 7x + 1	\( 2^{4}\cdot 5^{6}\cdot 17^{4} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.22992263424.7	x^8 - 2x^7 + 4x^6 - 22x^5 - 4x^4 + 14x^3 + 268x^2 - 386x + 139	\( 2^{8}\cdot 3^{12}\cdot 13^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.24321026304.8	x^8 - 4x^7 + 2x^5 + 34x^4 + 84x^3 + 45x^2 + 18x + 21	\( 2^{8}\cdot 3^{6}\cdot 19^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.4.26244000000.1	x^8 - 2x^7 - 4x^6 + 4x^5 + 19x^4 - 28x^3 - 16x^2 + 56x - 29	\( 2^{8}\cdot 3^{8}\cdot 5^{6} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.28860573456.2	x^8 - 2x^7 - 3x^6 - 2x^5 + 7x^4 + 6x^3 + 27x^2 + 30x + 12	\( 2^{4}\cdot 3^{6}\cdot 11^{4}\cdot 13^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.29859840000.38	x^8 - 4x^6 + 56x^2 - 120x + 79	\( 2^{16}\cdot 3^{6}\cdot 5^{4} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.29948379136.3	x^8 - 4x^7 + 14x^6 - 12x^5 + 8x^4 + 56x^3 - 24x^2 + 24x + 106	\( 2^{20}\cdot 13^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.32998902336.2	x^8 - x^6 - 3x^5 + 27x^4 - 42x^3 + 65x^2 - 51x + 28	\( 2^{6}\cdot 3^{6}\cdot 29^{4} \)	$V_4^2:S_3$ (as 8T34)	$[6]$
8.0.33695374969.1	x^8 + 6x^6 - 16x^5 + 14x^4 - 2x^3 + 10x^2 - 17x + 12	\( 23^{4}\cdot 347^{2} \)	$V_4^2:S_3$ (as 8T34)	$[3]$
8.0.34828517376.3	x^8 + 6x^6 - 8x^5 + 39x^4 - 96x^3 + 100x^2 - 48x + 9	\( 2^{16}\cdot 3^{12} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.38848410000.3	x^8 - x^7 + 9x^6 + 8x^5 + 34x^4 + 96x^3 + 96x^2 + 72x + 36	\( 2^{4}\cdot 3^{6}\cdot 5^{4}\cdot 73^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.41400854784.2	x^8 - 2x^7 - 8x^6 + 36x^5 - 24x^4 - 168x^3 + 384x^2 - 240x + 48	\( 2^{8}\cdot 3^{8}\cdot 157^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.41943040000.11	x^8 - 8x^5 + 38x^4 - 56x^3 + 40x^2 - 16x + 3	\( 2^{26}\cdot 5^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.43001487424.8	x^8 - x^7 + 5x^6 + 7x^5 + 16x^4 + 16x^3 + 14x^2 + 10x + 4	\( 2^{6}\cdot 7^{4}\cdot 23^{4} \)	$V_4^2:S_3$ (as 8T34)	$[6]$
8.0.43237380096.17	x^8 - 2x^7 - 11x^6 + 16x^5 + 42x^4 - 46x^3 - 38x^2 + 152x + 133	\( 2^{12}\cdot 3^{4}\cdot 19^{4} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.43932160000.3	x^8 - 4x^7 + 4x^6 - 8x^5 + 19x^4 + 4x^3 + 26x^2 - 12x + 11	\( 2^{12}\cdot 5^{4}\cdot 131^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.45174951936.4	x^8 - 2x^7 + 2x^6 - 4x^5 - x^4 + 22x^3 - 28x^2 - 16x + 34	\( 2^{12}\cdot 3^{8}\cdot 41^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.45496890000.2	x^8 + 8x^6 + 21x^4 - 12x^3 + 26x^2 - 42x + 19	\( 2^{4}\cdot 3^{6}\cdot 5^{4}\cdot 79^{2} \)	$V_4^2:S_3$ (as 8T34)	$[4]$
8.0.49113651456.4	x^8 - 12x^6 - 16x^5 + 30x^4 + 96x^3 + 112x^2 + 84x + 36	\( 2^{8}\cdot 3^{12}\cdot 19^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.49401285696.3	x^8 - 2x^7 + 5x^6 - 11x^5 + 4x^4 + 14x^3 - 7x^2 - 7x + 7	\( 2^{6}\cdot 3^{8}\cdot 7^{6} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.51307686144.18	x^8 - 2x^7 - 4x^6 + 16x^5 - 29x^4 + 8x^3 + 164x^2 - 364x + 247	\( 2^{8}\cdot 3^{4}\cdot 11^{4}\cdot 13^{2} \)	$V_4^2:S_3$ (as 8T34)	$[2]$
8.0.51438240000.5	x^8 - 2x^7 + 16x^6 - 36x^5 + 45x^4 - 24x^3 - 12x^2 - 24x + 39	\( 2^{8}\cdot 3^{8}\cdot 5^{4}\cdot 7^{2} \)	$V_4^2:S_3$ (as 8T34)	Trivial
8.0.52225046784.2	x^8 + 4x^6 - 12x^5 - 21x^4 - 24x^3 - 92x^2 + 222x + 403	\( 2^{8}\cdot 3^{6}\cdot 23^{4} \)	$V_4^2:S_3$ (as 8T34)	$[2]$