Global number field search results

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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 14804)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.60886809.1	x^8 + 7x^6 + 18x^4 + 16x^2 + 1	\( 3^{6}\cdot 17^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.71639296.2	x^8 - x^6 - 3x^4 + 4x^2 + 4	\( 2^{8}\cdot 23^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.96059601.1	x^8 - x^7 - 2x^6 - 5x^5 + 11x^4 + x^3 + 4x^2 - x + 1	\( 3^{8}\cdot 11^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.116640000.2	x^8 - 2x^6 + 6x^4 - 12x^3 + 16x^2 - 12x + 4	\( 2^{8}\cdot 3^{6}\cdot 5^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.136048896.1	x^8 - 4x^7 + 4x^6 - 2x^5 + 5x^4 - 2x^3 + 4x^2 - 4x + 1	\( 2^{8}\cdot 3^{12} \)	$S_4$ (as 8T14)	Trivial
8.0.332150625.1	x^8 - x^7 + x^6 - 8x^5 + 5x^4 - 2x^3 + 16x^2 - 4x + 1	\( 3^{12}\cdot 5^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.333135504.3	x^8 + 4x^6 + 12x^4 + 28x^2 + 16	\( 2^{4}\cdot 3^{6}\cdot 13^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.429981696.1	x^8 - 2x^6 + 15x^4 + 10x^2 + 1	\( 2^{16}\cdot 3^{8} \)	$S_4$ (as 8T14)	Trivial
8.0.429981696.3	x^8 - 6x^6 - 8x^5 + 9x^4 + 24x^3 + 22x^2 + 12x + 3	\( 2^{16}\cdot 3^{8} \)	$S_4$ (as 8T14)	Trivial
8.0.448084224.10	x^8 - 4x^7 + 4x^6 + 2x^5 - 5x^4 + 2x^3 + 28x^2 - 28x + 7	\( 2^{8}\cdot 3^{6}\cdot 7^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.453519616.1	x^8 - 4x^7 + 12x^6 - 22x^5 + 27x^4 - 22x^3 + 16x^2 - 8x + 3	\( 2^{8}\cdot 11^{6} \)	$S_4$ (as 8T14)	Trivial
8.0.479785216.2	x^8 + 4x^6 - 4x^5 + 11x^4 - 8x^3 + 18x^2 - 14x + 3	\( 2^{8}\cdot 37^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.479785216.3	x^8 + 3x^6 + 13x^4 + 20x^2 + 4	\( 2^{8}\cdot 37^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.752734096.1	x^8 - 3x^7 + 5x^6 - 2x^4 + 5x^2 - 3x + 1	\( 2^{4}\cdot 19^{6} \)	$S_4$ (as 8T14)	Trivial
8.0.835210000.1	x^8 - 3x^7 + 11x^6 - 18x^5 + 34x^4 - 18x^3 + 11x^2 - 3x + 1	\( 2^{4}\cdot 5^{4}\cdot 17^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.875213056.2	x^8 + 4x^6 - 4x^5 + 7x^4 - 8x^3 + 10x^2 - 6x + 13	\( 2^{8}\cdot 43^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.959512576.3	x^8 + 2x^6 - 8x^5 + 13x^4 - 8x^3 + 6x^2 - 4x + 3	\( 2^{16}\cdot 11^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.959512576.4	x^8 - 4x^5 + 5x^4 - 12x^3 + 8x^2 + 8x + 4	\( 2^{16}\cdot 11^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.1049760000.2	x^8 - 8x^5 + 21x^4 - 4x^2 + 6x + 9	\( 2^{8}\cdot 3^{8}\cdot 5^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.1049760000.4	x^8 - 2x^7 + 4x^6 + 8x^5 - 7x^4 - 4x^3 + 16x^2 + 4x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.1146228736.6	x^8 - 4x^7 + 8x^6 - 10x^5 + 17x^4 - 22x^3 + 42x^2 - 32x + 26	\( 2^{12}\cdot 23^{4} \)	$S_4$ (as 8T14)	$[3]$
8.0.1222830961.1	x^8 - 3x^7 + 7x^6 - 13x^5 + 16x^4 - 18x^3 + 13x^2 - 3x + 2	\( 11^{4}\cdot 17^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.1275989841.1	x^8 - x^7 - 8x^6 - 3x^5 + 21x^4 + 33x^3 + 30x^2 + 15x + 3	\( 3^{12}\cdot 7^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.1366263369.2	x^8 - x^7 - 2x^6 + 11x^5 + x^4 - 19x^3 + 46x^2 - 7x + 1	\( 3^{6}\cdot 37^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.1640250000.1	x^8 - 3x^7 + 4x^6 - 7x^5 + 6x^4 + 5x^3 + 5x^2 - 30x + 20	\( 2^{4}\cdot 3^{8}\cdot 5^{6} \)	$S_4$ (as 8T14)	$[4]$
8.0.1871773696.6	x^8 - 4x^5 - x^4 - 4x^3 + 8x^2 + 4x + 1	\( 2^{16}\cdot 13^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.2176782336.3	x^8 - 2x^7 + 4x^6 + 8x^5 - 10x^4 + 8x^3 + 16x^2 - 8x + 4	\( 2^{12}\cdot 3^{12} \)	$S_4$ (as 8T14)	$[2]$
8.0.2176782336.5	x^8 + 9x^4 + 48x^2 - 108x + 81	\( 2^{12}\cdot 3^{12} \)	$S_4$ (as 8T14)	$[4]$
8.0.2621440000.14	x^8 + 4x^6 - 8x^5 + 24x^2 + 16x + 12	\( 2^{22}\cdot 5^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.2621440000.15	x^8 + 4x^6 + 24x^2 + 4	\( 2^{22}\cdot 5^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.2702336256.3	x^8 - 4x^7 + 10x^6 - 10x^5 + 21x^4 - 26x^3 - 8x^2 + 16x + 7	\( 2^{8}\cdot 3^{4}\cdot 19^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.2702336256.4	x^8 - 2x^7 - 4x^6 + 16x^5 - 11x^4 - 10x^3 + 38x^2 - 76x + 76	\( 2^{8}\cdot 3^{4}\cdot 19^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.2732361984.9	x^8 - 8x^6 + 6x^4 + 52x^2 + 25	\( 2^{8}\cdot 3^{6}\cdot 11^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.2750058481.1	x^8 + 4x^6 - 14x^5 + 35x^4 - 28x^3 + 111x^2 - 217x + 183	\( 229^{4} \)	$S_4$ (as 8T14)	$[3]$
8.0.2897022976.2	x^8 + 4x^6 + x^4 + 4x^2 - 12x + 9	\( 2^{12}\cdot 29^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.2998219536.1	x^8 - 3x^7 + 11x^6 - 20x^5 + 36x^4 - 40x^3 + 48x^2 - 36x + 12	\( 2^{4}\cdot 3^{8}\cdot 13^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.3049800625.1	x^8 - 2x^7 + 6x^6 - 11x^5 + 23x^4 - 22x^3 + 24x^2 - 16x + 16	\( 5^{4}\cdot 47^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.3102044416.2	x^8 + 5x^6 - 8x^4 - 19x^2 + 25	\( 2^{8}\cdot 59^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.3264065424.1	x^8 - x^7 - 2x^6 - 13x^5 + 16x^4 + 11x^3 + 31x^2 - 10x + 4	\( 2^{4}\cdot 3^{6}\cdot 23^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.3317760000.18	x^8 + 4x^6 - 8x^5 + 14x^4 - 16x^3 + 24x^2 + 8x + 4	\( 2^{16}\cdot 3^{4}\cdot 5^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.3782742016.4	x^8 + 6x^6 - 16x^5 + 41x^4 - 48x^3 + 36x^2 - 8x + 8	\( 2^{12}\cdot 31^{4} \)	$S_4$ (as 8T14)	$[3]$
8.0.4032758016.2	x^8 - 2x^7 - 2x^6 + 12x^5 - 3x^4 - 12x^3 + 12x^2 - 12x + 15	\( 2^{8}\cdot 3^{8}\cdot 7^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.4032758016.3	x^8 - 4x^7 - 2x^6 + 18x^5 + 3x^4 - 30x^3 - 12x^2 + 24x + 21	\( 2^{8}\cdot 3^{8}\cdot 7^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.4362470401.1	x^8 + 14x^6 - 6x^5 + 82x^4 - 42x^3 + 240x^2 - 99x + 208	\( 257^{4} \)	$S_4$ (as 8T14)	$[3]$
8.0.4569760000.12	x^8 - 4x^7 + 6x^6 - 2x^5 - 11x^4 + 18x^3 + 6x^2 - 8x + 3	\( 2^{8}\cdot 5^{4}\cdot 13^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.4640470641.1	x^8 - 3x^7 + 7x^6 - 19x^5 + 30x^4 - 31x^3 + 35x^2 - 18x + 5	\( 3^{8}\cdot 29^{4} \)	$S_4$ (as 8T14)	Trivial
8.0.4857532416.13	x^8 + 6x^6 - 13x^4 + 18x^2 + 1	\( 2^{12}\cdot 3^{4}\cdot 11^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.5082121521.1	x^8 - 2x^7 + 4x^6 - 4x^5 + 11x^4 + 38x^3 + 49x^2 - 41x + 7	\( 3^{4}\cdot 89^{4} \)	$S_4$ (as 8T14)	$[2]$
8.0.5314410000.3	x^8 - x^7 - 8x^6 + 3x^5 + 6x^4 - 15x^3 + 120x^2 - 39x + 129	\( 2^{4}\cdot 3^{12}\cdot 5^{4} \)	$S_4$ (as 8T14)	$[4]$
8.0.5752160649.1	x^8 - 3x^7 + 6x^6 - 9x^5 + 3x^4 + 27x^3 + 18x^2 - 27x + 9	\( 3^{6}\cdot 53^{4} \)	$S_4$ (as 8T14)	Trivial