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 60683)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.31443200.1	x^8 - 2x^7 + 3x^6 - 6x^5 + 13x^4 - 20x^3 + 21x^2 - 14x + 5	\( 2^{8}\cdot 5^{2}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.31443200.2	x^8 - x^6 - 4x^5 - 2x^4 + 4x^3 + 12x^2 + 6x + 1	\( 2^{8}\cdot 5^{2}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.40960000.1	x^8 - 4x^6 + 5x^4 - 2x^2 - 1	\( -\,2^{16}\cdot 5^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.40960000.2	x^8 - x^4 - 1	\( -\,2^{16}\cdot 5^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.70304000.1	x^8 + x^6 - 2x^5 + 5x^4 - 2x^3 + x^2 + 1	\( 2^{8}\cdot 5^{3}\cdot 13^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.70304000.2	x^8 - 4x^7 + 7x^6 - 2x^5 - 8x^4 + 8x^3 + 2x^2 - 4x + 1	\( 2^{8}\cdot 5^{3}\cdot 13^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.131274675.1	x^8 - 2x^7 + 4x^6 - 5x^5 + x^4 - 5x^3 + 4x^2 - 2x + 1	\( -\,3^{7}\cdot 5^{2}\cdot 7^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.131274675.2	x^8 - x^7 + x^6 - 4x^5 + x^4 - 4x^3 + x^2 - x + 1	\( -\,3^{7}\cdot 5^{2}\cdot 7^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.143327232.1	x^8 - 3x^4 + 3	\( 2^{16}\cdot 3^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.143327232.2	x^8 - 6x^6 + 15x^4 - 12x^2 + 3	\( 2^{16}\cdot 3^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.212556032.1	x^8 - 2x^7 + 5x^6 - 10x^5 + 23x^4 - 36x^3 + 51x^2 - 48x + 17	\( 2^{8}\cdot 13^{2}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.212556032.2	x^8 - 4x^7 + x^6 + 8x^5 + 5x^4 - 14x^3 - 13x^2 + 4x + 17	\( 2^{8}\cdot 13^{2}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.342102016.1	x^8 - 4x^6 + 5x^4 - 2x^2 - 4	\( -\,2^{12}\cdot 17^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.342102016.2	x^8 - 8x^4 - 1	\( -\,2^{12}\cdot 17^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.359661568.1	x^8 - 4x^5 + 8x^3 + 4x^2 + 4x + 1	\( -\,2^{20}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.359661568.2	x^8 - 4x^6 - 4x^5 + 2x^4 - 2	\( -\,2^{20}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.518711875.1	x^8 - 6x^6 - x^5 + 4x^4 + 13x^3 + 9x^2 + 10x - 5	\( -\,5^{4}\cdot 11^{2}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.518711875.2	x^8 - x^7 - 6x^6 + 8x^5 + 11x^4 - 15x^3 - 29x^2 + 55x - 25	\( -\,5^{4}\cdot 11^{2}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.693388917.1	x^8 - 3x^7 - 2x^6 + 15x^5 - 20x^4 + 15x^3 + 30x^2 - 108x + 81	\( 3^{4}\cdot 13^{2}\cdot 37^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.693388917.2	x^8 - 3x^7 - 5x^6 + 27x^5 - 11x^4 - 60x^3 + 69x^2 - 18x + 9	\( 3^{4}\cdot 13^{2}\cdot 37^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.2.1024000000.1	x^8 - 15x^4 - 50x^2 - 25	\( -\,2^{16}\cdot 5^{6} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1024000000.2	x^8 - 5x^4 - 25	\( -\,2^{16}\cdot 5^{6} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1057749248.1	x^8 - 2x^7 - 3x^6 + 10x^5 - 6x^4 - 28x^3 + 46x^2 + 110x + 53	\( 2^{8}\cdot 17^{3}\cdot 29^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1057749248.2	x^8 - 2x^7 - 7x^6 + 14x^5 + 15x^4 - 48x^3 - 17x^2 + 96x + 73	\( 2^{8}\cdot 17^{3}\cdot 29^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1097440000.1	x^8 + 5x^6 + 3x^4 - 15x^2 - 19	\( -\,2^{8}\cdot 5^{4}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.2.1097440000.2	x^8 - 5x^6 + 3x^4 + 15x^2 - 19	\( -\,2^{8}\cdot 5^{4}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1119744000.1	x^8 - 2x^7 + x^6 + 4x^5 - 5x^4 + 4x^3 + x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{7}\cdot 5^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1119744000.2	x^8 - 2x^7 + x^6 - 8x^5 + x^4 - 8x^3 + x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{7}\cdot 5^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1287913472.1	x^8 - 10x^6 + 42x^4 - 84x^2 + 68	\( 2^{18}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1287913472.2	x^8 - 2x^6 + 10x^4 - 4x^2 + 68	\( 2^{18}\cdot 17^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1344252672.1	x^8 + 3x^6 - 6x^2 - 3	\( -\,2^{8}\cdot 3^{7}\cdot 7^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1344252672.2	x^8 - 3x^6 + 6x^2 - 3	\( -\,2^{8}\cdot 3^{7}\cdot 7^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1517535243.1	x^8 - x^7 + 4x^6 - x^5 + 7x^4 - 10x^3 - 8x^2 + 14x - 5	\( -\,3^{7}\cdot 7^{4}\cdot 17^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1517535243.2	x^8 - x^7 - 5x^6 + 8x^5 + 4x^4 - 25x^3 - 5x^2 + 11x - 5	\( -\,3^{7}\cdot 7^{4}\cdot 17^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1686616064.1	x^8 + 7x^6 + 21x^4 + 21x^2 + 14	\( 2^{11}\cdot 7^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.1686616064.2	x^8 - 2x^7 + 7x^4 - 14x^3 + 12x + 4	\( 2^{11}\cdot 7^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1715072373.1	x^8 - 2x^7 - 2x^5 + 7x^4 - 9x^3 + 27x^2 - 42x + 21	\( 3^{6}\cdot 7^{3}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.1715072373.2	x^8 - 4x^7 + x^6 + 11x^5 - 14x^4 + 5x^3 + 28x^2 - 28x + 49	\( 3^{6}\cdot 7^{3}\cdot 19^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.1721829632.1	x^8 - 2x^7 - 5x^6 + 24x^5 + 16x^4 - 72x^3 - 36x^2 + 74x + 53	\( 2^{8}\cdot 17^{3}\cdot 37^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1721829632.2	x^8 - 4x^7 + 3x^6 + 9x^4 + 28x^3 - 89x^2 - 36x + 149	\( 2^{8}\cdot 17^{3}\cdot 37^{2} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1809375813.1	x^8 - 3x^7 + 11x^6 - 33x^5 + 57x^4 - 108x^3 + 149x^2 - 90x + 127	\( 3^{6}\cdot 7^{2}\cdot 37^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.1809375813.2	x^8 - 3x^7 + 14x^6 - 27x^5 + 66x^4 - 57x^3 + 116x^2 + 6x + 13	\( 3^{6}\cdot 7^{2}\cdot 37^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	$[2]$
8.0.1820786688.1	x^8 + 2x^6 - x^4 - 8x^2 + 7	\( 2^{16}\cdot 3^{4}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1820786688.2	x^8 - 8x^6 + 20x^4 - 16x^2 + 7	\( 2^{16}\cdot 3^{4}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1820786688.3	x^8 + 8x^6 + 20x^4 + 16x^2 + 7	\( 2^{16}\cdot 3^{4}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.0.1820786688.4	x^8 - 2x^6 - x^4 + 8x^2 + 7	\( 2^{16}\cdot 3^{4}\cdot 7^{3} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1871773696.1	x^8 - 2x^6 - 8x^4 + 22x^2 - 9	\( -\,2^{16}\cdot 13^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1871773696.2	x^8 - 3x^4 - 1	\( -\,2^{16}\cdot 13^{4} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1897443072.1	x^8 - 2x^7 + 7x^2 - 2x - 3	\( -\,2^{8}\cdot 3^{2}\cdot 7^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial
8.2.1897443072.2	x^8 - 2x^7 + 7x^6 - 14x^5 + 14x^4 - 14x^2 + 12x - 3	\( -\,2^{8}\cdot 3^{2}\cdot 7^{7} \)	$Z_8 : Z_8^\times$ (as 8T15)	Trivial