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 12880)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.12008989.1	x^8 - x^7 + 4x^5 - 2x^4 + 3x^2 - x + 1	\( 229^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.22665187.1	x^8 - x^7 - 4x^5 + 2x^4 + 3x^2 - x - 1	\( -\,283^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.36264691.1	x^8 - 3x^7 + 7x^6 - 7x^5 + 4x^4 + 2x^3 - x^2 - x - 1	\( -\,331^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.49836032.1	x^8 - 2x^7 + 2x^6 - 4x^5 + 5x^4 - 4x^3 + 2x^2 - 2x + 1	\( -\,2^{12}\cdot 23^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.51868672.1	x^8 - 2x^7 + 4x^5 - 4x^3 + 2x + 1	\( 2^{10}\cdot 37^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.81415168.1	x^8 - 4x^7 + 8x^6 - 8x^5 + 2x^4 + 6x^3 - 12x^2 + 6x - 1	\( -\,2^{10}\cdot 43^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.118370771.1	x^8 - 3x^7 + x^6 + 3x^5 - 4x^4 + 10x^3 - 7x^2 + 5x - 3	\( -\,491^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.122023936.1	x^8 - 2x^7 + 2x^6 - 4x^5 + x^4 + 6x^2 + 6x + 1	\( -\,2^{12}\cdot 31^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.150730227.1	x^8 - x^7 - x^6 + 4x^5 - 4x^4 + 2x^3 - 8x^2 + 5x - 1	\( -\,3^{7}\cdot 41^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.150730227.2	x^8 - 2x^7 - 2x^6 + 3x^5 + 6x^4 - 3x^3 - 10x^2 - x - 1	\( -\,3^{7}\cdot 41^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.160016229.1	x^8 - 2x^7 + 3x^6 - 2x^5 + x^4 + 3x^3 - x^2 - x + 3	\( 3^{8}\cdot 29^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.167042000.1	x^8 - 4x^7 + 9x^6 - 13x^5 + 18x^4 - 19x^3 + 14x^2 - 6x + 2	\( 2^{4}\cdot 5^{3}\cdot 17^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.199344128.1	x^8 - 2x^7 + 2x^6 + 2x^5 - 4x^4 + 6x^3 + 6x^2 - 2x - 3	\( -\,2^{14}\cdot 23^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.207474688.1	x^8 - 2x^7 + 2x^6 - 8x^5 + 12x^4 - 10x^3 + 12x^2 - 4x + 3	\( 2^{12}\cdot 37^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.286557184.1	x^8 + 4x^6 - 7x^4 + 2x^2 - 4	\( -\,2^{10}\cdot 23^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.286557184.2	x^8 - 2x^7 - 2x^5 + 11x^4 - 14x^3 + 10x^2 - 4x - 1	\( -\,2^{10}\cdot 23^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.311441744.1	x^8 + 5x^6 - 3x^5 - 2x^4 + 5x^3 - 4x^2 - 2x + 2	\( 2^{4}\cdot 269^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.325660672.1	x^8 - 2x^7 + 8x^6 - 10x^5 + 6x^4 + 2x^2 - 4x - 2	\( -\,2^{12}\cdot 43^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.338608873.1	x^8 - 3x^7 + 4x^5 + 6x^4 - 12x^3 + 2x^2 - 4x + 7	\( 17^{3}\cdot 41^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.338608873.2	x^8 - 4x^7 + 4x^6 + 2x^5 - 6x^4 + 4x^3 - x + 3	\( 17^{3}\cdot 41^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.357453677.1	x^8 - 3x^7 + 6x^6 - 5x^5 + 10x^4 - 10x^3 + 8x^2 - 7x + 5	\( 7^{4}\cdot 53^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.390617891.1	x^8 - x^7 + 3x^6 - 8x^5 + 6x^4 - 4x^3 + 6x^2 - x - 3	\( -\,17^{3}\cdot 43^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.488095744.2	x^8 - 2x^7 - 4x^6 + 8x^5 + 8x^4 - 12x^3 - 12x^2 + 16x - 2	\( -\,2^{14}\cdot 31^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.489303872.1	x^8 - 3x^7 + x^6 - x^5 + 7x^4 + x^3 + 9x^2 - 3x + 4	\( 2^{6}\cdot 197^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.609960125.1	x^8 - 2x^7 + 3x^6 + 3x^5 + 2x^4 - 8x^3 + 12x^2 - 5x + 1	\( 5^{3}\cdot 47^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.680136784.1	x^8 - 2x^7 + 3x^6 + 3x^5 + 2x^4 - x^3 - 4x^2 + 2	\( 2^{4}\cdot 349^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.768144384.1	x^8 - 4x^7 + 10x^6 - 12x^5 + 6x^4 - 6x^3 - 6x^2 + 12x + 6	\( 2^{10}\cdot 3^{7}\cdot 7^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.768144384.2	x^8 - 2x^7 - 2x^6 + 2x^5 + 8x^4 + 14x^3 + 14x^2 + 8x + 2	\( 2^{10}\cdot 3^{7}\cdot 7^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.771656704.1	x^8 - 2x^7 + 4x^5 - 6x^4 + 20x^3 - 12x^2 + 6x - 1	\( -\,2^{10}\cdot 7^{3}\cdot 13^{3} \)	$Q_8:S_4$ (as 8T40)	$[2]$
8.0.839808000.1	x^8 - 4x^7 + 10x^6 - 14x^5 + 14x^4 - 14x^3 + 14x^2 - 8x + 2	\( 2^{10}\cdot 3^{8}\cdot 5^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.878080000.1	x^8 - 2x^7 + 2x^6 - 3x^4 + 2x^2 - 2x + 1	\( -\,2^{12}\cdot 5^{4}\cdot 7^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.922529088.1	x^8 - x^7 + 8x^6 - 2x^5 + 8x^4 + 2x^3 + 8x^2 - 2x + 4	\( 2^{6}\cdot 3^{8}\cdot 13^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.941821904.1	x^8 - 2x^7 + 3x^6 - 5x^5 + 8x^4 + x^3 + 6x^2 - 6x + 2	\( 2^{4}\cdot 389^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.959512576.1	x^8 + 2x^6 + x^4 - 8x^2 - 16	\( -\,2^{16}\cdot 11^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.959512576.2	x^8 + 12x^4 - 4x^2 - 1	\( -\,2^{16}\cdot 11^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.972728109.1	x^8 - x^7 + x^6 - 12x^5 + 11x^4 - 7x^3 + 27x^2 - 6x + 73	\( 3^{4}\cdot 229^{3} \)	$Q_8:S_4$ (as 8T40)	$[2]$
8.0.1055028224.1	x^8 - 4x^5 - 2x^4 + 14x^3 + 6x^2 - 4x + 2	\( 2^{10}\cdot 101^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.1086373952.1	x^8 - 3x^7 - 3x^6 + 9x^5 + 34x^4 - 32x^3 - 81x^2 + 35x + 62	\( 2^{6}\cdot 257^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.1086373952.2	x^8 - 3x^7 + 13x^6 - 30x^5 + 77x^4 - 139x^3 + 188x^2 - 155x + 71	\( 2^{6}\cdot 257^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1105805439.1	x^8 - 2x^7 + 4x^6 - 8x^4 + 14x^3 - 24x^2 + 21x - 8	\( -\,3^{4}\cdot 239^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1105805439.2	x^8 - 2x^7 + 7x^5 - 6x^4 - 14x^3 + 11x^2 + 9x - 11	\( -\,3^{4}\cdot 239^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1119744000.3	x^8 - 4x^7 + 12x^6 - 22x^5 + 37x^4 - 42x^3 + 40x^2 - 22x + 3	\( -\,2^{12}\cdot 3^{7}\cdot 5^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1119744000.4	x^8 - 4x^7 + 10x^6 - 16x^5 + 13x^4 - 4x^3 - 16x^2 + 16x - 4	\( -\,2^{12}\cdot 3^{7}\cdot 5^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1146228736.1	x^8 - 3x^6 + 4x^4 - 3x^2 - 1	\( -\,2^{12}\cdot 23^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1146228736.2	x^8 + 3x^6 + 4x^4 + 3x^2 - 1	\( -\,2^{12}\cdot 23^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.2.1327373299.1	x^8 - 3x^7 - x^6 + 8x^5 + x^4 - 3x^3 + x^2 + 2x - 5	\( -\,7^{3}\cdot 157^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.1406080000.1	x^8 - 4x^6 + 2x^4 + 13	\( 2^{10}\cdot 5^{4}\cdot 13^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.1440146061.1	x^8 - 6x^6 - 5x^5 + 9x^4 + 21x^3 + 19x^2 + 9x + 3	\( 3^{10}\cdot 29^{3} \)	$Q_8:S_4$ (as 8T40)	$[2]$
8.0.1448511488.1	x^8 - 3x^6 + 3x^4 + 6x^2 + 2	\( 2^{11}\cdot 29^{4} \)	$Q_8:S_4$ (as 8T40)	Trivial
8.0.1488770000.1	x^8 - 3x^7 + 10x^6 - 23x^5 + 32x^4 - 19x^3 + 5x + 5	\( 2^{4}\cdot 5^{4}\cdot 53^{3} \)	$Q_8:S_4$ (as 8T40)	Trivial