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 259)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.275653125.1	x^8 - 2x^7 + 7x^6 - 11x^5 + 19x^4 - 20x^3 + 20x^2 - 10x + 5	\( 3^{6}\cdot 5^{5}\cdot 11^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.402753125.1	x^8 - x^7 + x^5 - 4x^4 + 5x^3 + 6x^2 - 2x - 1	\( 5^{5}\cdot 359^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.583200000.1	x^8 - 2x^7 + 2x^6 - 6x^4 + 12x^3 + 7x^2 - 2x - 1	\( 2^{8}\cdot 3^{6}\cdot 5^{5} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.635628125.1	x^8 - 5x^6 - x^5 + 6x^4 + 5x^3 - 6x^2 + 2x - 1	\( 5^{5}\cdot 11^{2}\cdot 41^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1018878125.1	x^8 - 2x^7 + 3x^5 - 9x^4 - 5x^3 + 14x^2 + 4x - 1	\( 5^{5}\cdot 571^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1479200000.1	x^8 - x^6 - 10x^5 + x^4 + 19x^2 - 10x + 1	\( 2^{8}\cdot 5^{5}\cdot 43^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1544403125.1	x^8 - x^7 - 3x^6 + x^5 + x^4 + 5x + 5	\( 5^{5}\cdot 19^{2}\cdot 37^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1644167168.1	x^8 - 8x^3 - 8x^2 + 1	\( 2^{25}\cdot 7^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1692800000.1	x^8 - 2x^7 + x^6 - x^4 - 4x^3 - 10x^2 + 4	\( 2^{10}\cdot 5^{5}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1767725973.1	x^8 - x^7 + 4x^6 - 4x^5 + 2x^4 - 3x^3 - 18x^2 + 27x - 9	\( 3^{2}\cdot 13^{5}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1805000000.1	x^8 - 3x^7 - 2x^6 + 14x^5 - 15x^4 - 6x^3 + 18x^2 - 13x + 1	\( 2^{6}\cdot 5^{7}\cdot 19^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.1960200000.1	x^8 - x^7 - 2x^6 - 11x^4 + 16x^3 + 18x^2 - 9x - 11	\( 2^{6}\cdot 3^{4}\cdot 5^{5}\cdot 11^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2015028125.1	x^8 - x^7 + 5x^5 - 16x^4 + 17x^3 - 17x^2 + 6x + 4	\( 5^{5}\cdot 11^{2}\cdot 73^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2189278125.1	x^8 - 4x^7 + 7x^6 - 5x^5 - 4x^4 + 10x^3 - 23x^2 + 26x + 1	\( 3^{6}\cdot 5^{5}\cdot 31^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.0.2496135168.1	x^8 + 11x^4 - 12x^3 + 14x^2 - 12x + 14	\( 2^{19}\cdot 3^{2}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2604903125.1	x^8 - 3x^7 + 6x^6 - 4x^5 - 14x^4 + 30x^3 - 51x^2 + 35x - 5	\( 5^{5}\cdot 11^{2}\cdot 83^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2645000000.1	x^8 - 2x^7 + 3x^6 + x^5 - 10x^4 + 21x^3 - 17x^2 + 3x + 1	\( 2^{6}\cdot 5^{7}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2731953125.1	x^8 - 3x^7 + 3x^6 + 4x^5 - 20x^4 + 14x^3 - 2x^2 - 3x + 1	\( 5^{7}\cdot 11^{2}\cdot 17^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2767128125.1	x^8 - 7x^5 - 9x^4 - 5x^3 + x^2 + 14x + 4	\( 5^{5}\cdot 941^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2784800000.1	x^8 - 2x^5 - 4x^4 + 10x^3 + x^2 - 6x - 1	\( 2^{8}\cdot 5^{5}\cdot 59^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2790703125.1	x^8 - 3x^7 - 2x^6 + 14x^5 - 15x^4 - x^3 + 13x^2 - 3x + 1	\( 3^{6}\cdot 5^{7}\cdot 7^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2793930752.1	x^8 - 4x^6 + x^4 - 4x^3 + 2x^2 + 4x + 2	\( 2^{19}\cdot 73^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.2976800000.1	x^8 - x^6 - 16x^4 - 30x^3 - 10x^2 + 10x + 5	\( 2^{8}\cdot 5^{5}\cdot 61^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.0.3025800000.1	x^8 - 4x^7 + 9x^6 - 10x^5 + 14x^4 - 18x^3 + 15x^2 + 9	\( 2^{6}\cdot 3^{2}\cdot 5^{5}\cdot 41^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.3075200000.1	x^8 - 2x^7 - x^6 + 12x^5 - 11x^4 - 8x^3 + 12x^2 - 4	\( 2^{10}\cdot 5^{5}\cdot 31^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.3230793728.1	x^8 - 2x^7 + 5x^6 - 14x^5 + 7x^4 + 12x^3 - 10x^2 + 4x - 2	\( 2^{17}\cdot 157^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.3465028125.1	x^8 - 3x^7 - 5x^6 + 20x^5 - 6x^4 - 34x^3 + 32x^2 + 27x - 31	\( 3^{8}\cdot 5^{5}\cdot 13^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4032800000.1	x^8 - 4x^7 + 5x^6 - 6x^4 - 2x^3 - 7x^2 - 6x - 1	\( 2^{8}\cdot 5^{5}\cdot 71^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4032800000.2	x^8 - 4x^7 + 7x^6 + 4x^5 - 19x^4 + 10x^3 + 15x^2 - 10x - 5	\( 2^{8}\cdot 5^{5}\cdot 71^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4032800000.3	x^8 - 2x^7 - 3x^6 + 4x^5 - x^4 + 10x^3 - 5x^2 - 5	\( 2^{8}\cdot 5^{5}\cdot 71^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4197753125.1	x^8 - 3x^7 - 2x^6 + 11x^5 - 4x^4 - 20x^3 + 10x^2 + 17x - 1	\( 5^{5}\cdot 19^{2}\cdot 61^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4682022912.2	x^8 - 2x^7 - 7x^6 + 10x^5 + 7x^4 - 4x^3 - 2x^2 + 4x + 2	\( 2^{17}\cdot 3^{6}\cdot 7^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.4743200000.1	x^8 - 2x^7 - 2x^6 + 2x^5 + 16x^4 - 17x^2 + 8x - 1	\( 2^{8}\cdot 5^{5}\cdot 7^{2}\cdot 11^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.5248800000.1	x^8 - 2x^7 - 7x^6 + 20x^5 - 19x^4 + 10x^3 - 7x^2 + 2x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{5} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.6336800000.1	x^8 - 2x^7 + x^6 - 10x^5 + 15x^4 + 20x^3 - 45x^2 + 25	\( 2^{8}\cdot 5^{5}\cdot 89^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.6993800000.1	x^8 - x^7 - 7x^6 + 15x^5 + 4x^4 - 39x^3 + 43x^2 - 14x - 1	\( 2^{6}\cdot 5^{5}\cdot 11^{2}\cdot 17^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.7517503125.1	x^8 - 3x^6 - 7x^5 + 4x^4 + 13x^3 + 4x^2 - 8x + 1	\( 3^{2}\cdot 5^{5}\cdot 11^{2}\cdot 47^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.7699131648.1	x^8 - 11x^6 - 10x^5 + 23x^4 + 42x^3 + 21x^2 - 6x - 9	\( 2^{8}\cdot 3^{4}\cdot 13^{5} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.8323596288.1	x^8 - 2x^6 - 12x^5 - 31x^4 + 12x^3 + 20x^2 - 2	\( 2^{21}\cdot 3^{4}\cdot 7^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.8394753125.1	x^8 - 3x^7 + 15x^5 - 26x^4 + 11x^3 + 12x^2 - 8x - 1	\( 5^{5}\cdot 11^{2}\cdot 149^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.8621628125.1	x^8 - 2x^7 + 6x^5 - 5x^4 + 9x^3 - 23x^2 - 10x - 1	\( 5^{5}\cdot 11^{2}\cdot 151^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.9148503125.1	x^8 - 3x^7 + 5x^6 - 11x^5 + 25x^4 - 14x^3 - 23x^2 + 10x - 1	\( 5^{5}\cdot 29^{2}\cdot 59^{2} \)	$A_4^2:C_4$ (as 8T46)	$[2]$
8.4.9331200000.1	x^8 - 4x^7 + 10x^6 - 12x^5 + 9x^4 - 20x^2 + 20x - 5	\( 2^{12}\cdot 3^{6}\cdot 5^{5} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.9680000000.1	x^8 - 5x^6 - 10x^5 + 20x^4 + 40x^3 - 75x^2 + 30x - 5	\( 2^{10}\cdot 5^{7}\cdot 11^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.9768665088.1	x^8 - 2x^7 + 7x^6 - 14x^5 + 12x^4 - 22x^3 + 25x^2 - 10x + 1	\( 2^{17}\cdot 3^{2}\cdot 7^{2}\cdot 13^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.9779253125.1	x^8 - x^7 - 4x^6 + 4x^5 - 6x^4 - 9x^3 + 8x^2 - 5x + 1	\( 5^{5}\cdot 29^{2}\cdot 61^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.0.9984540672.1	x^8 - 4x^7 + 2x^6 + 4x^5 + 11x^4 - 24x^3 + 18	\( 2^{21}\cdot 3^{2}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.0.9984540672.2	x^8 + 6x^6 - 4x^5 + 15x^4 - 20x^3 + 32x^2 - 40x + 46	\( 2^{21}\cdot 3^{2}\cdot 23^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.10764800000.1	x^8 - 4x^7 + 6x^6 - 4x^5 - 6x^4 + 4x^3 + 8x^2 - 4	\( 2^{12}\cdot 5^{5}\cdot 29^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial
8.4.10764800000.2	x^8 - 4x^7 + 2x^6 + 6x^5 - 9x^4 - 10x^3 - 8x^2 - 6x - 1	\( 2^{12}\cdot 5^{5}\cdot 29^{2} \)	$A_4^2:C_4$ (as 8T46)	Trivial