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 6360)

Label	Polynomial	Discriminant	Galois group	Class group
8.2.22665187.2	x^8 - x^7 + x^6 - 2x^5 + x^4 - 9x^3 + 7x^2 - 6x + 1	\( -\,283^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.22665187.3	x^8 - 3x^7 + 4x^6 - 8x^5 + 8x^4 - x^3 + 2x^2 - 3x - 1	\( -\,283^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.32019867.1	x^8 - 4x^7 + 7x^6 - 7x^5 + 7x^4 - 7x^3 + 2x^2 + x - 1	\( -\,3^{7}\cdot 11^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.32019867.2	x^8 - x^7 + x^6 - 2x^5 - x^4 - 2x^3 + x^2 - x + 1	\( -\,3^{7}\cdot 11^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.36264691.2	x^8 - 4x^7 + 5x^6 - x^5 - 3x^4 + 3x^3 - x - 1	\( -\,331^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.36264691.3	x^8 - 2x^7 + 3x^6 - 7x^4 + 17x^3 - 17x^2 + 11x - 1	\( -\,331^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.81415168.2	x^8 - 4x^7 + 8x^6 - 8x^5 + 6x^3 - 2x^2 - 2	\( -\,2^{10}\cdot 43^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.81415168.3	x^8 - 4x^7 + 10x^6 - 14x^5 + 10x^4 + 2x^3 - 10x^2 + 8x - 2	\( -\,2^{10}\cdot 43^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.110716875.1	x^8 - 4x^7 + 5x^6 - x^5 - 2x^4 + x^3 + 4x^2 - 4x - 1	\( -\,3^{11}\cdot 5^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.110716875.2	x^8 - 4x^7 + 7x^6 - 7x^5 + 4x^4 - x^3 - 4x^2 + 4x - 1	\( -\,3^{11}\cdot 5^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.118370771.2	x^8 - 2x^7 - x^5 + 7x^3 + x - 9	\( -\,491^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.118370771.3	x^8 - 3x^7 + 7x^6 - 10x^5 + 11x^4 - 5x^3 + 3x^2 - 2x - 3	\( -\,491^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.150730227.3	x^8 - 2x^7 + 2x^6 - x^5 + 2x^4 + x^3 - 5x^2 + 4x - 1	\( -\,3^{7}\cdot 41^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.150730227.4	x^8 + 2x^6 - 2x^5 - 3x^4 - 7x^3 - 11x^2 - 6x - 1	\( -\,3^{7}\cdot 41^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.150730227.5	x^8 - 4x^7 + 7x^6 - 6x^5 - 3x^4 + 9x^3 - x^2 - 5x - 1	\( -\,3^{7}\cdot 41^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.150730227.6	x^8 - x^7 + x^6 + 5x^5 - 11x^4 + 8x^3 - 7x^2 + 4x - 1	\( -\,3^{7}\cdot 41^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.178453547.1	x^8 - x^7 - 2x^6 + 6x^5 - 11x^3 + 5x^2 + 8x - 3	\( -\,563^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.178453547.2	x^8 - 2x^7 + 3x^6 + x^5 - 4x^4 + 12x^3 - 7x^2 + 2x - 9	\( -\,563^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.181398528.1	x^8 - 6x^4 + 4x^2 - 3	\( -\,2^{10}\cdot 3^{11} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.181398528.2	x^8 - 2x^6 - 2x^5 - 2x^3 - 2x^2 + 1	\( -\,2^{10}\cdot 3^{11} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.182660427.1	x^8 - 4x^7 + 7x^6 - 7x^5 + 4x^4 - x^3 + 4x^2 - 4x + 1	\( -\,3^{7}\cdot 17^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.182660427.2	x^8 - x^7 + 4x^6 - 4x^5 - 2x^4 - 4x^3 - 5x^2 - x + 1	\( -\,3^{7}\cdot 17^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.265847707.1	x^8 - 2x^7 + 3x^6 + x^5 - 7x^4 + 18x^3 - 12x^2 + 4x - 1	\( -\,643^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.265847707.2	x^8 - x^7 - x^6 + 5x^5 - 3x^4 + 2x^3 - 6x^2 + 9x - 1	\( -\,643^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.286557184.3	x^8 + 5x^6 + 6x^4 - 3x^2 - 1	\( -\,2^{10}\cdot 23^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.286557184.4	x^8 - 5x^6 + 6x^4 + 3x^2 - 1	\( -\,2^{10}\cdot 23^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.325660672.2	x^8 - 2x^7 + 4x^6 - 12x^5 + 16x^4 - 18x^3 + 10x^2 - 1	\( -\,2^{12}\cdot 43^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.325660672.3	x^8 - 2x^7 + 6x^6 - 12x^5 + 16x^4 - 10x^3 - 4x^2 + 4x - 1	\( -\,2^{12}\cdot 43^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.423564751.1	x^8 - x^7 - 2x^6 + 4x^5 - 9x^4 + 17x^3 - 21x^2 + 7x - 4	\( -\,751^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.423564751.2	x^8 - 2x^7 + 2x^6 - 4x^5 - 4x^4 + 20x^3 - 14x^2 + 13x - 4	\( -\,751^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.425329947.1	x^8 - x^7 - 3x^6 + 2x^5 + 4x^4 + 3x^3 - 5x^2 - 7x - 3	\( -\,3^{11}\cdot 7^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.425329947.2	x^8 - 6x^4 - x^2 - 3	\( -\,3^{11}\cdot 7^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.725594112.1	x^8 - 6x^4 - 4x^2 - 3	\( -\,2^{12}\cdot 3^{11} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.725594112.2	x^8 - 4x^6 + 12x^2 - 12	\( -\,2^{12}\cdot 3^{11} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.941391011.1	x^8 + 2x^6 - 9x^4 + 6x^2 - 11	\( -\,11^{3}\cdot 29^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.941391011.2	x^8 - 2x^7 - 2x^6 + 17x^5 - 32x^4 + 31x^3 - 15x^2 + 4x - 1	\( -\,11^{3}\cdot 29^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.999406512.1	x^8 - 4x^7 + 7x^6 - 7x^5 - 2x^4 + 11x^3 - 2x^2 - 4x - 2	\( -\,2^{4}\cdot 3^{7}\cdot 13^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.999406512.2	x^8 - 4x^7 + x^6 + 11x^5 - 11x^4 - x^3 + 4x^2 - x - 2	\( -\,2^{4}\cdot 3^{7}\cdot 13^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1280239375.1	x^8 - 4x^7 + 10x^6 - 16x^5 + 18x^4 - 14x^3 + 4x^2 + x - 1	\( -\,5^{4}\cdot 127^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1280239375.2	x^8 - 2x^7 + 5x^5 - 6x^4 - 10x^3 + 21x^2 + 5x - 13	\( -\,5^{4}\cdot 127^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1327373299.2	x^8 - 3x^7 + 2x^6 - 3x^4 + 11x^3 - 13x^2 + 15x - 11	\( -\,7^{3}\cdot 157^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1327373299.3	x^8 - x^7 - 2x^6 - 6x^5 + 10x^4 + 15x^3 - 6x^2 - 5x - 7	\( -\,7^{3}\cdot 157^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1327373299.4	x^8 - 6x^6 - 5x^5 + 19x^4 + 21x^3 - 18x^2 - 36x - 5	\( -\,7^{3}\cdot 157^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1327373299.5	x^8 - x^7 - 4x^6 + 4x^5 + 4x^4 - 9x^3 + 2x^2 - 3x - 5	\( -\,7^{3}\cdot 157^{3} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1399680000.1	x^8 - 6x^4 - 12x^2 - 3	\( -\,2^{10}\cdot 3^{7}\cdot 5^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1399680000.2	x^8 - 6x^6 + 12x^4 - 6x^3 - 6x^2 + 18x - 3	\( -\,2^{10}\cdot 3^{7}\cdot 5^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1626347584.1	x^8 - x^7 - x^6 - 4x^5 + 6x^4 - 4x^3 - x^2 - x + 1	\( -\,2^{6}\cdot 71^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1626347584.2	x^8 - 8x^6 + 19x^4 - 16x^2 - 4	\( -\,2^{6}\cdot 71^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1673730583.1	x^8 - 4x^7 + 6x^6 - 4x^5 + 2x^3 - 4x^2 + 3x - 4	\( -\,7^{3}\cdot 47^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial
8.2.1673730583.2	x^8 - 4x^7 + 12x^6 - 22x^5 + 32x^4 - 32x^3 + 8x^2 + 5x - 2	\( -\,7^{3}\cdot 47^{4} \)	$\textrm{GL(2,3)}$ (as 8T23)	Trivial