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 1205)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.5473632256.1	x^10 - 2x^9 + 2x^8 - 2x^6 + 4x^4 + x^2 + 2x + 2	\( -\,2^{16}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.5508110403.1	x^10 - 4x^8 + 4x^6 + 3x^4 - 6x^2 + 3	\( -\,3^{9}\cdot 23^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.24657753125.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 12x^6 - 16x^5 + 12x^4 - 10x^3 + 6x^2 - 3x + 1	\( 5^{5}\cdot 53^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.46352367616.1	x^10 + 4x^8 + 10x^6 + 16x^4 + 17x^2 + 4	\( -\,2^{16}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.67292260083.1	x^10 - 3x^9 + 2x^8 - 4x^7 + 10x^6 - 8x^5 + 10x^4 - 4x^3 + 2x^2 - 3x + 1	\( -\,3^{9}\cdot 43^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.79411503125.1	x^10 - 5x^9 + 11x^8 - 14x^7 + 14x^6 - 14x^5 + 14x^4 - 11x^3 + 9x^2 - 5x + 1	\( 5^{5}\cdot 71^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.83130789888.1	x^10 - x^9 + x^8 - 4x^7 + 4x^6 - 2x^5 + 6x^4 - 4x^3 - 4x + 4	\( -\,2^{12}\cdot 3^{5}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.83405440000.1	x^10 - 5x^8 + 13x^6 - 19x^4 + 19x^2 + 1	\( -\,2^{10}\cdot 5^{4}\cdot 19^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.88744503125.1	x^10 - 2x^9 + 4x^8 - x^7 - 4x^6 + 9x^5 - 4x^4 - x^3 + 4x^2 - 2x + 1	\( 5^{5}\cdot 73^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.133159451283.1	x^10 - 5x^9 + 7x^8 + 2x^7 - 7x^6 - 7x^5 + 10x^4 + 4x^3 - 2x^2 - 3x + 3	\( -\,3^{13}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.175156232192.1	x^10 + 2x^8 + 2x^6 - 4x^4 + x^2 + 2	\( -\,2^{21}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.175156232192.1	x^10 - 2x^8 + 2x^6 + 4x^4 + x^2 - 2	\( 2^{21}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.180111751875.2	x^10 + 5x^8 + 7x^6 - 3x^4 - 6x^2 + 3	\( -\,3^{9}\cdot 5^{4}\cdot 11^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.207773767683.1	x^10 - x^9 + 4x^8 + x^7 + 5x^6 - 14x^5 + 4x^4 - x^3 + 13x^2 - 12x + 3	\( -\,3^{13}\cdot 19^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.224054542336.2	x^10 - 4x^8 - 2x^7 + 4x^6 + 2x^5 - 2x^4 + 6x^3 + 17x^2 + 18x + 10	\( -\,2^{16}\cdot 43^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.268738560000.1	x^10 + 4x^8 - 8x^6 - 8x^4 + 4x^2 + 16	\( -\,2^{16}\cdot 3^{8}\cdot 5^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.300186253125.1	x^10 - x^9 + 2x^8 - 6x^7 + 6x^6 - 13x^5 + 6x^4 - 6x^3 + 2x^2 - x + 1	\( 3^{8}\cdot 5^{5}\cdot 11^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.342896882653.1	x^10 - 2x^9 + 4x^8 - 8x^7 + 5x^6 - 4x^5 + 13x^4 - 12x^3 + 2x^2 - x + 1	\( 13^{5}\cdot 31^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.351353851875.1	x^10 - x^9 - 7x^7 + 4x^6 - 6x^5 + 18x^3 + 27x^2 + 81	\( -\,3^{9}\cdot 5^{4}\cdot 13^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.396634514643.1	x^10 - 3x^9 + 4x^8 - 3x^7 - 2x^6 + 6x^5 - 3x^2 + 3	\( -\,3^{9}\cdot 67^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.412290560000.1	x^10 - x^9 - 3x^8 + 8x^7 + 11x^6 - 7x^5 + 11x^4 + 8x^3 - 3x^2 - x + 1	\( -\,2^{12}\cdot 5^{4}\cdot 11^{5} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.453496320000.1	x^10 + 2x^8 - 8x^7 + 10x^6 - 4x^5 + 4x^4 - 8x^3 + 20x^2 - 24x + 16	\( -\,2^{12}\cdot 3^{11}\cdot 5^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.496172202448.1	x^10 - x^9 + x^8 + 4x^7 + 9x^6 + 11x^5 - 9x^4 + 4x^3 - x^2 - x - 1	\( 2^{4}\cdot 13^{5}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.500178117123.1	x^10 - x^9 + 2x^7 - 8x^6 - 24x^5 + 6x^4 + 84x^3 + 111x^2 + 60x + 12	\( -\,3^{9}\cdot 71^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.532362855424.1	x^10 - 8x^7 + 11x^6 - 10x^5 + 32x^4 - 38x^3 + 25x^2 - 10x + 2	\( -\,2^{10}\cdot 151^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.584929280000.2	x^10 - 2x^9 + 5x^8 + 4x^7 + x^6 + 14x^5 + x^4 + 4x^3 + 5x^2 - 2x + 1	\( 2^{15}\cdot 5^{4}\cdot 13^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.599695360000.1	x^10 - 4x^8 + 2x^6 + 8x^4 + 9x^2 + 4	\( -\,2^{16}\cdot 5^{4}\cdot 11^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.660311932928.1	x^10 + 2x^8 + 11x^6 + 18x^4 + 17x^2 - 8	\( 2^{15}\cdot 67^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.703976583168.1	x^10 + 2x^8 - 4x^7 + x^6 - 6x^5 + 10x^4 - 2x^3 + 13x^2 - 6x + 4	\( -\,2^{12}\cdot 3^{5}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.703976583168.3	x^10 - 3x^9 + 3x^8 - x^6 - 9x^5 + 57x^4 - 132x^3 + 157x^2 - 99x + 27	\( -\,2^{12}\cdot 3^{5}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.740756291584.1	x^10 - 4x^7 + 14x^6 - 20x^5 + 8x^4 + 20x^3 + x^2 + 4x + 8	\( -\,2^{18}\cdot 41^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.796463432704.1	x^10 - 2x^9 + 7x^8 - 14x^7 + 33x^6 - 48x^5 + 33x^4 - 14x^3 + 7x^2 - 2x + 1	\( -\,2^{10}\cdot 167^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.889911260208.1	x^10 - x^9 - 4x^8 - 9x^7 + 32x^6 + 7x^5 - 21x^4 - 80x^3 + 140x^2 - 80x + 16	\( -\,2^{4}\cdot 3^{9}\cdot 41^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.1004237878817.1	x^10 + x^8 - x^7 - 4x^6 - 11x^5 - 4x^4 - x^3 + x^2 + 1	\( 17^{5}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1007907991552.1	x^10 - x^9 - 6x^8 + 14x^7 + 10x^6 - 46x^5 + 20x^4 + 56x^3 - 48x^2 - 16x + 32	\( -\,2^{12}\cdot 7^{5}\cdot 11^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.1069068800000.1	x^10 - x^9 - x^8 + 8x^7 - 8x^6 + 14x^5 + 10x^4 + 4x^3 - 8x^2 - 4x - 4	\( 2^{12}\cdot 5^{5}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1127634365763.1	x^10 - 2x^9 - 2x^7 + 4x^6 + 9x^5 - 21x^4 + 6x^3 + 27x^2 - 18x + 9	\( -\,3^{13}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1315900528659.1	x^10 - 5x^9 + 11x^8 - 14x^7 + 9x^6 + x^5 - 8x^3 + 28x^2 - 23x + 17	\( -\,3^{12}\cdot 19^{5} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1320623865856.1	x^10 - 4x^8 + 16x^6 - 8x^4 + 4x^2 + 16	\( -\,2^{16}\cdot 67^{4} \)	$A_5\times C_2$ (as 10T11)	$[3]$
10.2.1330092638208.1	x^10 - 2x^9 + 5x^8 - 10x^7 + 16x^6 - 8x^5 + 8x^4 - 16x^3 - 78x^2 - 12x + 22	\( 2^{16}\cdot 3^{5}\cdot 17^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1472390771283.1	x^10 - x^9 + 12x^8 - 14x^7 + 44x^6 - 48x^5 + 44x^4 - 14x^3 + 12x^2 - x + 1	\( -\,3^{13}\cdot 31^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1483275763712.1	x^10 + 2x^8 - 6x^6 + 12x^4 - 7x^2 + 2	\( -\,2^{21}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.1483275763712.1	x^10 - 2x^8 - 6x^6 - 12x^4 - 7x^2 - 2	\( 2^{21}\cdot 29^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.1680747204608.1	x^10 - 3x^9 + 16x^7 - 13x^6 - 25x^5 + 34x^4 + 22x^3 - 26x^2 + 14x - 4	\( 2^{12}\cdot 17^{7} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.1713111675629.1	x^10 - 2x^9 + 6x^8 - 7x^7 + 6x^6 - 5x^5 - 6x^4 - 7x^3 - 6x^2 - 2x - 1	\( 17^{4}\cdot 29^{5} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.1861107122176.1	x^10 - 4x^8 + 24x^4 + 36x^2 + 16	\( -\,2^{16}\cdot 73^{4} \)	$A_5\times C_2$ (as 10T11)	$[3]$
10.0.1966181281792.1	x^10 - 5x^9 + 12x^8 - 14x^7 + 6x^6 + 6x^5 - 18x^4 + 18x^3 + 21x^2 + 3x + 2	\( -\,2^{12}\cdot 7^{5}\cdot 13^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.2.2099520000000.3	x^10 - 4x^9 + 4x^8 + 6x^7 - 21x^6 + 24x^5 - 8x^4 + 8x^3 - 53x^2 + 78x - 36	\( 2^{12}\cdot 3^{8}\cdot 5^{7} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.2152350613963.1	x^10 - 4x^9 + 3x^8 + 3x^7 + 4x^6 - 10x^5 + 31x^4 - 25x^3 + 18x^2 - 5x + 1	\( -\,11^{4}\cdot 43^{5} \)	$A_5\times C_2$ (as 10T11)	Trivial
10.0.2302632603648.1	x^10 - x^9 - x^8 + 16x^7 - 14x^6 - 12x^5 + 138x^4 - 240x^3 + 345x^2 - 231x + 147	\( -\,2^{12}\cdot 3^{9}\cdot 13^{4} \)	$A_5\times C_2$ (as 10T11)	Trivial