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 3564)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.12075625.1	x^8 - x^7 + 2x^4 - 2x^3 + 2x^2 - 2x + 1	\( 5^{4}\cdot 139^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.38340864.1	x^8 + 4x^6 - 4x^5 + 6x^4 - 8x^3 + 8x^2 - 4x + 4	\( 2^{8}\cdot 3^{4}\cdot 43^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.43454464.1	x^8 - 2x^7 + 5x^6 - 6x^5 + 9x^4 - 10x^3 + 8x^2 - 4x + 1	\( 2^{12}\cdot 103^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.45373696.1	x^8 - 2x^7 - x^6 + 4x^5 + 2x^4 - 4x^3 - 3x^2 + 2x + 2	\( 2^{8}\cdot 421^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.48664576.1	x^8 - 2x^7 - 2x^4 + 8x^3 - 8x + 4	\( 2^{12}\cdot 109^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.53275401.1	x^8 - 3x^7 + 6x^6 - 11x^5 + 11x^4 - 9x^3 + 10x^2 - 5x + 1	\( 3^{4}\cdot 811^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.57760000.3	x^8 + 4x^6 - 6x^5 + 7x^4 - 12x^3 + 10x^2 - 4x + 1	\( 2^{8}\cdot 5^{4}\cdot 19^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.60964864.1	x^8 - 2x^7 + 4x^4 - 4x^3 + 2	\( 2^{14}\cdot 61^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.61449921.1	x^8 - x^7 - 4x^6 + 4x^5 + 8x^4 - 8x^3 - 7x^2 + 6x + 4	\( 3^{4}\cdot 13^{2}\cdot 67^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.62410000.1	x^8 - x^7 + x^6 + 2x^5 + 4x^4 + 2x^3 + 3x^2 + 3x + 1	\( 2^{4}\cdot 5^{4}\cdot 79^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.74926336.1	x^8 - 2x^7 + 4x^5 - 3x^4 - 6x^3 + 3x^2 + 6x + 2	\( 2^{8}\cdot 541^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.93083904.2	x^8 - 2x^7 - 2x^6 + 4x^5 - 3x^4 + 2x^3 + 10x^2 - 4x + 1	\( 2^{8}\cdot 3^{4}\cdot 67^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.97831881.1	x^8 - 2x^7 + x^6 - 2x^5 + 6x^4 - 13x^3 + 16x^2 - 7x + 1	\( 3^{4}\cdot 7^{2}\cdot 157^{2} \)	$A_4\wr C_2$ (as 8T42)	$[2]$
8.0.119771136.4	x^8 - 2x^7 - 4x^5 + 13x^4 - 16x^2 + 2x + 7	\( 2^{12}\cdot 3^{4}\cdot 19^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.123743376.1	x^8 + 4x^6 + 9x^4 - 6x^3 + 10x^2 - 6x + 1	\( 2^{4}\cdot 3^{6}\cdot 103^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.129413376.3	x^8 - 2x^6 - 2x^5 - 4x^3 + 2x^2 + 10x + 7	\( 2^{8}\cdot 3^{4}\cdot 79^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.130028409.2	x^8 - x^7 - 7x^6 + 4x^5 + 17x^4 - 2x^3 - 13x^2 + 4	\( 3^{4}\cdot 7^{2}\cdot 181^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.153760000.2	x^8 + 2x^6 - 4x^5 - x^4 - 4x^3 + 12x^2 - 6x + 1	\( 2^{8}\cdot 5^{4}\cdot 31^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.154157056.1	x^8 - 2x^7 + 8x^4 - 12x^3 + 4x^2 + 2	\( 2^{14}\cdot 97^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.155825289.1	x^8 - 2x^7 + 5x^6 - 9x^5 + 14x^4 - 9x^3 + 17x^2 - 2x + 4	\( 3^{4}\cdot 19^{2}\cdot 73^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.171714816.10	x^8 - 2x^7 + 2x^6 - 6x^5 + 3x^4 + 8x^3 - 2x^2 - 6x + 3	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 13^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.174556944.1	x^8 - 3x^7 + 6x^6 - 3x^5 - 4x^4 + 9x^3 - 3x + 1	\( 2^{4}\cdot 3^{4}\cdot 367^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.177209344.3	x^8 - 4x^6 - 4x^5 + 2x^4 + 8x^3 + 12x^2 + 8x + 2	\( 2^{20}\cdot 13^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.186267904.1	x^8 - 4x^7 + 4x^6 + 5x^4 - 10x^3 - x^2 + 2x + 5	\( 2^{8}\cdot 853^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.192876544.2	x^8 + 2x^6 - 2x^5 + x^4 - 2x^3 + 3x^2 - 2x + 1	\( 2^{12}\cdot 7^{2}\cdot 31^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.196897024.1	x^8 - 5x^6 - 2x^5 + 12x^4 + 2x^3 - 11x^2 + 4	\( 2^{8}\cdot 877^{2} \)	$A_4\wr C_2$ (as 8T42)	$[2]$
8.0.203689984.5	x^8 - 2x^7 + 3x^6 - 2x^5 + 6x^4 - 6x^3 + 5x^2 - 2x + 1	\( 2^{12}\cdot 223^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.216825625.2	x^8 - x^7 + 3x^6 - 6x^5 + 7x^4 - 6x^3 + 11x^2 - 2x + 4	\( 5^{4}\cdot 19^{2}\cdot 31^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.242705241.1	x^8 + 4x^6 - 6x^5 + 3x^4 - 12x^3 + x^2 + 12x + 4	\( 3^{6}\cdot 577^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.247212729.1	x^8 - 3x^7 + 9x^6 - 20x^5 + 26x^4 - 27x^3 + 22x^2 - 8x + 1	\( 3^{4}\cdot 1747^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.260112384.9	x^8 + 4x^6 - 4x^5 + 4x^4 - 8x^3 + 16x^2 - 12x + 3	\( 2^{16}\cdot 3^{4}\cdot 7^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.283855104.1	x^8 - 2x^7 - 2x^6 + 2x^5 + 11x^4 - 4x^3 - 20x^2 + 4x + 13	\( 2^{8}\cdot 3^{8}\cdot 13^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.304537401.1	x^8 - x^7 - 4x^5 - 2x^4 + 24x^3 - 18x + 9	\( 3^{4}\cdot 7^{2}\cdot 277^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.327610000.1	x^8 - 3x^7 + 9x^6 - 16x^5 + 28x^4 - 30x^3 + 28x^2 - 12x + 4	\( 2^{4}\cdot 5^{4}\cdot 181^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.336098889.3	x^8 - 2x^7 + 2x^6 + x^5 - 5x^4 + 8x^3 - x^2 - 10x + 7	\( 3^{6}\cdot 7^{2}\cdot 97^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.338412816.1	x^8 - x^7 + 5x^6 + 16x^4 + 8x^3 + 21x^2 + 7x + 7	\( 2^{4}\cdot 3^{4}\cdot 7^{2}\cdot 73^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.344882041.1	x^8 - x^7 + x^6 - 3x^5 - 4x^4 + 3x^3 + 10x^2 + 7x + 2	\( 7^{4}\cdot 379^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.349428249.2	x^8 - x^7 - 4x^6 + 6x^5 + 6x^4 - 14x^3 - 8x^2 + 12x + 9	\( 3^{4}\cdot 31^{2}\cdot 67^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.366799104.7	x^8 + 6x^6 - 6x^5 + 11x^4 - 24x^3 + 6x^2 + 6x + 1	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 19^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.366799104.8	x^8 - 2x^7 + 4x^6 + 6x^5 - 16x^4 + 4x^3 + 12x^2 - 12x + 4	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 19^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.381069441.1	x^8 - 2x^7 + x^6 + 4x^5 - 5x^4 + x^3 + 16x^2 - 8x + 1	\( 3^{8}\cdot 241^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.384591321.1	x^8 - x^7 + x^6 - 10x^5 + 21x^4 - 26x^3 + 22x^2 - 8x + 1	\( 3^{4}\cdot 2179^{2} \)	$A_4\wr C_2$ (as 8T42)	$[2]$
8.0.400280049.2	x^8 - 3x^7 - 2x^5 + 12x^4 + 6x^3 - 8x^2 + 3	\( 3^{8}\cdot 13^{2}\cdot 19^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.400640256.3	x^8 - 6x^6 - 2x^5 + 11x^4 + 12x^3 + 10x^2 + 4x + 1	\( 2^{8}\cdot 3^{4}\cdot 139^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.416649744.1	x^8 - 3x^7 + 5x^5 + 6x^4 - 15x^3 - 2x^2 + 9x + 3	\( 2^{4}\cdot 3^{12}\cdot 7^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.434847609.2	x^8 - 2x^7 - 2x^6 + 6x^5 - x^4 + 4x^3 + 21x^2 - 9x + 1	\( 3^{4}\cdot 7^{2}\cdot 331^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.454201344.2	x^8 - 2x^7 - 4x^6 + 14x^5 - 4x^4 - 22x^3 + 20x^2 - 6x + 7	\( 2^{12}\cdot 3^{4}\cdot 37^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.465178624.4	x^8 - 2x^6 - 2x^5 + 3x^4 + 2x^3 + x^2 - 4x + 2	\( 2^{12}\cdot 337^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.471628089.1	x^8 - 3x^7 + x^6 + 8x^5 - 13x^4 - 8x^3 + 39x^2 - 44x + 28	\( 3^{4}\cdot 19^{2}\cdot 127^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial
8.0.472801536.1	x^8 - 2x^6 - 6x^5 + 3x^4 + 24x^3 + 52x^2 + 48x + 19	\( 2^{8}\cdot 3^{4}\cdot 151^{2} \)	$A_4\wr C_2$ (as 8T42)	Trivial