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 12055)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.24255625.1	x^8 - 2x^7 + 4x^6 - 6x^5 + 6x^4 - 4x^3 + 4x^2 - 3x + 1	\( 5^{4}\cdot 197^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.40347904.2	x^8 - 4x^7 + 5x^6 - x^4 - 4x^3 + x^2 + 2x + 1	\( 2^{8}\cdot 397^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.58247424.1	x^8 - 2x^7 + 6x^6 - 4x^5 + 10x^4 - 6x^3 + 5x^2 - 4x + 1	\( 2^{8}\cdot 3^{4}\cdot 53^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.79227801.1	x^8 - 2x^7 + 4x^6 - 4x^5 + 4x^4 - 6x^3 + 10x^2 - 9x + 3	\( 3^{4}\cdot 23^{2}\cdot 43^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.121176064.1	x^8 + 4x^6 - 4x^5 + 2x^4 - 4x^3 + 4x^2 - 4x + 2	\( 2^{16}\cdot 43^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.122589184.1	x^8 - 2x^7 + 3x^6 - 2x^4 - 2x^3 + 6x^2 - 4x + 1	\( 2^{12}\cdot 173^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.122943744.2	x^8 - 4x^7 + 8x^6 - 6x^5 - 5x^4 + 14x^3 - 6x^2 - 8x + 7	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.125955729.1	x^8 + 5x^6 - x^5 + 6x^4 - 7x^3 + 3x^2 - 4x + 4	\( 3^{4}\cdot 29^{2}\cdot 43^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.131056704.2	x^8 - 3x^7 + 4x^6 - 6x^5 + 3x^4 + 4x^2 + 3x + 1	\( 2^{6}\cdot 3^{6}\cdot 53^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.142850304.1	x^8 - 4x^7 + 7x^6 - 6x^5 + 8x^4 - 16x^3 + 24x^2 - 18x + 7	\( 2^{8}\cdot 3^{4}\cdot 83^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.147671104.1	x^8 - x^7 + 3x^6 - 2x^5 + 6x^4 - 5x^3 + 7x^2 - 2x + 1	\( 2^{6}\cdot 7^{4}\cdot 31^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.162613504.2	x^8 - 2x^7 - 2x^6 + 2x^5 + 10x^4 - 6x^3 - 11x^2 + 4x + 5	\( 2^{8}\cdot 797^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.164249856.1	x^8 - 2x^7 + 2x^6 + 2x^5 - 10x^4 + 2x^3 + 11x^2 - 6x + 1	\( 2^{8}\cdot 3^{4}\cdot 89^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.175509504.1	x^8 - 2x^7 + 6x^6 - 12x^5 + 11x^4 - 4x^3 + 4x^2 - 6x + 3	\( 2^{12}\cdot 3^{4}\cdot 23^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.176703849.1	x^8 - x^7 - 6x^5 + 3x^4 + 8x^3 + 20x^2 + 17x + 7	\( 3^{4}\cdot 7^{2}\cdot 211^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.203233536.1	x^8 - 2x^7 + x^6 + 6x^5 - 9x^4 - 12x^3 + 9x^2 + 12x + 3	\( 2^{8}\cdot 3^{8}\cdot 11^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.208138329.1	x^8 - x^7 + 2x^6 - 5x^5 + 10x^4 - 6x^3 + 9x^2 - 18x + 9	\( 3^{4}\cdot 7^{2}\cdot 229^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.213160000.2	x^8 - x^7 - 4x^5 + 3x^4 + 4x^3 + 2x^2 - 8x + 4	\( 2^{6}\cdot 5^{4}\cdot 73^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.245862400.1	x^8 - 2x^6 - 2x^5 + 7x^4 + 16x^3 + 16x^2 + 8x + 2	\( 2^{12}\cdot 5^{2}\cdot 7^{4} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.249892864.1	x^8 - 2x^7 - 4x^6 + 8x^5 + 10x^4 - 18x^3 - 6x^2 + 8x + 5	\( 2^{12}\cdot 13^{2}\cdot 19^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.4.258405625.1	x^8 - 3x^7 + 4x^6 - 5x^5 + x^4 + x^3 + 8x^2 - 7x + 1	\( 5^{4}\cdot 643^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.264647824.1	x^8 + 3x^6 - x^5 + 5x^4 - 5x^3 + 7x^2 - 4x + 2	\( 2^{4}\cdot 7^{4}\cdot 83^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.264777984.1	x^8 - 4x^6 - 2x^5 + 6x^4 - 2x^3 + 3x^2 + 4x + 1	\( 2^{8}\cdot 3^{4}\cdot 113^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.267420609.1	x^8 - 3x^7 + 11x^6 - 19x^5 + 32x^4 - 34x^3 + 29x^2 - 20x + 7	\( 3^{4}\cdot 23^{2}\cdot 79^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.270964521.1	x^8 - x^7 + x^6 + 3x^5 - 4x^4 + 11x^3 + 21x^2 + 6x + 1	\( 3^{4}\cdot 31^{2}\cdot 59^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.279023616.1	x^8 - 2x^7 + 2x^6 - 2x^5 + 9x^4 - 6x^3 + 4x + 1	\( 2^{12}\cdot 3^{4}\cdot 29^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.293642496.1	x^8 - 2x^7 + 8x^5 - 13x^4 - 4x^3 + 18x^2 - 8x + 1	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 17^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.310217769.1	x^8 - x^7 + 9x^6 - 8x^5 + 25x^4 - 18x^3 + 20x^2 - 8x + 1	\( 3^{4}\cdot 19^{2}\cdot 103^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	$[2]$
8.0.313714944.2	x^8 - 2x^7 - 4x^6 + 10x^5 + 13x^4 - 10x^3 - 16x^2 + 2x + 7	\( 2^{8}\cdot 3^{6}\cdot 41^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.316270656.1	x^8 - 3x^7 + 7x^6 - 13x^5 + 15x^4 - 14x^3 + 14x^2 - 4x + 4	\( 2^{6}\cdot 3^{4}\cdot 13^{2}\cdot 19^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.333281536.1	x^8 - 5x^6 - 2x^5 + 8x^4 + 8x^3 - 6x^2 - 8x + 5	\( 2^{8}\cdot 7^{2}\cdot 163^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.4.333975625.1	x^8 - x^7 - 3x^6 + 8x^5 - 3x^4 - 8x^3 + 14x^2 - 8x + 1	\( 5^{4}\cdot 17^{2}\cdot 43^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.345067776.3	x^8 - 2x^7 - x^6 - 2x^5 - 2x^4 + 14x^3 + 20x^2 + 8x + 1	\( 2^{8}\cdot 3^{6}\cdot 43^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.348046336.1	x^8 - 2x^7 + x^6 - 6x^5 + 4x^4 + 2x^3 + 10x^2 + 4x + 2	\( 2^{10}\cdot 11^{2}\cdot 53^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.349428249.1	x^8 - 2x^7 + 9x^6 - 11x^5 + 24x^4 - 23x^3 + 23x^2 - 12x + 4	\( 3^{4}\cdot 31^{2}\cdot 67^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.353440000.1	x^8 + 7x^6 - 2x^5 + 13x^4 - 12x^3 + 3x^2 - 2x + 1	\( 2^{8}\cdot 5^{4}\cdot 47^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.355850496.1	x^8 - 2x^7 + 8x^6 - 6x^5 + 15x^4 - 10x^3 + 10x^2 - 6x + 3	\( 2^{8}\cdot 3^{4}\cdot 131^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.359936784.1	x^8 - x^7 - 5x^6 + 6x^5 + 4x^4 - 8x^3 + 12x^2 - 12x + 4	\( 2^{4}\cdot 3^{4}\cdot 17^{2}\cdot 31^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.363741184.2	x^8 - 2x^7 + 8x^5 - 9x^4 - 2x^3 + 12x^2 - 8x + 2	\( 2^{14}\cdot 149^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.377913600.1	x^8 - 4x^7 + x^6 + 10x^5 + 2x^4 - 26x^3 + 10x^2 + 8x + 1	\( 2^{8}\cdot 3^{10}\cdot 5^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.389193984.1	x^8 - 4x^7 + 7x^6 - 6x^5 + 4x^4 - 8x^3 + 6x + 7	\( 2^{8}\cdot 3^{4}\cdot 137^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.391683681.1	x^8 - x^7 - 5x^6 + 5x^5 - 2x^4 - 4x^3 + 31x^2 - 10x + 1	\( 3^{6}\cdot 733^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.407514969.1	x^8 - 3x^7 + 7x^6 - 16x^5 + 25x^4 - 32x^3 + 34x^2 - 24x + 9	\( 3^{4}\cdot 2243^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	$[2]$
8.0.416813056.1	x^8 - 2x^7 - 4x^6 + 6x^5 + 4x^4 + 2x^2 - 4x + 2	\( 2^{12}\cdot 11^{2}\cdot 29^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.424030464.2	x^8 - 2x^7 + 14x^4 - 40x^3 + 52x^2 - 36x + 12	\( 2^{8}\cdot 3^{4}\cdot 11^{2}\cdot 13^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	$[2]$
8.0.433347489.1	x^8 - 3x^7 + 6x^6 - 13x^5 + 27x^4 - 45x^3 + 58x^2 - 51x + 21	\( 3^{8}\cdot 257^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	$[2]$
8.0.434847609.1	x^8 - 2x^7 + 3x^6 - 8x^5 + 6x^4 - 5x^3 + 8x^2 + 3x + 1	\( 3^{4}\cdot 7^{2}\cdot 331^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.457617664.2	x^8 - 2x^7 - 2x^6 + 8x^5 + 3x^4 - 24x^3 + 30x^2 - 10x + 1	\( 2^{8}\cdot 7^{2}\cdot 191^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.461046784.1	x^8 - 2x^7 - 2x^5 + 10x^4 - 4x^3 + 2x^2 - 8x + 8	\( 2^{10}\cdot 11^{2}\cdot 61^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial
8.0.471975625.2	x^8 + x^6 - 6x^5 - 2x^4 + 2x^3 + 11x^2 + 8x + 4	\( 5^{4}\cdot 11^{2}\cdot 79^{2} \)	$V_4^2:(S_3\times C_2)$ (as 8T41)	Trivial