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 125)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.20912329.1	x^8 - x^7 + 2x^6 - 3x^5 + 2x^4 - x^3 + 3x^2 - 3x + 1	\( 17^{2}\cdot 269^{2} \)	$A_8$ (as 8T49)	Trivial
8.0.34904464.1	x^8 - 3x^7 + 3x^6 - x^5 + 2x^4 - 3x^3 + x^2 + x + 1	\( 2^{4}\cdot 7^{2}\cdot 211^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.144889369.1	x^8 - 2x^7 + 3x^5 - 5x^4 + 2x^3 + 2x^2 - x + 1	\( 12037^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.164326761.1	x^8 - x^7 - 2x^6 + x^5 - 3x^4 + 6x^2 + 3x - 1	\( 3^{2}\cdot 4273^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.229583104.1	x^8 - 2x^7 + x^6 - 2x^5 + 4x^3 - 2x^2 + 4x - 3	\( 2^{8}\cdot 947^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.405780736.1	x^8 - 2x^7 - 5x^6 + 10x^5 + 6x^4 - 14x^3 + 2x^2 + 2x - 1	\( 2^{8}\cdot 1259^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.797497600.1	x^8 - 4x^6 - 4x^5 + 8x^4 + 8x^3 - 2x^2 - 10x + 2	\( 2^{8}\cdot 5^{2}\cdot 353^{2} \)	$A_8$ (as 8T49)	Trivial
8.0.2916000000.11	x^8 - 2x^7 + 6x^6 - 12x^5 + 30x^4 - 38x^3 + 36x^2 - 18x + 6	\( 2^{8}\cdot 3^{6}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.0.10000000000.1	x^8 - 3x^7 - 2x^6 + 9x^5 + 10x^4 - 27x^3 - 4x^2 + 19x + 7	\( 2^{10}\cdot 5^{10} \)	$A_8$ (as 8T49)	Trivial
8.8.46664208361.1	x^8 - 2x^7 - 11x^6 + 6x^5 + 30x^4 - 2x^3 - 22x^2 + x + 3	\( 17^{2}\cdot 97^{2}\cdot 131^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.82944000000.3	x^8 - 8x^6 - 8x^5 - 28x^3 - 60x^2 - 36x - 6	\( 2^{16}\cdot 3^{4}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.8.137172455424.1	x^8 - 2x^7 - 10x^6 + 16x^5 + 32x^4 - 36x^3 - 32x^2 + 24x + 4	\( 2^{12}\cdot 3^{4}\cdot 643^{2} \)	$A_8$ (as 8T49)	Trivial
8.0.186624000000.6	x^8 - 2x^7 + 5x^6 - 4x^5 + 20x^4 + 4x^3 + 22x^2 + 40x + 14	\( 2^{14}\cdot 3^{6}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.4.440301256704.1	x^8 - 4x^6 - 8x^5 + 8x^3 + 8x^2 - 2	\( 2^{26}\cdot 3^{8} \)	$A_8$ (as 8T49)	Trivial
8.0.576650390625.1	x^8 - x^7 + 2x^6 - 3x^5 + 15x^4 - 21x^3 + 6x^2 + 3x + 3	\( 3^{10}\cdot 5^{10} \)	$A_8$ (as 8T49)	Trivial
8.0.640000000000.1	x^8 - 4x^7 + 12x^6 - 12x^5 + 10x^4 + 60x^3 + 60x^2 + 20x + 5	\( 2^{16}\cdot 5^{10} \)	$A_8$ (as 8T49)	$[2]$
8.0.656100000000.1	x^8 - 2x^7 + 5x^6 - 4x^5 + 5x^4 - 8x^3 + 36x^2 + 27	\( 2^{8}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	Trivial
8.0.1476225000000.1	x^8 - x^7 + x^6 - x^5 + 10x^4 - 10x^3 + 10x^2 - 10x + 10	\( 2^{6}\cdot 3^{10}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[2]$
8.4.1679616000000.1	x^8 - 2x^7 - 4x^6 - 12x^5 + 120x^3 + 270	\( 2^{14}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.0.1679616000000.16	x^8 - 2x^7 + 11x^6 - 12x^5 - 12x^3 + 14x^2 + 8x + 4	\( 2^{14}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.0.3572100000000.1	x^8 - 4x^7 + 22x^6 - 32x^5 + 125x^4 - 86x^3 + 364x^2 - 112x + 532	\( 2^{8}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.4.5143824000000.1	x^8 - 3x^7 + 15x^6 - 15x^5 - 45x^4 + 81x^3 - 153x^2 - 135x + 270	\( 2^{10}\cdot 3^{8}\cdot 5^{6}\cdot 7^{2} \)	$A_8$ (as 8T49)	Trivial
8.4.5308416000000.54	x^8 - 4x^6 - 8x^5 - 60x^4 + 128x^3 + 160x^2 - 192x + 56	\( 2^{22}\cdot 3^{4}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial
8.0.5904900000000.1	x^8 - 8x^6 - 2x^5 + 30x^4 + 10x^3 - 50x^2 - 30x + 55	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[2]$
8.4.6718464000000.6	x^8 - 4x^7 + 10x^6 - 12x^5 + 15x^4 + 48x^3 - 82x^2 - 20x - 1	\( 2^{16}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	$[2]$
8.0.6718464000000.16	x^8 - 4x^7 + 10x^6 - 15x^4 - 24x^3 + 86x^2 - 80x + 35	\( 2^{16}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.4.10497600000000.1	x^8 - 32x^5 + 96x^3 - 320x^2 + 48	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.0.10497600000000.1	x^8 - 2x^7 - 2x^6 + 6x^5 + 24x^3 + 32x^2 - 88x + 194	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	Trivial
8.0.10497600000000.2	x^8 - 4x^7 + 22x^6 - 52x^5 + 145x^4 - 112x^3 + 208x^2 - 184x + 244	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.4.11943936000000.14	x^8 - 4x^7 + 4x^6 + 10x^4 - 40x^2 + 20	\( 2^{20}\cdot 3^{6}\cdot 5^{6} \)	$A_8$ (as 8T49)	$[2, 2]$
8.0.15850845241344.1	x^8 - 8x^5 - 12x^4 + 40x^2 + 48x + 18	\( 2^{28}\cdot 3^{10} \)	$A_8$ (as 8T49)	$[4]$
8.4.16402500000000.1	x^8 - 2x^7 + 56x^5 - 70x^4 + 42x^3 - 89x^2 + 40x - 3	\( 2^{8}\cdot 3^{8}\cdot 5^{10} \)	$A_8$ (as 8T49)	Trivial
8.0.26214400000000.1	x^8 - 8x^3 + 10	\( 2^{26}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[2]$
8.4.40960000000000.1	x^8 - 4x^7 - 8x^6 + 28x^5 - 40x^4 + 60x^3 - 40x^2 + 20x + 5	\( 2^{22}\cdot 5^{10} \)	$A_8$ (as 8T49)	Trivial
8.0.41990400000000.1	x^8 - 2x^7 + 23x^6 + 4x^5 + 145x^4 + 158x^3 + 579x^2 + 444x + 762	\( 2^{14}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.0.63734036889600.1	x^8 + 24x^6 - 20x^5 + 192x^4 - 336x^3 + 672x^2 - 1404x + 1539	\( 2^{16}\cdot 3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2} \)	$A_8$ (as 8T49)	$[2]$
8.0.65610000000000.1	x^8 - 4x^7 + 7x^6 + 8x^5 - 5x^4 + 122x^3 + 57x^2 - 126x + 66	\( 2^{10}\cdot 3^{8}\cdot 5^{10} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.0.68797071360000.2	x^8 - 48x^3 + 360	\( 2^{24}\cdot 3^{8}\cdot 5^{4} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.0.74649600000000.1	x^8 + 10x^6 - 44x^5 + 90x^4 - 128x^3 + 210x^2 - 180x + 57	\( 2^{18}\cdot 3^{6}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[4]$ (GRH)
8.4.113820562243584.1	x^8 - x^7 + 8x^6 - 76x^5 - 38x^4 + 766x^3 - 824x^2 - 496x + 704	\( 2^{14}\cdot 3^{10}\cdot 7^{6} \)	$A_8$ (as 8T49)	$[2]$
8.4.115201238777856.1	x^8 - 22x^6 + 77x^4 - 176x^3 + 308x^2 + 880x - 1452	\( 2^{14}\cdot 3^{4}\cdot 7^{2}\cdot 11^{6} \)	$A_8$ (as 8T49)	Trivial
8.0.298598400000000.1	x^8 - 4x^7 + 32x^6 - 52x^5 + 40x^4 + 40x^3 + 80x^2 + 40x + 10	\( 2^{20}\cdot 3^{6}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.4.429981696000000.5	x^8 - 24x^6 - 72x^5 + 90x^4 + 480x^3 + 440x^2 - 1320x - 135	\( 2^{22}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.0.1184787066781696.7	x^8 - 4x^7 + 4802	\( 2^{22}\cdot 7^{10} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.0.1547476985184256.7	x^8 - 128x + 224	\( 2^{28}\cdot 7^{8} \)	$A_8$ (as 8T49)	$[8]$
8.4.1719926784000000.21	x^8 - 32x^5 + 240x^3 - 320x^2 + 120	\( 2^{24}\cdot 3^{8}\cdot 5^{6} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.0.2687385600000000.1	x^8 - 32x^5 + 400x^2 + 900	\( 2^{20}\cdot 3^{8}\cdot 5^{8} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.0.4199040000000000.1	x^8 - 20x^5 + 120x^4 + 288x^3 + 1440x^2 + 45	\( 2^{16}\cdot 3^{8}\cdot 5^{10} \)	$A_8$ (as 8T49)	$[2]$ (GRH)
8.0.4592206902398976.1	x^8 - 4x^7 + 21x^6 + 98x^5 + 294x^4 + 448x^3 + 1680x^2 + 1588x + 494	\( 2^{12}\cdot 3^{4}\cdot 7^{12} \)	$A_8$ (as 8T49)	Trivial (GRH)
8.4.5898240000000000.1	x^8 - 80x^5 + 600x^3 - 2000x^2 + 750	\( 2^{26}\cdot 3^{2}\cdot 5^{10} \)	$A_8$ (as 8T49)	$[2]$ (GRH)