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 8052)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.55115776.1	x^8 + 2x^6 - 4x^5 + x^4 - 4x^3 + 4x^2 + 1	\( 2^{16}\cdot 29^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.81721600.1	x^8 - 2x^7 + 3x^6 - 2x^5 + x^4 + x^2 + 2x + 1	\( 2^{8}\cdot 5^{2}\cdot 113^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.118810000.1	x^8 - x^7 - 4x^6 + 4x^5 + 7x^4 - 8x^3 - 4x^2 + 5x - 1	\( 2^{4}\cdot 5^{4}\cdot 109^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.129413376.1	x^8 - 2x^7 + 5x^6 - 12x^5 + 18x^4 - 16x^3 + 10x^2 - 6x + 3	\( 2^{8}\cdot 3^{4}\cdot 79^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.144769024.1	x^8 - 3x^4 - 2x^2 - 4x - 1	\( 2^{16}\cdot 47^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.156725361.2	x^8 - 3x^7 - 2x^6 + 11x^5 - 14x^3 + 11x^2 - 4x + 1	\( 3^{4}\cdot 13^{2}\cdot 107^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	$[2]$
8.0.156950784.1	x^8 - 4x^7 + 11x^6 - 16x^5 + 19x^4 - 14x^3 + 5x^2 - 2x + 1	\( 2^{8}\cdot 3^{6}\cdot 29^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.161798400.1	x^8 - 2x^7 + 3x^6 - 2x^4 + 6x^3 - 2x + 1	\( 2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 53^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.215737344.1	x^8 - 2x^7 + 2x^6 - 4x^5 + 8x^4 - 2x^3 + 8x^2 - 4x + 1	\( 2^{10}\cdot 3^{6}\cdot 17^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.231800625.1	x^8 - 2x^7 + 5x^6 - 5x^5 + 6x^4 - 3x^3 + x^2 + 2x + 4	\( 3^{2}\cdot 5^{4}\cdot 7^{2}\cdot 29^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.234916929.2	x^8 - 2x^7 + 8x^6 - 13x^5 + 20x^4 - 22x^3 + 11x^2 - 3x + 1	\( 3^{4}\cdot 13^{2}\cdot 131^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.235469025.1	x^8 - 5x^6 + 5x^4 - 3x^3 + 8x^2 + 6x + 1	\( 3^{4}\cdot 5^{2}\cdot 11^{2}\cdot 31^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.237899776.1	x^8 - 2x^7 - 4x^5 + 9x^4 + 2x^3 - 2x^2 - 4x + 4	\( 2^{12}\cdot 241^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.242580625.1	x^8 - 2x^7 - 2x^6 + 3x^4 + 8x^3 + 5x^2 - x - 1	\( 5^{4}\cdot 7^{2}\cdot 89^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.266342400.1	x^8 + 2x^6 - 2x^5 + 2x^2 + 4x + 2	\( 2^{12}\cdot 3^{2}\cdot 5^{2}\cdot 17^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.290361600.1	x^8 - x^6 + 7x^4 - 6x^3 + x^2 + 2x + 1	\( 2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 71^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.293642496.2	x^8 - 2x^7 + 3x^6 - 10x^5 + 22x^4 - 30x^3 + 26x^2 - 16x + 7	\( 2^{8}\cdot 3^{4}\cdot 7^{2}\cdot 17^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.298598400.1	x^8 - 2x^7 + 2x^6 - 8x^5 + 10x^4 - 4x^3 + 16x^2 - 8x + 2	\( 2^{14}\cdot 3^{6}\cdot 5^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.309760000.3	x^8 - 4x^7 + 6x^6 - 2x^5 - 6x^4 + 8x^3 - 7x^2 + 2x + 1	\( 2^{12}\cdot 5^{4}\cdot 11^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.330366976.1	x^8 - 4x^6 + 9x^4 - 8x^3 - 2x^2 + 4x - 1	\( 2^{16}\cdot 71^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.382124304.1	x^8 - x^7 + 3x^6 - 7x^5 + 4x^4 - 9x^3 + 9x^2 + 3	\( 2^{4}\cdot 3^{6}\cdot 181^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.383885649.1	x^8 - 2x^7 + 6x^5 - 4x^4 - 4x^3 + 4x^2 + 3x + 3	\( 3^{4}\cdot 7^{2}\cdot 311^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.390615696.1	x^8 - 2x^7 - 2x^6 + 3x^5 + 6x^4 + 3x + 3	\( 2^{4}\cdot 3^{8}\cdot 61^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.396328464.1	x^8 - x^7 - 4x^6 + 4x^5 - x^3 + 10x^2 - 6x + 1	\( 2^{4}\cdot 3^{4}\cdot 7^{2}\cdot 79^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.416160000.1	x^8 - 4x^6 - 6x^5 + 7x^4 + 12x^3 - 2x^2 - 4x + 1	\( 2^{8}\cdot 3^{2}\cdot 5^{4}\cdot 17^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.437855625.1	x^8 - 3x^7 + 7x^6 - 14x^5 + 15x^4 - 14x^3 + 8x^2 - 1	\( 3^{6}\cdot 5^{4}\cdot 31^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.504631296.10	x^8 - 2x^7 + 8x^6 - 14x^5 + 22x^4 - 10x^3 - 4x^2 + 2x + 1	\( 2^{12}\cdot 3^{6}\cdot 13^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.515290000.1	x^8 - x^7 - 5x^6 + 8x^4 + 10x^3 - 8x - 4	\( 2^{4}\cdot 5^{4}\cdot 227^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.517653504.1	x^8 - x^6 - x^4 - 6x^3 + 16x^2 - 12x + 4	\( 2^{10}\cdot 3^{4}\cdot 79^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.524410000.1	x^8 - 2x^7 - x^6 - x^5 + 2x^4 + 5x^3 + 3x^2 + 3x + 1	\( 2^{4}\cdot 5^{4}\cdot 229^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.544195584.1	x^8 - 2x^7 + 7x^6 - 8x^5 + 16x^4 - 2x^3 + x^2 + 16x + 7	\( 2^{10}\cdot 3^{12} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.546297129.1	x^8 - 3x^7 + 5x^6 - 7x^5 + 9x^4 - x^3 + 6x^2 + 5x + 1	\( 3^{4}\cdot 7^{4}\cdot 53^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.554696704.2	x^8 - 4x^7 + 8x^6 - 4x^5 - 8x^4 + 12x^3 + 4x^2 - 4x - 1	\( 2^{20}\cdot 23^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.559417104.1	x^8 - 3x^7 + 3x^6 + x^5 - 6x^4 + 3x^3 + 7x^2 - 12x + 9	\( 2^{4}\cdot 3^{8}\cdot 73^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.571210000.1	x^8 - 2x^7 + 11x^5 - 9x^4 - 12x^3 + 14x^2 - 4	\( 2^{4}\cdot 5^{4}\cdot 239^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.571401216.1	x^8 - 3x^6 - 2x^5 + x^4 + 7x^2 + 2x - 2	\( 2^{10}\cdot 3^{4}\cdot 83^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.581774400.1	x^8 - x^7 + 8x^6 - 2x^5 + 21x^4 + 2x^3 + 22x^2 + 3x + 7	\( 2^{6}\cdot 3^{4}\cdot 5^{2}\cdot 67^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.582160384.3	x^8 - 2x^7 - 4x^6 + 10x^5 + 7x^4 - 24x^3 - 2x^2 + 24x + 10	\( 2^{12}\cdot 13^{2}\cdot 29^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.586559961.1	x^8 - 3x^7 + 12x^6 - 31x^5 + 57x^4 - 84x^3 + 85x^2 - 48x + 12	\( 3^{8}\cdot 13^{2}\cdot 23^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	$[2]$
8.0.590490000.1	x^8 - x^7 - 2x^6 - 4x^5 + 13x^4 + 8x^3 - 20x^2 - 7x + 13	\( 2^{4}\cdot 3^{10}\cdot 5^{4} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.597704704.1	x^8 - 4x^5 - 5x^4 + 2x^2 + 4x - 2	\( 2^{14}\cdot 191^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.605061604.1	x^8 - 4x^7 + 8x^6 - 9x^5 + 3x^4 + 4x^3 - 4x^2 - 2x + 4	\( 2^{2}\cdot 7^{4}\cdot 251^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.610090000.1	x^8 - x^7 + x^6 + 3x^5 - 5x^4 - 4x^3 - 10x^2 - 8x + 4	\( 2^{4}\cdot 5^{4}\cdot 13^{2}\cdot 19^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.616628224.1	x^8 - 4x^7 + 8x^6 - 8x^5 - 3x^4 + 16x^3 - 18x^2 + 8x - 1	\( 2^{16}\cdot 97^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.4.642318336.1	x^8 - 4x^6 - 4x^5 + 6x^4 + 8x^3 - 4x - 2	\( 2^{16}\cdot 3^{4}\cdot 11^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.642318336.4	x^8 + x^4 - 4x^3 + 8x^2 - 8x + 11	\( 2^{16}\cdot 3^{4}\cdot 11^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.643941376.1	x^8 - 4x^7 + x^6 + 6x^5 + 5x^4 - 5x^2 - 2x + 2	\( 2^{10}\cdot 13^{2}\cdot 61^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.658846224.1	x^8 - x^7 - 4x^6 + 6x^5 + 9x^4 - 14x^3 - 14x^2 + 12x + 12	\( 2^{4}\cdot 3^{4}\cdot 23^{2}\cdot 31^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.669360384.1	x^8 - 4x^7 + 11x^6 - 16x^5 + 17x^4 - 12x^3 + 8x^2 - 6x + 2	\( 2^{8}\cdot 3^{2}\cdot 7^{4}\cdot 11^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial
8.0.671846400.2	x^8 - 2x^7 + 8x^6 - 10x^5 + 23x^4 - 20x^3 + 26x^2 - 16x + 10	\( 2^{12}\cdot 3^{8}\cdot 5^{2} \)	$(A_4\wr C_2):C_2$ (as 8T45)	Trivial