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 67382)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.167186432.1	x^8 - 2x^7 + 2x^6 + x^4 + 2x^2 + 2x + 1	\( 2^{12}\cdot 7^{4}\cdot 17 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.324538368.1	x^8 - 2x^7 + 6x^5 - x^4 - 6x^3 + 7	\( 2^{12}\cdot 3\cdot 7^{4}\cdot 11 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.374863125.1	x^8 - 4x^7 + 3x^6 + 5x^5 - 5x^4 - 3x^3 + 5x^2 - 2x + 1	\( 3\cdot 5^{4}\cdot 7\cdot 13^{4} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.374863125.2	x^8 - x^7 + 2x^6 + x^5 + 8x^4 + 4x^3 + 8x^2 + 1	\( 3\cdot 5^{4}\cdot 7\cdot 13^{4} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.560566272.1	x^8 - 2x^7 + 8x^6 - 10x^5 + 16x^4 - 14x^3 + 8x^2 - 6x + 3	\( 2^{12}\cdot 3\cdot 7^{4}\cdot 19 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.668745728.1	x^8 - 2x^7 + 2x^6 + 2x^5 - 2x^3 + 2x^2 + 2x + 1	\( 2^{14}\cdot 7^{4}\cdot 17 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.717918208.1	x^8 - 4x^7 + 6x^6 - 4x^5 + 3x^4 - 4x^3 + 10x^2 - 8x + 9	\( 2^{12}\cdot 7^{4}\cdot 73 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.785427500.1	x^8 - x^6 + 7x^4 - 4x^2 + 11	\( 2^{2}\cdot 5^{4}\cdot 11\cdot 13^{4} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.785427500.2	x^8 - 2x^7 + 6x^6 - 6x^5 + 13x^4 - 2x^3 + 9x^2 + 4x + 1	\( 2^{2}\cdot 5^{4}\cdot 11\cdot 13^{4} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.786759680.1	x^8 + 4x^6 - 4x^5 + 2x^4 - 8x^3 + 4x^2 + 4x + 9	\( 2^{16}\cdot 5\cdot 7^{4} \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.786759680.2	x^8 - 8x^5 + 6x^4 + 8x^3 + 1	\( 2^{16}\cdot 5\cdot 7^{4} \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.875270144.1	x^8 - 4x^6 - 6x^5 + x^4 + 18x^3 + 18x^2 + 8x + 6	\( 2^{12}\cdot 7^{4}\cdot 89 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.886837248.1	x^8 - 2x^7 - 2x^6 + 9x^4 - 2x^2 - 2x + 1	\( 2^{12}\cdot 3^{9}\cdot 11 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.886837248.2	x^8 + 4x^6 - 8x^5 + 18x^4 - 8x^3 + 4x^2 + 1	\( 2^{12}\cdot 3^{9}\cdot 11 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1032622080.1	x^8 - 4x^7 + 6x^6 - 4x^5 + 5x^4 - 8x^3 - 4x^2 + 8x + 8	\( 2^{12}\cdot 3\cdot 5\cdot 7^{5} \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1032622080.2	x^8 - 2x^7 - 4x^6 + 6x^5 + 8x^4 - 14x^3 + 16x^2 - 6x + 3	\( 2^{12}\cdot 3\cdot 5\cdot 7^{5} \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1101828096.1	x^8 - 2x^7 + 2x^6 - 3x^4 + 2x^2 + 2x + 1	\( 2^{12}\cdot 3^{8}\cdot 41 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1298153472.1	x^8 - 2x^7 - 8x^5 + 12x^4 + 20x^2 - 12x + 14	\( 2^{14}\cdot 3\cdot 7^{4}\cdot 11 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1347325952.11	x^8 - 2x^7 + 6x^6 - 4x^5 + 5x^4 - 12x^3 + 22x^2 - 18x + 5	\( 2^{12}\cdot 7^{4}\cdot 137 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1583353856.3	x^8 - 2x^6 - 4x^5 - x^4 + 12x^3 + 10x^2 + 4x + 5	\( 2^{12}\cdot 7^{5}\cdot 23 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1583353856.4	x^8 - 2x^7 + 8x^6 - 18x^5 + 31x^4 - 46x^3 + 48x^2 - 28x + 7	\( 2^{12}\cdot 7^{5}\cdot 23 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1740705792.1	x^8 - 2x^7 + 6x^6 - 18x^5 + 31x^4 - 28x^3 + 16x^2 - 8x + 4	\( 2^{12}\cdot 3\cdot 7^{4}\cdot 59 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1746800640.1	x^8 - 4x^6 - 8x^5 + 18x^4 + 8x^3 - 4x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 5\cdot 13 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1802913125.2	x^8 - 2x^7 - x^5 + 5x^4 - 3x^3 + 9x^2 - 19x + 14	\( 5^{4}\cdot 13^{4}\cdot 101 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1802913125.3	x^8 - x^7 - 4x^6 + 10x^4 - 4x^2 + x + 1	\( 5^{4}\cdot 13^{4}\cdot 101 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1819381760.1	x^8 - 4x^7 + 6x^6 - 4x^5 + 9x^4 - 16x^3 + 8x + 4	\( 2^{12}\cdot 5\cdot 7^{4}\cdot 37 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1856465000.1	x^8 - 2x^7 - x^6 - x^5 + 6x^4 + x^3 - x^2 + 2x + 1	\( 2^{3}\cdot 5^{4}\cdot 13^{5} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1856465000.2	x^8 - 3x^7 + 6x^6 - 2x^5 + 2x^3 + 6x^2 + 3x + 1	\( 2^{3}\cdot 5^{4}\cdot 13^{5} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1856465000.3	x^8 - x^7 + 6x^6 - 2x^5 + 20x^4 + 6x^3 + 25x^2 + 12x + 4	\( 2^{3}\cdot 5^{4}\cdot 13^{5} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1856465000.4	x^8 + 4x^6 - 4x^5 + x^4 + 12x^3 - 7x^2 - 4x + 6	\( 2^{3}\cdot 5^{4}\cdot 13^{5} \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.1898057728.1	x^8 - 4x^7 + 12x^6 - 22x^5 + 33x^4 - 34x^3 + 30x^2 - 16x + 10	\( 2^{12}\cdot 7^{4}\cdot 193 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1976733696.1	x^8 - 2x^7 - 2x^6 + 10x^5 - 13x^4 - 4x^3 + 28x^2 - 24x + 8	\( 2^{12}\cdot 3\cdot 7^{4}\cdot 67 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.1988759552.1	x^8 + 4x^6 - 8x^5 + 2x^4 + 8x^3 + 4x^2 + 1	\( 2^{12}\cdot 13^{4}\cdot 17 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2055409664.1	x^8 + 2x^6 - 4x^5 - 3x^4 - 4x^3 + 4x^2 + 8x + 8	\( 2^{12}\cdot 7^{4}\cdot 11\cdot 19 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2134085632.1	x^8 - 4x^6 - 2x^5 + 13x^4 + 10x^3 + 12x^2 + 2x + 3	\( 2^{12}\cdot 7^{5}\cdot 31 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2134085632.2	x^8 - 4x^6 - 10x^5 + x^4 + 22x^3 + 28x^2 + 14x + 7	\( 2^{12}\cdot 7^{5}\cdot 31 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2149908480.1	x^8 - 2x^6 - 4x^5 + 6x^4 - 4x^3 + 22x^2 - 12x + 7	\( 2^{16}\cdot 3^{8}\cdot 5 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2149908480.2	x^8 + 2x^6 - 8x^5 + 6x^4 - 4x^3 + 16x^2 + 12x + 2	\( 2^{16}\cdot 3^{8}\cdot 5 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2242265088.1	x^8 - 2x^7 + 12x^5 - 12x^4 + 24x^2 - 24x + 22	\( 2^{14}\cdot 3\cdot 7^{4}\cdot 19 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.2291437568.8	x^8 - 2x^7 + 2x^6 - 4x^5 + 6x^4 - 24x^3 + 44x^2 - 24x + 4	\( 2^{12}\cdot 7^{4}\cdot 233 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2370113536.1	x^8 - 6x^6 - 4x^5 + x^4 + 12x^3 + 32x^2 + 16x + 4	\( 2^{12}\cdot 7^{4}\cdot 241 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2527465472.1	x^8 - 2x^7 + 8x^6 - 14x^5 + 24x^4 - 14x^3 + 16x^2 - 2x + 11	\( 2^{12}\cdot 7^{4}\cdot 257 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2606141440.1	x^8 - 2x^7 - 2x^6 + 4x^5 + 5x^4 - 4x^3 - 2x^2 + 2x + 1	\( 2^{12}\cdot 5\cdot 7^{4}\cdot 53 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2606764032.3	x^8 - 4x^7 + 4x^6 + 2x^5 + x^4 - 10x^3 + 2x^2 + 4x + 2	\( 2^{12}\cdot 3^{8}\cdot 97 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2821754880.1	x^8 - 2x^7 - 2x^5 + 4x^4 - 6x^3 + 4x^2 + 10x + 15	\( 2^{12}\cdot 3^{9}\cdot 5\cdot 7 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2821754880.2	x^8 - 2x^7 - 2x^6 + 12x^5 - 3x^4 + 26x^2 - 10x + 5	\( 2^{12}\cdot 3^{9}\cdot 5\cdot 7 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2871672832.1	x^8 - 2x^7 + 8x^5 - 4x^4 - 16x^3 + 28x^2 - 28x + 14	\( 2^{14}\cdot 7^{4}\cdot 73 \)	$C_2\wr A_4$ (as 8T38)	$[2]$
8.0.2920845312.1	x^8 - 2x^7 - 8x^5 + 23x^4 - 10x^3 + 22x^2 - 52x + 34	\( 2^{12}\cdot 3^{3}\cdot 7^{4}\cdot 11 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.2999521280.1	x^8 - 2x^7 + 8x^6 - 6x^5 + 32x^4 - 22x^3 + 24x^2 - 10x + 3	\( 2^{12}\cdot 5\cdot 7^{4}\cdot 61 \)	$C_2\wr A_4$ (as 8T38)	Trivial
8.0.3036745728.2	x^8 - 2x^7 + 8x^6 - 10x^5 + 20x^4 - 14x^3 + 24x^2 - 6x + 15	\( 2^{12}\cdot 3^{8}\cdot 113 \)	$C_2\wr A_4$ (as 8T38)	Trivial