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 10208)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.33554432.1	x^8 - 4x^6 + 6x^4 - 4x^2 + 2	\( 2^{25} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.115200000.1	x^8 - 2x^7 + 4x^6 + 4x^5 - 11x^4 + 8x^3 + 6x^2 - 10x + 5	\( 2^{12}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.115200000.2	x^8 - 2x^7 - 2x^6 + 10x^5 + 6x^4 - 10x^3 - 2x^2 + 2x + 1	\( 2^{12}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.204800000.2	x^8 - 4x^6 + 9x^4 - 10x^2 + 5	\( 2^{16}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.204800000.3	x^8 - 2x^6 + x^4 + 5	\( 2^{16}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.301989888.1	x^8 - 8x^6 + 26x^4 - 36x^2 + 18	\( 2^{25}\cdot 3^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.301989888.2	x^8 - 4x^6 - 2x^4 + 12x^2 + 18	\( 2^{25}\cdot 3^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.627200000.1	x^8 - 2x^7 + 6x^5 + 10x^4 + 14x^3 + 32x^2 + 30x + 9	\( 2^{12}\cdot 5^{5}\cdot 7^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.627200000.2	x^8 - 2x^7 - 2x^6 + 12x^5 + 16x^4 - 20x^3 - 12x^2 + 8x + 4	\( 2^{12}\cdot 5^{5}\cdot 7^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.819200000.2	x^8 - 2x^6 + 6x^4 - 20x^2 + 20	\( 2^{18}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.819200000.3	x^8 - 6x^6 + 14x^4 - 20x^2 + 20	\( 2^{18}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.838860800.3	x^8 - 4x^6 + 22x^4 - 60x^2 + 50	\( 2^{25}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.838860800.4	x^8 - 8x^6 + 34x^4 - 60x^2 + 50	\( 2^{25}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.1644167168.1	x^8 - 8x^6 + 66x^4 - 140x^2 + 98	\( 2^{25}\cdot 7^{2} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.1644167168.2	x^8 - 8x^6 + 34x^4 - 84x^2 + 98	\( 2^{25}\cdot 7^{2} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.1843200000.1	x^8 - 8x^6 + 31x^4 - 60x^2 + 45	\( 2^{16}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.1843200000.2	x^8 - 4x^6 - x^4 + 45	\( 2^{16}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.1924782912.1	x^8 - 3x^7 + 2x^6 - 8x^5 + 37x^4 - 56x^3 + 40x^2 - 24x + 12	\( 2^{6}\cdot 3^{4}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.1924782912.2	x^8 + 12x^6 + 49x^4 + 78x^2 + 52	\( 2^{6}\cdot 3^{4}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2241903125.1	x^8 - 2x^7 - 4x^6 + 9x^5 + 11x^4 - 5x^3 - 11x^2 - 10x + 20	\( 5^{5}\cdot 7^{2}\cdot 11^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2241903125.2	x^8 - 2x^7 + x^6 + 3x^5 - x^4 - 2x^3 + 16x^2 + 3x + 1	\( 5^{5}\cdot 7^{2}\cdot 11^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2717908992.1	x^8 - 12x^6 + 54x^4 - 108x^2 + 162	\( 2^{25}\cdot 3^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2832334848.3	x^8 - 2x^6 + 11x^4 - 24x^2 + 18	\( 2^{17}\cdot 3^{2}\cdot 7^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2832334848.4	x^8 - 4x^5 - 3x^4 + 32x^2 + 48x + 18	\( 2^{17}\cdot 3^{2}\cdot 7^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2928200000.1	x^8 - 4x^6 + 9x^4 - 10x^2 + 20	\( 2^{6}\cdot 5^{5}\cdot 11^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.2928200000.2	x^8 - 3x^7 + 7x^6 - 11x^5 + 4x^4 + 11x^3 + 7x^2 + 3x + 1	\( 2^{6}\cdot 5^{5}\cdot 11^{4} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.3639042693.1	x^8 - x^7 - 3x^6 + x^5 + 6x^4 - 13x^3 + 49x^2 - 78x + 39	\( 3^{4}\cdot 11^{2}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.3639042693.2	x^8 - 2x^7 + 12x^6 - 17x^5 + 50x^4 - 37x^3 + 70x^2 - 12x + 43	\( 3^{4}\cdot 11^{2}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[2]$
8.0.4060086272.4	x^8 - 16x^6 + 90x^4 - 220x^2 + 242	\( 2^{25}\cdot 11^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.4060086272.5	x^8 - 4x^6 - 2x^4 + 132x^2 + 242	\( 2^{25}\cdot 11^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.5670699008.3	x^8 - 8x^6 + 66x^4 - 260x^2 + 338	\( 2^{25}\cdot 13^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.5670699008.4	x^8 - 12x^6 + 86x^4 - 260x^2 + 338	\( 2^{25}\cdot 13^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.5815734272.3	x^8 - 2x^6 + x^4 + 68	\( 2^{12}\cdot 17^{5} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.6516050000.1	x^8 - 3x^7 + 11x^6 - 18x^5 + 24x^4 - 8x^3 + 21x^2 + 7x + 1	\( 2^{4}\cdot 5^{5}\cdot 19^{4} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.6516050000.2	x^8 - x^6 + 9x^4 - 40x^2 + 80	\( 2^{4}\cdot 5^{5}\cdot 19^{4} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.6766814925.1	x^8 - 2x^7 - 9x^6 + 25x^5 + 7x^4 - 72x^3 + 81x^2 - 42x + 12	\( 3^{6}\cdot 5^{2}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.6766814925.2	x^8 - 4x^7 + x^6 + 11x^5 - 14x^4 + 5x^3 + x^2 - x + 103	\( 3^{6}\cdot 5^{2}\cdot 13^{5} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.6771200000.5	x^8 - 2x^7 - 4x^6 + 30x^5 + 19x^4 - 74x^3 - 30x^2 + 80x + 89	\( 2^{12}\cdot 5^{5}\cdot 23^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.6771200000.6	x^8 - 2x^7 - 6x^6 + 24x^4 - 4x^3 + 20x^2 + 144x + 244	\( 2^{12}\cdot 5^{5}\cdot 23^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7372800000.1	x^8 - 14x^6 + 74x^4 - 180x^2 + 180	\( 2^{18}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7372800000.2	x^8 - 2x^6 + 26x^4 - 60x^2 + 180	\( 2^{18}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7372800000.3	x^8 - 6x^6 + 34x^4 - 60x^2 + 180	\( 2^{18}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7372800000.4	x^8 - 2x^6 - 14x^4 + 60x^2 + 180	\( 2^{18}\cdot 3^{2}\cdot 5^{5} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7549747200.3	x^8 - 20x^6 + 142x^4 - 420x^2 + 450	\( 2^{25}\cdot 3^{2}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7549747200.4	x^8 - 16x^6 + 106x^4 - 300x^2 + 450	\( 2^{25}\cdot 3^{2}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7549747200.5	x^8 - 8x^6 - 22x^4 + 180x^2 + 450	\( 2^{25}\cdot 3^{2}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7549747200.6	x^8 - 4x^6 + 14x^4 + 180x^2 + 450	\( 2^{25}\cdot 3^{2}\cdot 5^{2} \)	$C_2^3: C_4$ (as 8T21)	Trivial
8.0.7867596800.1	x^8 - 2x^7 + 3x^6 - 8x^5 + 17x^4 - 2x^3 - 23x^2 + 12x + 18	\( 2^{17}\cdot 5^{2}\cdot 7^{4} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.0.7867596800.2	x^8 - 2x^7 + x^6 + 2x^5 - 4x^4 + 2x^3 + 15x^2 - 2x + 1	\( 2^{17}\cdot 5^{2}\cdot 7^{4} \)	$C_2^3: C_4$ (as 8T21)	$[4]$
8.4.8830503125.1	x^8 - x^6 - 36x^4 + 95x^2 + 5	\( 5^{5}\cdot 41^{4} \)	$C_2^3: C_4$ (as 8T21)	Trivial