Global number field search results

Further refine search

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 924)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.11103890625.1	x^10 - 3x^9 + 5x^8 - 9x^7 + 11x^6 - 14x^5 + 18x^4 - 16x^3 + 12x^2 - 5x + 1	\( 3^{2}\cdot 5^{6}\cdot 281^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.64262250000.1	x^10 - 2x^9 + 2x^8 - 5x^7 + 11x^6 - 14x^5 + 12x^4 - 18x^3 + 24x^2 - 16x + 4	\( 2^{4}\cdot 3^{2}\cdot 5^{6}\cdot 13^{4} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.85629390625.1	x^10 - 2x^8 - 4x^7 + x^6 + 2x^5 - 6x^4 + 7x^3 + 4x^2 - 5x + 1	\( 5^{6}\cdot 2341^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.88729515625.1	x^10 - 2x^9 - 2x^8 + 11x^7 - 6x^6 - 14x^5 + 23x^4 - 2x^3 - 15x^2 + 12x - 1	\( 5^{6}\cdot 2383^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.92112250000.1	x^10 - 4x^9 + 3x^8 + 5x^7 - 4x^6 - 10x^5 + 12x^4 + 2x^3 - 4x^2 - 5x + 5	\( 2^{4}\cdot 5^{6}\cdot 607^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.106194515625.1	x^10 - 3x^9 + 4x^8 - 5x^7 + 2x^6 - x^5 + 4x^4 + 7x^3 + 6x^2 + 4x + 1	\( 3^{2}\cdot 5^{6}\cdot 11^{2}\cdot 79^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.111556000000.1	x^10 - x^9 - 4x^8 + 3x^7 - x^6 + 2x^5 + 10x^4 - 12x^3 + 11x^2 - 5x + 1	\( 2^{8}\cdot 5^{6}\cdot 167^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.113498914816.1	x^10 - 4x^9 + 4x^8 + 2x^7 - 5x^6 + 2x^5 + 3x^4 - 4x^3 - 2x^2 + 4x - 2	\( 2^{20}\cdot 7^{2}\cdot 47^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.142223265625.1	x^10 - x^9 + x^8 - 4x^7 + 2x^6 - 7x^5 + 2x^4 - 6x^3 + 3x^2 - 3x + 1	\( 5^{6}\cdot 7^{2}\cdot 431^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.369056250000.1	x^10 - 4x^9 + 9x^8 - 15x^7 + 20x^6 - 30x^5 + 40x^4 - 40x^3 + 30x^2 - 15x + 5	\( 2^{4}\cdot 3^{10}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.419904000000.1	x^10 - x^9 + 5x^7 + 3x^6 + 12x^5 + 14x^4 + 8x^3 + 9x^2 + 3x + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.477757440000.1	x^10 - 4x^9 + 10x^8 - 14x^7 + 14x^6 - 6x^5 + x^4 + 2x^3 + 7x^2 - 2x - 1	\( 2^{20}\cdot 3^{6}\cdot 5^{4} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.490000000000.1	x^10 + 5x^8 + 5x^6 - 2x^5 + 25x^4 + 10x^3 + 25x^2 + 10x + 1	\( 2^{10}\cdot 5^{10}\cdot 7^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.576650390625.1	x^10 + 5x^6 - 18x^5 + 25x^4 - 25x^3 + 15x^2 - 5x + 1	\( 3^{10}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.625878765625.1	x^10 - 2x^9 - 5x^8 + 3x^7 + 19x^6 + 4x^5 - 17x^4 - 19x^3 - 7x^2 + 2x + 1	\( 5^{6}\cdot 6329^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.1166400000000.2	x^10 - 3x^9 + 7x^8 - 8x^7 - 8x^6 + 12x^5 - 8x^4 + 12x^3 + 7x^2 + 7x + 1	\( 2^{12}\cdot 3^{6}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.1476225000000.1	x^10 - x^9 + x^7 - 2x^6 + 4x^4 - 5x^3 - 9x^2 + 3x - 1	\( 2^{6}\cdot 3^{10}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.1665712890625.1	x^10 - 5x^8 - 5x^7 + 5x^6 + 18x^5 + 5x^4 - 25x^3 - 15x^2 + 1	\( 5^{10}\cdot 7^{2}\cdot 59^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.1822500000000.2	x^10 + 5x^8 + 10x^6 - 12x^5 + 15x^4 - 30x^3 - 9	\( 2^{8}\cdot 3^{6}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.2250000000000.1	x^10 - 5x^8 - 10x^7 - 10x^6 + 6x^5 + 25x^4 + 30x^3 + 25x^2 + 10x + 4	\( 2^{10}\cdot 3^{2}\cdot 5^{12} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.2624400000000.2	x^10 - 3x^9 + 5x^8 - 18x^7 + 43x^6 - 45x^5 + 31x^4 - 30x^3 + 11x^2 + 9x + 1	\( 2^{10}\cdot 3^{8}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.2985984000000.1	x^10 - 3x^9 + x^8 - 8x^7 + 10x^6 - 6x^5 + 22x^4 - 12x^3 - 8x^2 + 4x + 4	\( 2^{18}\cdot 3^{6}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.2985984000000.2	x^10 - 2x^9 - 7x^6 - 18x^5 - 2x^4 + 15x^2 - 2x - 4	\( 2^{18}\cdot 3^{6}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.3779136000000.2	x^10 - x^9 - 7x^8 + 4x^7 + 16x^6 - 18x^5 - 26x^4 + 20x^3 + 20x^2 - 20x - 20	\( 2^{12}\cdot 3^{10}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.3779136000000.4	x^10 - 3x^9 + 5x^8 + 2x^7 - 20x^6 + 22x^5 - 10x^4 + 8x^3 - 32x^2 + 12x - 4	\( 2^{12}\cdot 3^{10}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.5438807015625.1	x^10 - x^9 - 9x^8 + 8x^7 + 39x^6 - 3x^5 - 75x^4 - 22x^3 + 51x^2 + 20x - 4	\( 3^{6}\cdot 5^{6}\cdot 691^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.5760000000000.2	x^10 + 5x^6 - 12x^5 - 5x^2 + 16	\( 2^{16}\cdot 3^{2}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.5904900000000.1	x^10 - x^9 - x^8 + 14x^7 - 6x^6 + 26x^5 - 3x^4 + 47x^3 - 38x^2 + 17x - 1	\( 2^{8}\cdot 3^{10}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.6191736422400.1	x^10 - 2x^9 - 3x^8 + 4x^7 + 9x^6 - 6x^5 - 25x^4 + 16x^3 + 24x^2 - 24x - 2	\( 2^{22}\cdot 3^{10}\cdot 5^{2} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.6718464000000.2	x^10 - 3x^9 + 3x^8 - 2x^7 + 11x^6 - 15x^5 - 7x^4 - 8x^3 + 9x^2 + 5x + 5	\( 2^{16}\cdot 3^{8}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.7290000000000.1	x^10 + 5x^6 - 6x^5 - 5x^4 + 20x^3 - 30x^2 + 10x - 11	\( 2^{10}\cdot 3^{6}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.9226406250000.1	x^10 - 5x^9 + 5x^8 + 5x^7 + 10x^6 - 39x^5 - 20x^4 + 85x^3 - 25x^2 - 10x - 11	\( 2^{4}\cdot 3^{10}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.10497600000000.2	x^10 - 2x^9 - 2x^8 + 6x^7 - 5x^6 + 6x^5 - 2x^4 - 2x^3 + x^2 - 5	\( 2^{12}\cdot 3^{8}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.11943936000000.1	x^10 - 3x^9 + x^8 - 8x^6 - 4x^5 + 4x^4 + 20x^3 + 11x^2 - x - 1	\( 2^{20}\cdot 3^{6}\cdot 5^{6} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.13286025000000.1	x^10 - 4x^9 + 11x^8 - 24x^7 + 41x^6 - 35x^5 - 5x^4 + 45x^3 - 35x^2 + 5x + 5	\( 2^{6}\cdot 3^{12}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.16000000000000.1	x^10 - 5x^9 + 5x^8 + 5x^6 - x^5 + 55x^4 - 50x^3 + 5x^2 + 5x - 1	\( 2^{16}\cdot 5^{12} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.16402500000000.1	x^10 - 10x^8 + 40x^6 - 95x^4 - 90x^3 - 85x^2 - 90x - 20	\( 2^{8}\cdot 3^{8}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.16402500000000.2	x^10 + 5x^8 - 10x^7 + 25x^6 - 20x^5 - 5x^4 + 50x^3 - 70x^2 + 60x - 20	\( 2^{8}\cdot 3^{8}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.16402500000000.3	x^10 + 5x^8 - 10x^7 - 5x^6 - 32x^5 - 25x^4 + 20x^3 - 65x^2 + 30x - 19	\( 2^{8}\cdot 3^{8}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.18662400000000.1	x^10 - 3x^9 + 9x^8 - 20x^7 + 26x^6 - 30x^5 + 42x^4 - 36x^3 + 36x - 36	\( 2^{16}\cdot 3^{6}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.18662400000000.2	x^10 - 2x^9 + 4x^8 - 4x^6 - 8x^4 + 16x^3 - 20x^2 + 24x - 16	\( 2^{16}\cdot 3^{6}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.18662400000000.3	x^10 - 2x^9 + 6x^8 - 8x^7 - x^6 + 42x^5 + 88x^4 + 136x^3 + 117x^2 + 34x - 4	\( 2^{16}\cdot 3^{6}\cdot 5^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.19518724000000.1	x^10 - 2x^8 - 6x^7 + x^6 - 2x^5 + 4x^4 - 32x^3 - 56x^2 + 16	\( 2^{8}\cdot 5^{6}\cdot 47^{4} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.23040000000000.1	x^10 - 5x^8 + 10x^6 - 56x^5 - 30x^4 - 40x^3 + 4	\( 2^{18}\cdot 3^{2}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.23040000000000.2	x^10 + 5x^8 - 24x^5 - 10x^4 + 60x^2 - 36	\( 2^{18}\cdot 3^{2}\cdot 5^{10} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.25628906250000.1	x^10 - 10x^8 - 15x^7 - 10x^6 - 7x^5 - 5x^4 + 35x^3 - 5x^2 - 5x + 1	\( 2^{4}\cdot 3^{8}\cdot 5^{12} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.25628906250000.2	x^10 - 10x^8 - 5x^7 + 25x^6 - x^5 - 35x^4 + 115x^3 + 290x^2 + 210x + 49	\( 2^{4}\cdot 3^{8}\cdot 5^{12} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.6.28179280429056.1	x^10 - 2x^8 - 16x^7 + 10x^6 + 40x^5 - 12x^4 - 32x^3 - x^2 + 8x + 2	\( 2^{32}\cdot 3^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.28179280429056.1	x^10 + 2x^8 - 16x^7 - 14x^6 - 32x^5 - 8x^4 - 16x^3 - 7x^2 - 2	\( 2^{32}\cdot 3^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial
10.2.28179280429056.3	x^10 - 4x^9 + 14x^8 - 48x^7 + 104x^6 - 128x^5 + 96x^4 - 32x^3 + 2x^2 - 8x + 4	\( 2^{32}\cdot 3^{8} \)	$A_5^2 : C_4$ (as 10T42)	Trivial