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 1210)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.1844444809.1	x^10 - 2x^7 - x^5 + x^4 - x^3 + x^2 - x + 1	\( 67^{2}\cdot 641^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.4473335689.1	x^10 - x^9 + 2x^8 - 2x^7 - x^6 + x^5 - 3x^4 + 2x^3 + x^2 + 1	\( 66883^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.15249286144.1	x^10 + x^8 - 2x^5 - x^4 - 2x^3 - x^2 + 1	\( 2^{10}\cdot 17^{2}\cdot 227^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.6.51471358129.1	x^10 - x^9 - 3x^8 - 2x^7 + 2x^6 + 6x^5 + 4x^4 - 2x^3 - 5x^2 + 1	\( 307^{2}\cdot 739^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.6.527145698304.1	x^10 - 4x^9 + 2x^8 + 2x^7 + 5x^6 - 9x^4 + 4x^3 - 5x^2 + 1	\( 2^{10}\cdot 3^{4}\cdot 2521^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.7449493349376.1	x^10 - 4x^9 + 24x^7 - 42x^6 + 18x^5 + 12x^4 - 12x^3 + 9x^2 + 2x + 1	\( 2^{10}\cdot 3^{16}\cdot 13^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.19360000000000.1	x^10 + 5x^8 - 5x^6 - 32x^5 - 25x^4 + 40x^2 - 16	\( 2^{14}\cdot 5^{10}\cdot 11^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.35664401793024.1	x^10 - x^9 + 3x^8 + 8x^7 - 38x^6 + 54x^5 - 122x^4 + 80x^3 - 102x^2 + 30x - 42	\( 2^{26}\cdot 3^{12} \)	$A_{10}$ (as 10T44)	Trivial
10.2.39062500000000.1	x^10 - 5x^9 + 20x^7 - 48x^5 - 10x^4 + 60x^3 + 35x^2 - 35x - 26	\( 2^{8}\cdot 5^{16} \)	$A_{10}$ (as 10T44)	Trivial
10.2.40960000000000.4	x^10 - 4x^9 + 8x^8 - 16x^7 + 37x^6 - 60x^5 + 52x^4 - 4x^3 - 42x^2 + 44x - 14	\( 2^{22}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.40960000000000.8	x^10 - 5x^8 - 16x^5 + 20x^4 + 16	\( 2^{22}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.40960000000000.9	x^10 - 12x^5 - 50x^4 - 64	\( 2^{22}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.69774697265625.1	x^10 - 10x^7 - 15x^6 + 39x^5 - 10x^4 + 15x^3 + 90x^2 - 65x - 123	\( 3^{10}\cdot 5^{10}\cdot 11^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.89302500000000.1	x^10 + 10x^8 - 10x^7 + 30x^6 - 36x^5 + 60x^4 - 60x^2 + 30x + 12	\( 2^{8}\cdot 3^{6}\cdot 5^{10}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.94478400000000.1	x^10 - x^9 - 8x^8 + 11x^7 + 28x^6 - 43x^5 - 61x^4 + 112x^3 + 56x^2 - 192x + 96	\( 2^{12}\cdot 3^{10}\cdot 5^{8} \)	$A_{10}$ (as 10T44)	Trivial
10.2.100000000000000.1	x^10 - 10x^7 + 5x^6 - 14x^5 + 25x^4 + 50x^3 - 30x^2 - 10x - 1	\( 2^{14}\cdot 5^{14} \)	$A_{10}$ (as 10T44)	Trivial
10.2.104231337890625.1	x^10 - 15x^7 + 5x^6 + 6x^5 + 45x^4 - 45x^3 + 45x - 9	\( 3^{6}\cdot 5^{10}\cdot 11^{4} \)	$A_{10}$ (as 10T44)	Trivial
10.2.108160000000000.1	x^10 - 6x^5 - 25x^4 - 16	\( 2^{16}\cdot 5^{10}\cdot 13^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.109222230491136.1	x^10 - 4x^9 + 3x^8 + 12x^7 - 27x^6 + 45x^4 - 36x^3 - 21x^2 + 28x - 7	\( 2^{22}\cdot 3^{12}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.138234385465344.1	x^10 - 4x^9 + 24x^7 - 42x^6 + 84x^4 - 120x^3 + 81x^2 - 20x + 8	\( 2^{16}\cdot 3^{16}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.147622500000000.4	x^10 - 30x^6 - 30x^5 + 180x^2 + 270x + 108	\( 2^{8}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.207360000000000.1	x^10 - 16x^5 + 75x^2 - 36	\( 2^{18}\cdot 3^{4}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.222902511206400.4	x^10 - 2x^9 + 9x^8 - 12x^7 + 30x^6 - 72x^5 + 60x^4 - 312x^3 + 54x^2 - 444x - 66	\( 2^{24}\cdot 3^{12}\cdot 5^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.452093906250000.1	x^10 - 10x^7 - 9x^5 + 25x^4 - 60x^3 + 192	\( 2^{4}\cdot 3^{10}\cdot 5^{10}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.485980261401600.1	x^10 - 2x^9 + 243x^2 - 486x + 243	\( 2^{10}\cdot 3^{18}\cdot 5^{2}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.590490000000000.16	x^10 - 5x^9 + 10x^8 + 10x^7 - 60x^6 + 86x^5 + 30x^4 - 110x^3 + 20x^2 + 40x - 16	\( 2^{10}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	$[2]$ (GRH)
10.2.590490000000000.18	x^10 - 5x^8 - 5x^6 - 6x^5 + 25x^4 + 40x^2 + 16	\( 2^{10}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.590490000000000.27	x^10 - 5x^9 + 20x^7 + 5x^6 - 33x^5 + 10x^4 - 140x^3 + 30x^2 + 270x + 120	\( 2^{10}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.729000000000000.1	x^10 + 5x^8 - 10x^7 + 55x^6 + 16x^5 + 25x^4 - 10x^3 + 20x^2 - 2	\( 2^{12}\cdot 3^{6}\cdot 5^{12} \)	$A_{10}$ (as 10T44)	Trivial
10.2.829440000000000.6	x^10 - 10x^8 + 50x^6 - 24x^5 - 80x^4 + 120x^2 - 72	\( 2^{20}\cdot 3^{4}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.1049760000000000.19	x^10 - 5x^8 - 30x^7 - 35x^6 + 24x^5 + 185x^4 + 150x^3 - 160x^2 - 360x - 112	\( 2^{14}\cdot 3^{8}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.1239040000000000.2	x^10 - 10x^8 - 10x^7 + 30x^6 - 40x^5 - 25x^4 + 60x^3 - 140x^2 + 120x - 58	\( 2^{20}\cdot 5^{10}\cdot 11^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.1328602500000000.1	x^10 - 2x^9 + 6x^8 + 12x^7 - 66x^6 + 180x^5 - 288x^4 + 324x^3 - 252x^2 + 126x - 36	\( 2^{8}\cdot 3^{12}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.1328602500000000.5	x^10 - 30x^7 + 192x^5 - 180x^4 - 240x^3 + 600x^2 - 520x + 96	\( 2^{8}\cdot 3^{12}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	$[2]$ (GRH)
10.2.1474560000000000.13	x^10 + 5x^8 - 32x^5 - 20x^4 + 144	\( 2^{24}\cdot 3^{2}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial
10.2.1640250000000000.8	x^10 + 10x^8 + 40x^6 - 12x^5 + 65x^4 - 60x^3 + 20x^2 - 120x + 20	\( 2^{10}\cdot 3^{8}\cdot 5^{12} \)	$A_{10}$ (as 10T44)	Trivial
10.2.1666598976000000.1	x^10 - 4x^9 + 17x^8 - 44x^7 + 88x^6 - 90x^5 + 24x^4 + 36x^3 - 21x^2 - 6x + 3	\( 2^{12}\cdot 3^{12}\cdot 5^{6}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.2007040000000000.1	x^10 - 5x^8 + 5x^6 - 8x^5 - 15x^4 + 5x^2 - 1	\( 2^{22}\cdot 5^{10}\cdot 7^{2} \)	$A_{10}$ (as 10T44)	Trivial
10.2.2361960000000000.9	x^10 + 5x^8 - 5x^6 - 48x^5 - 25x^4 + 40x^2 - 16	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2361960000000000.10	x^10 + 5x^8 - 5x^6 - 36x^5 - 25x^4 + 40x^2 - 16	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	$[2]$ (GRH)
10.2.2361960000000000.17	x^10 - 5x^8 - 5x^6 - 24x^5 + 25x^4 + 40x^2 + 16	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2361960000000000.20	x^10 - 18x^5 - 75x^4 - 144	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2361960000000000.22	x^10 - 18x^5 + 150x^4 - 144	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2361960000000000.23	x^10 - 5x^9 + 20x^7 - 40x^6 + 80x^4 - 160x^3 + 160x - 128	\( 2^{12}\cdot 3^{10}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2538998916710400.1	x^10 - 4x^9 + 24x^7 - 42x^6 + 84x^4 - 120x^3 + 81x^2 - 156x - 60	\( 2^{18}\cdot 3^{18}\cdot 5^{2} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2538998916710400.2	x^10 - 9x^8 + 18x^6 + 54x^4 - 243x^2 - 1024x + 243	\( 2^{18}\cdot 3^{18}\cdot 5^{2} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.2687385600000000.3	x^10 - 4x^9 + 10x^8 - 36x^7 + 78x^6 - 120x^5 + 164x^4 - 140x^3 + 41x^2 + 12x - 306	\( 2^{20}\cdot 3^{8}\cdot 5^{8} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.3317760000000000.4	x^10 - 10x^8 + 30x^6 - 16x^5 - 60x^4 + 40x^2 - 16	\( 2^{22}\cdot 3^{4}\cdot 5^{10} \)	$A_{10}$ (as 10T44)	$[2]$
10.2.3690562500000000.2	x^10 + 10x^8 + 10x^6 - 60x^5 - 100x^4 - 180x^3 - 100x^2 - 60x - 16	\( 2^{8}\cdot 3^{10}\cdot 5^{12} \)	$A_{10}$ (as 10T44)	Trivial (GRH)
10.2.3690562500000000.7	x^10 - 5x^9 + 10x^8 + 10x^7 - 80x^6 + 208x^5 + 150x^4 - 30x^3 - 45x^2 + 45x + 24	\( 2^{8}\cdot 3^{10}\cdot 5^{12} \)	$A_{10}$ (as 10T44)	Trivial (GRH)