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 1081)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.67162921875.1	x^10 - x^9 - x^8 + 6x^7 + 7x^6 - 6x^5 + x^4 + 24x^3 + 23x^2 + 8x + 1	\( -\,3^{5}\cdot 5^{6}\cdot 7^{2}\cdot 19^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.112960521216.1	x^10 - 2x^9 - 3x^8 + 4x^7 + 11x^6 - 6x^5 - 17x^4 - 2x^3 + 27x^2 - 14x + 2	\( -\,2^{10}\cdot 3^{6}\cdot 389^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.186624000000.1	x^10 - 4x^9 + 11x^8 - 16x^7 + 22x^6 - 18x^5 + 16x^4 - 4x^3 - x^2 + 2x + 1	\( -\,2^{14}\cdot 3^{6}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.284419350000.1	x^10 - x^9 + 3x^8 - 3x^7 - 3x^4 + 3x^3 + 3x^2 - x + 4	\( -\,2^{4}\cdot 3^{9}\cdot 5^{5}\cdot 17^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.389763200000.1	x^10 + 3x^6 - 2x^5 + x^2 + 2x + 1	\( -\,2^{10}\cdot 5^{5}\cdot 349^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.401044921875.1	x^10 + 10x^8 + 35x^6 - x^5 + 50x^4 - 5x^3 + 25x^2 - 5x + 1	\( -\,3^{5}\cdot 5^{10}\cdot 13^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.409600000000.1	x^10 + 15x^6 - 4x^5 + 25x^2 + 20x + 4	\( -\,2^{20}\cdot 5^{8} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.1046513671875.1	x^10 - 10x^8 + 35x^6 - x^5 - 50x^4 + 5x^3 + 25x^2 - 5x + 1	\( -\,3^{7}\cdot 5^{10}\cdot 7^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.1690000000000.2	x^10 - 10x^8 + 35x^6 - 8x^5 - 50x^4 + 40x^3 + 25x^2 - 40x + 32	\( -\,2^{10}\cdot 5^{10}\cdot 13^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.1828915200000.1	x^10 - 4x^9 + 9x^8 - 16x^7 + 20x^6 - 22x^5 + 26x^4 - 24x^3 + 29x^2 - 14x + 9	\( -\,2^{14}\cdot 3^{6}\cdot 5^{5}\cdot 7^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.1990656000000.1	x^10 - 4x^8 + 10x^6 - 4x^5 + 8x^3 + 4	\( -\,2^{19}\cdot 3^{5}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.2.2367488000000.1	x^10 - 4x^9 + 4x^8 + 12x^7 - 42x^6 + 64x^5 - 54x^4 + 28x^3 - 3x^2 - 4x + 2	\( 2^{19}\cdot 5^{6}\cdot 17^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.3097158156288.1	x^10 - x^9 + 9x^8 - 6x^7 + 36x^6 - 18x^5 + 72x^4 - 18x^3 + 63x^2 - x + 19	\( -\,2^{16}\cdot 3^{9}\cdot 7^{4} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.5467500000000.2	x^10 - 10x^8 + 35x^6 - 2x^5 - 50x^4 + 10x^3 + 25x^2 - 10x + 4	\( -\,2^{8}\cdot 3^{7}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.6422528000000.1	x^10 - 2x^9 + 7x^8 - 8x^7 + 9x^6 - 2x^5 - 7x^4 + 8x^3 - 9x^2 - 2x - 23	\( 2^{23}\cdot 5^{6}\cdot 7^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.7290000000000.1	x^10 + 4x^8 - 14x^7 + 52x^6 - 104x^5 + 145x^4 - 128x^3 + 73x^2 - 24x + 4	\( -\,2^{10}\cdot 3^{6}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.10077696000000.2	x^10 - 6x^7 - 6x^6 + 12x^5 + 15x^4 + 30x^3 + 3x^2 - 12x + 60	\( -\,2^{15}\cdot 3^{9}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.10240000000000.7	x^10 + 10x^8 + 35x^6 - 16x^5 + 50x^4 - 80x^3 + 25x^2 - 80x + 100	\( -\,2^{20}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.10504375000000.1	x^10 + 10x^8 + 35x^6 - x^5 + 50x^4 - 5x^3 + 25x^2 - 5x + 2	\( -\,2^{6}\cdot 5^{10}\cdot 7^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.11943936000000.2	x^10 - 4x^9 + 11x^8 - 28x^7 + 51x^6 - 88x^5 + 129x^4 - 136x^3 + 133x^2 - 76x + 17	\( -\,2^{20}\cdot 3^{6}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.14269871030272.1	x^10 - 2x^9 + 5x^8 - 12x^7 + 22x^6 - 36x^5 + 46x^4 - 60x^3 + 87x^2 - 50x + 25	\( -\,2^{19}\cdot 11^{5}\cdot 13^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.6.15680000000000.1	x^10 - 10x^8 + 35x^6 - 2x^5 - 50x^4 + 10x^3 + 25x^2 - 10x - 1	\( 2^{15}\cdot 5^{10}\cdot 7^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.16511297126400.4	x^10 - 4x^9 + 6x^8 - 12x^7 + 12x^6 - 12x^5 + 12x^4 - 12x^3 + 9x^2 - 16x + 10	\( 2^{25}\cdot 3^{9}\cdot 5^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.19110297600000.1	x^10 - 4x^9 + 8x^7 + 47x^6 - 184x^5 + 260x^4 - 204x^3 + 101x^2 - 32x + 6	\( 2^{23}\cdot 3^{6}\cdot 5^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.2.21587207078125.1	x^10 - x^9 - 3x^8 + 14x^7 - 11x^6 + 3x^5 + 3x^4 + 11x^3 + 11x^2 - 2x - 3	\( 5^{6}\cdot 13^{5}\cdot 61^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.22717712000000.1	x^10 - x^9 - 6x^8 + 10x^7 + 11x^6 - 35x^5 - 4x^4 + 50x^3 - x^2 - x + 26	\( 2^{10}\cdot 5^{6}\cdot 17^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.6.23554400190464.1	x^10 - 4x^9 + 2x^8 + 20x^7 - 20x^6 - 24x^5 + 38x^4 - 4x^3 - 30x^2 + 12x + 10	\( 2^{19}\cdot 11^{2}\cdot 13^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.26214400000000.1	x^10 - 4x^9 + 5x^8 - 8x^5 - 8x^4 + 25x^2 + 20x + 5	\( -\,2^{26}\cdot 5^{8} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.27040000000000.1	x^10 - 10x^8 + 35x^6 - 6x^5 - 50x^4 + 30x^3 + 25x^2 - 30x + 10	\( -\,2^{14}\cdot 5^{10}\cdot 13^{2} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.6.32633173828125.1	x^10 - 10x^8 + 35x^6 - x^5 - 50x^4 + 5x^3 + 25x^2 - 5x - 3	\( 3^{2}\cdot 5^{10}\cdot 13^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.33177600000000.1	x^10 - 2x^9 - x^8 + 12x^7 - 4x^6 - 52x^5 - 26x^4 + 72x^3 + 136x^2 + 88x + 20	\( -\,2^{20}\cdot 3^{4}\cdot 5^{8} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.35831808000000.1	x^10 - 2x^9 + 5x^8 - 8x^7 + 7x^6 - 6x^5 - 5x^4 + 28x^3 - 7x^2 + 10x + 13	\( 2^{20}\cdot 3^{7}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.61232239557632.1	x^10 - 2x^9 + 5x^8 - 16x^7 + 33x^6 - 58x^5 + 87x^4 - 136x^3 + 210x^2 - 216x + 108	\( -\,2^{10}\cdot 11^{5}\cdot 13^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[10]$
10.2.64497254400000.2	x^10 - 4x^9 + 9x^8 - 12x^7 - 3x^6 + 24x^5 - 9x^4 + 12x^3 - 69x^2 + 80x - 35	\( 2^{20}\cdot 3^{9}\cdot 5^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.6.81920000000000.1	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x - 4	\( 2^{23}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.87480000000000.6	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x + 52	\( -\,2^{12}\cdot 3^{7}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial (GRH)
10.0.109350000000000.1	x^10 - 5x^9 + 5x^8 - 5x^7 + 55x^6 - 103x^5 + 50x^4 + 20x^3 - 20x^2 + 6	\( -\,2^{10}\cdot 3^{7}\cdot 5^{11} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.116640000000000.14	x^10 - 10x^7 + 55x^6 - 78x^5 - 100x^4 + 140x^3 + 450x^2 - 840x + 392	\( -\,2^{14}\cdot 3^{6}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial (GRH)
10.0.119651396484375.1	x^10 + 20x^8 + 100x^6 - 3x^5 + 175x^4 - 30x^3 + 35x^2 + 4	\( -\,3^{6}\cdot 5^{10}\cdot 7^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.127401984000000.5	x^10 - 4x^9 + 2x^8 + 12x^7 - 8x^6 - 84x^5 + 292x^4 - 516x^3 + 569x^2 - 376x + 118	\( -\,2^{25}\cdot 3^{5}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.2.127401984000000.2	x^10 - 4x^9 + 8x^8 - 14x^6 + 4x^4 - 48x^3 + 65x^2 - 76x + 4	\( 2^{25}\cdot 3^{5}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.127401984000000.4	x^10 - 2x^9 + 7x^8 - 16x^7 + 24x^6 - 48x^5 + 80x^4 - 40x^3 + 45x^2 - 10x - 5	\( 2^{25}\cdot 3^{5}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.2.127401984000000.5	x^10 - 4x^9 + 16x^7 - 11x^6 - 32x^5 - 12x^4 + 20x^3 + 53x^2 + 32x + 10	\( 2^{25}\cdot 3^{5}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial (GRH)
10.0.128678593750000.1	x^10 - 10x^8 + 35x^6 - 3x^5 - 50x^4 + 15x^3 + 25x^2 - 15x + 4	\( -\,2^{4}\cdot 5^{10}\cdot 7^{7} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.135500669337600.1	x^10 - 2x^9 - 6x^7 + 24x^6 - 6x^5 - 6x^4 - 36x^3 + 30x^2 + 64x + 22	\( -\,2^{14}\cdot 3^{9}\cdot 5^{2}\cdot 7^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2, 2]$
10.0.155520000000000.10	x^10 - 50x^6 - 52x^5 + 925x^2 + 2380x + 1648	\( -\,2^{16}\cdot 3^{5}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.155520000000000.11	x^10 + 35x^6 - 96x^5 + 325x^2 - 1620x + 2352	\( -\,2^{16}\cdot 3^{5}\cdot 5^{10} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial
10.0.161243136000000.9	x^10 - 4x^9 + 12x^8 - 36x^7 + 81x^6 - 156x^5 + 258x^4 - 324x^3 + 297x^2 - 172x + 58	\( -\,2^{19}\cdot 3^{9}\cdot 5^{6} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$
10.0.168070000000000.2	x^10 - 10x^8 + 35x^6 - 2x^5 - 50x^4 + 10x^3 + 25x^2 - 10x + 8	\( -\,2^{10}\cdot 5^{10}\cdot 7^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	Trivial (GRH)
10.0.178861090118400.1	x^10 - 4x^9 + 18x^7 - 12x^6 - 48x^5 + 108x^4 - 144x^3 + 108x^2 - 40x + 100	\( -\,2^{8}\cdot 3^{9}\cdot 5^{2}\cdot 17^{5} \)	$(D_5 \wr C_2):C_2$ (as 10T27)	$[2]$