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 7317)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.1185762483.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 2x^6 - x^5 + 3x^4 - 4x^3 + x^2 + 1	\( -\,3^{5}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.1403737447.1	x^10 - 3x^9 + 6x^8 - 7x^7 + 6x^6 - 4x^5 + 4x^3 - 2x^2 - x + 1	\( -\,7^{5}\cdot 17^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.1917386883.1	x^10 - x^9 + 3x^8 - 4x^7 + 2x^6 - 2x^5 + x^4 + 6x^3 + 4x^2 + 6x + 3	\( -\,3^{5}\cdot 53^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.3409076657.1	x^10 - x^9 + 2x^8 - 4x^7 + 5x^6 - 7x^5 + 9x^4 - 8x^3 + 5x^2 - 4x + 1	\( 7^{4}\cdot 17^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.4599777611.1	x^10 - 5x^9 + 11x^8 - 14x^7 + 10x^6 - 2x^5 - 2x^4 + x^3 + 3x^2 - 3x + 1	\( -\,11^{5}\cdot 13^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.4996793344.3	x^10 - 3x^4 + 2x^2 + 1	\( -\,2^{10}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.5436100813.1	x^10 - 3x^9 + 6x^8 - 6x^7 + 3x^6 + 3x^5 - 9x^4 + 13x^3 - 12x^2 + 6x - 1	\( 11^{4}\cdot 13^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.9464869683.1	x^10 - x^9 + 3x^7 - 4x^6 + 3x^5 - 4x^3 + 7x^2 - 3x + 1	\( -\,3^{5}\cdot 79^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.15249003125.1	x^10 - 2x^9 + 2x^8 - 2x^6 + 9x^5 + 13x^4 + 8x^3 + 3x^2 - 1	\( 5^{5}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.25286677443.1	x^10 - 3x^8 - 2x^7 + 6x^6 - 8x^4 + 21x^3 + 12x^2 - 9x + 9	\( -\,3^{5}\cdot 101^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.27349864083.1	x^10 - 2x^9 + x^8 + 2x^6 - 4x^5 + 8x^4 - 9x^3 + 4x^2 + x + 1	\( -\,3^{5}\cdot 103^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.33873834933.1	x^10 - 4x^9 + 4x^8 + 4x^7 - 6x^6 - 11x^5 + 18x^4 + 4x^3 - 13x^2 - 7x - 1	\( 3^{4}\cdot 53^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.39884882944.4	x^10 - x^8 + 3x^6 + 5x^2 + 1	\( -\,2^{10}\cdot 79^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.48729742803.1	x^10 - x^9 + x^8 + 2x^7 - 4x^6 + 5x^5 - 3x^3 + 8x^2 - 3x + 1	\( -\,3^{5}\cdot 7^{4}\cdot 17^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.55730836701.1	x^10 - 4x^9 + 4x^8 - 4x^7 + 21x^6 - 28x^5 + 8x^4 - 26x^3 + 11x^2 - 13x + 1	\( 3^{5}\cdot 47^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.59326171875.1	x^10 - 10x^7 + 3x^5 + 25x^4 - 15x^2 + 9	\( -\,3^{5}\cdot 5^{12} \)	$D_{10}$ (as 10T3)	Trivial
10.0.61412507648.1	x^10 - 2x^9 - 3x^8 + 4x^7 + 5x^6 - 2x^5 + 5x^4 + 4x^3 - 3x^2 - 2x + 1	\( -\,2^{15}\cdot 37^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.63215147763.1	x^10 - x^9 + 3x^8 + 2x^6 + 3x^5 + 6x^4 - x^3 + 10x^2 - 3x + 1	\( -\,3^{5}\cdot 127^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.71563480803.1	x^10 - x^9 - x^8 + 2x^6 + 2x^5 + x^4 - 9x^3 + 3x^2 + 2x + 4	\( -\,3^{5}\cdot 131^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.82012798567.1	x^10 - 2x^9 + 2x^8 - 3x^7 + 4x^6 + 3x^5 + 4x^4 - 40x^3 + 24x^2 + 32	\( -\,7^{5}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.98876953125.1	x^10 - 5x^7 + 10x^6 + 9x^5 - 10x^4 - 5x^3 - 1	\( 3^{4}\cdot 5^{13} \)	$D_{10}$ (as 10T3)	Trivial
10.0.101613269043.1	x^10 - x^9 + 2x^8 + x^7 - 2x^6 + 5x^5 + 2x^4 - 2x^3 + 9x^2 - 3x + 1	\( -\,3^{5}\cdot 11^{4}\cdot 13^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.112027271168.1	x^10 + 4x^8 - 4x^7 + 5x^6 - 8x^5 + 10x^4 - 8x^3 - x^2 - 8x + 2	\( 2^{15}\cdot 43^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.113908312331.3	x^10 - 2x^9 + x^7 + 7x^6 - 16x^5 + 10x^4 + 6x^3 - 7x^2 - 2x + 3	\( -\,11^{5}\cdot 29^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.115252102144.4	x^10 - 2x^8 - x^6 - x^4 + 7x^2 + 1	\( -\,2^{10}\cdot 103^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.121719003125.1	x^10 - x^9 + 2x^8 - 7x^7 + 16x^6 - x^5 - 2x^4 + 2x^3 + 3x^2 - 3x - 1	\( 5^{5}\cdot 79^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.148307253125.1	x^10 + 6x^8 - 2x^7 + 14x^6 - 2x^5 + 11x^4 + 7x^3 + x^2 + 10x - 1	\( 5^{5}\cdot 83^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.159897387008.4	x^10 - 24x^4 + 32x^2 + 32	\( -\,2^{15}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.159897387008.2	x^10 + 24x^4 + 32x^2 - 32	\( 2^{15}\cdot 47^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.205346735104.4	x^10 + x^8 + 4x^6 + 3x^4 + 7x^2 + 1	\( -\,2^{10}\cdot 7^{4}\cdot 17^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.214296753125.1	x^10 - 2x^9 - 5x^8 + 8x^7 + 11x^6 - 15x^5 + 4x^4 - 6x^3 - x^2 + 5x + 5	\( 5^{5}\cdot 7^{4}\cdot 13^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.234849287168.5	x^10 - 2x^8 + 9x^6 - 8x^4 + 16x^2 - 47	\( 2^{10}\cdot 47^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.249470040483.1	x^10 - x^9 + x^8 - 6x^7 + 4x^6 + 11x^4 - 3x^3 - 5x^2 - 2x + 4	\( -\,3^{5}\cdot 179^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.250000000000.1	x^10 - 10x^7 - 8x^5 + 25x^4 + 40x^2 + 20	\( -\,2^{10}\cdot 5^{12} \)	$D_{10}$ (as 10T3)	Trivial
10.0.266388112384.4	x^10 + 5x^8 + 12x^6 + 15x^4 + 11x^2 + 1	\( -\,2^{10}\cdot 127^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.284032847872.1	x^10 - 3x^9 + 2x^8 + 5x^7 - 13x^6 + 2x^5 + 17x^4 - 5x^3 - 4x^2 + x - 7	\( 2^{12}\cdot 37^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.300015454375.1	x^10 - 2x^9 + 4x^8 - x^7 + x^5 + 9x^4 - 8x^3 + 11x^2 - 3x + 11	\( -\,5^{4}\cdot 7^{5}\cdot 13^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.300303732509.1	x^10 - 5x^9 + 11x^8 - 14x^7 + 10x^6 - 2x^5 + x^4 - 5x^3 + 9x^2 - 6x - 1	\( 11^{4}\cdot 29^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.301567919104.3	x^10 - 3x^8 + 4x^6 - 7x^4 + 5x^2 + 4	\( -\,2^{10}\cdot 131^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.312500000000.1	x^10 - 5x^9 + 10x^8 - 5x^7 - 15x^6 + 32x^5 - 15x^4 - 5x^3 + 10x^2 - 5x + 1	\( 2^{8}\cdot 5^{13} \)	$D_{10}$ (as 10T3)	Trivial
10.2.341108199621.1	x^10 - x^9 - 3x^8 + 8x^7 - 9x^6 + x^5 + 7x^4 + 17x^3 + 13x^2 + 2x + 1	\( 3^{5}\cdot 7^{5}\cdot 17^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.351721503125.1	x^10 - 2x^9 + 5x^8 - 6x^7 - 2x^6 + 10x^5 + 14x^4 + 15x^3 + 10x^2 + x - 1	\( 5^{5}\cdot 103^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.428197479424.4	x^10 + 3x^8 + 7x^6 + 8x^4 + 9x^2 + 1	\( -\,2^{10}\cdot 11^{4}\cdot 13^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.429162451875.1	x^10 - x^9 + 5x^8 - 13x^7 + 17x^6 - 7x^5 + 13x^4 - 54x^3 + 78x^2 - 45x + 9	\( -\,3^{5}\cdot 5^{4}\cdot 41^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.453700517888.1	x^10 - 4x^9 + 10x^8 - 18x^7 + 32x^6 - 52x^5 + 59x^4 - 48x^3 + 26x^2 - 8x + 4	\( -\,2^{15}\cdot 61^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.491300061184.2	x^10 - 5x^8 + 7x^6 - 7x^4 + 16x^2 + 4	\( -\,2^{18}\cdot 37^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.2.557171558125.1	x^10 - 2x^8 - 3x^7 - 12x^6 - 7x^5 + 12x^4 - 3x^3 + 2x^2 - 1	\( 5^{4}\cdot 7^{4}\cdot 13^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.0.602146582528.1	x^10 - x^9 + 2x^8 - 7x^7 + 17x^6 - 16x^5 + 21x^4 - 37x^3 + 46x^2 - 35x + 13	\( -\,2^{12}\cdot 43^{5} \)	$D_{10}$ (as 10T3)	Trivial
10.2.626668503125.1	x^10 - x^9 - x^8 - 4x^7 + 18x^6 + x^5 - 8x^4 + 3x^3 + 6x^2 - 3x - 1	\( 5^{5}\cdot 7^{4}\cdot 17^{4} \)	$D_{10}$ (as 10T3)	Trivial
10.0.645222795363.1	x^10 + x^8 - 4x^7 - 2x^6 - 6x^5 + 7x^4 - 2x^3 + 17x^2 - 12x + 16	\( -\,3^{5}\cdot 227^{4} \)	$D_{10}$ (as 10T3)	Trivial