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 411)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.593019904.1	x^10 - 4x^9 + 8x^8 - 10x^7 + 9x^6 - 6x^5 + 3x^4 - x^2 + 1	\( -\,2^{10}\cdot 761^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.788195043.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 4x^6 - 8x^5 + 14x^4 - 15x^3 + 11x^2 - 5x + 1	\( -\,3^{5}\cdot 1801^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.1128753125.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 2x^6 + 2x^5 - 4x^4 + 2x^3 - 2x + 1	\( 5^{5}\cdot 601^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.1220575232.1	x^10 - 2x^9 + 3x^8 - 4x^7 + x^6 + 4x^5 - 9x^4 + 10x^3 - 8x^2 + 4x - 1	\( 2^{15}\cdot 193^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.1284003125.1	x^10 - 3x^8 - x^7 + x^6 + 2x^5 + 4x^4 - 2x^3 - 4x^2 + 1	\( 5^{5}\cdot 641^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.1533364992.1	x^10 - 3x^9 + 3x^8 + 2x^7 - 7x^6 + 7x^5 + x^4 - 10x^3 + 11x^2 - 5x + 1	\( -\,2^{8}\cdot 3^{5}\cdot 157^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.1903198208.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + 2x^4 - 2x^3 - x^2 + 2x + 1	\( 2^{15}\cdot 241^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.2294728947.1	x^10 - 2x^9 + 6x^8 - 10x^7 + 16x^6 - 17x^5 + 19x^4 - 12x^3 + 9x^2 - 4x + 1	\( -\,3^{5}\cdot 7^{2}\cdot 439^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.2419065856.1	x^10 + 2x^8 + 4x^6 - 2x^5 + x^4 - 2x + 1	\( -\,2^{10}\cdot 29^{2}\cdot 53^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.2425503125.1	x^10 + x^8 + x^6 - 3x^5 + 6x^4 - 9x^3 + 6x^2 - 3x + 1	\( 5^{5}\cdot 881^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.2976800000.1	x^10 - x^9 - x^8 + 4x^7 - 3x^6 - 3x^5 + 7x^4 - 2x^3 - 3x^2 + 3x - 1	\( 2^{8}\cdot 5^{5}\cdot 61^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.3005737227.1	x^10 - x^9 + x^8 - x^6 + 3x^5 + 4x^4 + 6x^3 + 7x^2 + 4x + 1	\( -\,3^{5}\cdot 3517^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.3342873483.1	x^10 - 4x^9 + 9x^8 - 14x^7 + 16x^6 - 13x^5 + 7x^4 - 3x^2 + x + 1	\( -\,3^{5}\cdot 3709^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.3473918523.1	x^10 - 4x^9 + 5x^8 + 2x^7 - 10x^6 + 7x^5 + 3x^4 - 8x^3 + 7x^2 - 3x + 1	\( -\,3^{5}\cdot 19^{2}\cdot 199^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.3983253125.1	x^10 + x^8 + x^6 - x^5 - 4x^4 - 3x^3 - 4x^2 - x - 1	\( 5^{5}\cdot 1129^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.5289378125.1	x^10 - x^9 - x^8 - x^7 + x^6 + 2x^5 + x^4 + x^3 + 3x^2 - x - 1	\( 5^{5}\cdot 1301^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.5959878125.1	x^10 - 3x^9 + x^8 + 8x^7 - 14x^6 + 6x^5 + 9x^4 - 13x^3 + 8x^2 - 3x + 1	\( 5^{5}\cdot 1381^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.6204472587.1	x^10 - 3x^9 + 9x^8 - 14x^7 + 23x^6 - 22x^5 + 25x^4 - 14x^3 + 11x^2 - x + 1	\( -\,3^{5}\cdot 31^{2}\cdot 163^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.6606061568.1	x^10 - 2x^7 - x^6 - 5x^4 + x^2 - 2x - 1	\( 2^{15}\cdot 449^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.7025647347.1	x^10 - 3x^9 + 4x^8 - 2x^7 - 3x^6 + 9x^5 - 7x^4 - 3x^3 + 9x^2 - 5x + 1	\( -\,3^{5}\cdot 19^{2}\cdot 283^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.7864627203.1	x^10 - x^9 + 3x^8 - 3x^7 + 5x^6 - 9x^5 + 9x^4 - x^3 - 2x^2 + 1	\( -\,3^{5}\cdot 5689^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.8090253125.2	x^10 - x^8 - 3x^7 + 4x^6 + 3x^5 - 4x^4 - 2x^3 + 4x^2 - 1	\( 5^{5}\cdot 1609^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.8378733312.1	x^10 - 3x^9 + 6x^8 - 9x^7 + 13x^6 - 14x^5 + 15x^4 - 15x^3 + 16x^2 - 7x + 1	\( -\,2^{8}\cdot 3^{5}\cdot 367^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.8654936832.1	x^10 - 5x^9 + 13x^8 - 20x^7 + 17x^6 - 5x^5 - 3x^4 + 5x^2 - 3x + 1	\( -\,2^{8}\cdot 3^{5}\cdot 373^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.9504800000.1	x^10 - 3x^9 + 3x^8 - 3x^6 + 3x^5 + x^4 - 6x^3 + 9x^2 - 7x + 1	\( 2^{8}\cdot 5^{5}\cdot 109^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.9519514624.1	x^10 - 2x^9 + 3x^8 + 2x^5 + 3x^4 + 5x^2 + 4	\( -\,2^{10}\cdot 3049^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.11151003125.1	x^10 - 3x^9 + 4x^8 - 7x^6 + 11x^5 - 11x^4 + 7x^3 - 2x^2 + 1	\( 5^{5}\cdot 1889^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.11522834432.1	x^10 - 4x^9 + 8x^8 - 10x^7 + 10x^6 - 10x^5 + 9x^4 - 4x^3 + 1	\( -\,2^{15}\cdot 593^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.11825491968.1	x^10 - 3x^9 + 4x^8 - 5x^7 + 9x^6 - 14x^5 + 11x^4 - 7x^3 + 2x^2 + 5x + 1	\( -\,2^{12}\cdot 3^{5}\cdot 109^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.12642650667.1	x^10 - 3x^9 + 6x^8 - 7x^7 + 2x^6 + 7x^5 - 8x^4 - x^3 + 8x^2 - 5x + 1	\( -\,3^{5}\cdot 7213^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.13683333888.2	x^10 - 2x^9 + 2x^8 - 4x^7 + 8x^6 - 2x^5 - 8x^3 + 4x^2 + 4x + 4	\( -\,2^{8}\cdot 3^{5}\cdot 7^{2}\cdot 67^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.14164503125.1	x^10 - 3x^9 + 3x^8 + 4x^7 - 10x^6 + 6x^5 + 5x^4 - 6x^3 - 2x^2 + 2x + 1	\( 5^{5}\cdot 2129^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.14324628125.1	x^10 - x^9 - x^8 + 5x^6 + x^5 - 8x^4 + 5x^2 - 1	\( 5^{5}\cdot 2141^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.14841577472.1	x^10 - 2x^9 + 3x^8 - 6x^7 + 6x^6 - 6x^5 + 5x^4 - 2x^3 + 5x^2 - 4x + 4	\( -\,2^{15}\cdot 673^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.15138753125.1	x^10 - 4x^9 + 6x^8 - 2x^7 - 6x^5 + 8x^4 + x^3 - 6x^2 + 2x + 1	\( 5^{5}\cdot 31^{2}\cdot 71^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.15296742400.1	x^10 - 4x^9 + 5x^8 + 2x^7 - 11x^6 + 12x^5 - 2x^4 - 8x^3 + 9x^2 - 4x + 1	\( -\,2^{10}\cdot 5^{2}\cdot 773^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.15618166227.1	x^10 + 5x^8 - 3x^7 + 6x^6 - 7x^5 + 5x^4 - x^3 + 4x^2 - 4x + 1	\( -\,3^{5}\cdot 8017^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.17125878125.1	x^10 - 5x^9 + 14x^8 - 25x^7 + 31x^6 - 29x^5 + 24x^4 - 23x^3 + 21x^2 - 14x + 4	\( 5^{5}\cdot 2341^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.17760800000.2	x^10 - 5x^9 + 11x^8 - 12x^7 + 5x^6 + 5x^5 - 11x^4 + 12x^3 - 7x^2 + 3x - 1	\( 2^{8}\cdot 5^{5}\cdot 149^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.18043403427.1	x^10 - 4x^9 + 11x^8 - 17x^7 + 22x^6 - 19x^5 + 11x^4 - 5x^3 + 1	\( -\,3^{5}\cdot 7^{2}\cdot 1231^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.18907839963.1	x^10 - 3x^9 + 2x^8 + 3x^7 - 6x^6 + 7x^5 - 4x^4 - 5x^3 + 10x^2 - 5x + 1	\( -\,3^{5}\cdot 8821^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.19477958787.1	x^10 - 3x^9 + x^8 + x^7 + 5x^6 - x^5 - 3x^4 - 7x^3 - 2x^2 + 6x + 3	\( -\,3^{5}\cdot 7^{2}\cdot 1279^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.19739903067.1	x^10 + x^8 - 2x^7 - 4x^6 - x^5 + 9x^4 + 2x^3 - 5x^2 - 3x + 3	\( -\,3^{5}\cdot 9013^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.20240703125.1	x^10 - x^9 + 5x^8 - 6x^7 + 10x^6 - 6x^5 + 5x^4 - x^3 - 5x^2 + 4x - 1	\( 5^{7}\cdot 509^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.20561265664.1	x^10 - 4x^9 + 8x^8 - 10x^7 + 12x^6 - 18x^5 + 21x^4 - 12x^3 + 2x^2 + 1	\( -\,2^{10}\cdot 4481^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.21271503125.1	x^10 - 3x^6 - x^5 + 5x^3 + x^2 - x - 1	\( 5^{5}\cdot 2609^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.21549213027.1	x^10 - 3x^9 + 2x^8 + 3x^6 - 4x^4 - 3x^3 + x^2 + 3x + 3	\( -\,3^{7}\cdot 43^{2}\cdot 73^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.21622501827.1	x^10 - 3x^9 - 2x^8 + 10x^7 + 3x^6 - 15x^5 - x^4 + 3x^3 + 9x^2 - 5x + 1	\( -\,3^{5}\cdot 9433^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.2.21796503125.1	x^10 - 2x^8 - 3x^7 + x^6 + 4x^5 + x^4 - 6x^3 - 9x^2 - 5x - 1	\( 5^{5}\cdot 19^{2}\cdot 139^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial
10.0.21904000000.1	x^10 - 4x^9 + 9x^8 - 10x^7 + x^6 + 12x^5 - 14x^4 + 4x^3 + 5x^2 - 4x + 1	\( -\,2^{10}\cdot 5^{6}\cdot 37^{2} \)	$D_5^2 : C_2$ (as 10T21)	Trivial