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 1213)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.5841576387.1	x^10 - x^9 + 5x^8 - 3x^7 + 8x^6 - 4x^5 + 4x^4 - 3x^3 - x + 1	\( -\,3^{5}\cdot 4903^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.6381378125.1	x^10 - 4x^9 + 8x^8 - 12x^7 + 18x^6 - 21x^5 + 18x^4 - 9x^3 + x^2 + 2x - 1	\( 5^{5}\cdot 1429^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.6652128125.1	x^10 - x^9 - x^8 + x^7 - 2x^6 - 2x^3 + 3x^2 - x + 1	\( 5^{5}\cdot 1459^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.8160800000.1	x^10 - 3x^9 + 5x^8 - 10x^7 + 13x^6 - 11x^5 + 9x^4 - 8x^3 + 3x^2 + x - 1	\( 2^{8}\cdot 5^{5}\cdot 101^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.8171701443.1	x^10 - x^9 - 4x^8 - 4x^7 + 7x^6 + 12x^5 + 13x^4 + 5x^3 + 2x^2 - x + 1	\( -\,3^{7}\cdot 1933^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.8394753125.1	x^10 - 2x^9 + 2x^8 - 5x^7 + 6x^6 - 7x^5 + 10x^4 - 7x^3 + 5x^2 - 3x + 1	\( 5^{5}\cdot 11^{2}\cdot 149^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.12759961600.1	x^10 - 2x^7 + 3x^6 - 2x^5 + 3x^4 - 2x^3 + 4x^2 - 2x + 1	\( -\,2^{12}\cdot 5^{2}\cdot 353^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.14512578125.1	x^10 - x^9 + 4x^8 - 6x^7 + 7x^6 - 10x^5 + 8x^4 - 7x^3 + 3x^2 - x + 1	\( 5^{7}\cdot 431^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.14753809152.1	x^10 - x^9 + 3x^8 + 4x^6 + 8x^5 + 8x^4 + 12x^3 + 11x^2 + 5x + 1	\( -\,2^{8}\cdot 3^{5}\cdot 487^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.14974128125.1	x^10 - 3x^9 + 7x^8 - 9x^7 + 9x^6 - 7x^5 + 3x^4 + 4x^3 - 5x^2 + 1	\( 5^{5}\cdot 11^{2}\cdot 199^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.15462704547.1	x^10 - 2x^9 + 8x^8 - 11x^7 + 22x^6 - 18x^5 + 22x^4 - 8x^3 + 8x^2 - 2x + 1	\( -\,3^{7}\cdot 2659^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.16139161600.1	x^10 - 4x^9 + 7x^8 - 6x^7 + x^6 + 6x^5 - 10x^4 + 6x^3 + 2x^2 - 4x + 2	\( -\,2^{12}\cdot 5^{2}\cdot 397^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.16687871667.1	x^10 - 2x^9 - 2x^8 + 4x^7 + 6x^6 - 5x^5 - 4x^4 + 2x^3 + 2x^2 - 2x + 1	\( -\,3^{5}\cdot 8287^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.17243128125.1	x^10 - 3x^9 + 5x^8 - 4x^7 - x^6 + 3x^5 - 2x^4 + 2x^2 - x - 1	\( 3^{8}\cdot 5^{5}\cdot 29^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.17760800000.1	x^10 - x^9 + 3x^8 - 2x^7 + 2x^6 + 2x^5 - 2x^4 + 2x^3 + x^2 - x - 1	\( 2^{8}\cdot 5^{5}\cdot 149^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.18620253125.1	x^10 - 2x^9 + 3x^8 + x^7 - 5x^6 + 3x^5 + x^4 - 5x^3 - x^2 + 2x + 1	\( 5^{5}\cdot 2441^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.18801894400.1	x^10 - 2x^9 + x^8 + x^6 - 2x^4 - 2x^3 + x^2 + 2x + 1	\( -\,2^{10}\cdot 5^{2}\cdot 857^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.19546878125.1	x^10 - 2x^9 + 4x^8 - 4x^7 + x^6 - 3x^4 + x + 1	\( 5^{5}\cdot 41^{2}\cdot 61^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.20817378125.1	x^10 - x^9 + 2x^8 - 3x^7 + 5x^6 - x^5 - x^4 - 6x^2 + 6x - 1	\( 5^{5}\cdot 29^{2}\cdot 89^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.22194716672.1	x^10 - 4x^9 + 8x^8 - 14x^7 + 19x^6 - 20x^5 + 17x^4 - 8x^3 + 3x^2 - 2x + 1	\( 2^{15}\cdot 823^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.23103003125.1	x^10 - x^9 - 2x^8 + x^6 + 4x^5 + x^3 - 5x^2 + x - 1	\( 5^{5}\cdot 2719^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.29237507523.1	x^10 + 2x^8 - 3x^7 - 3x^6 - 5x^5 - 4x^4 + 4x^3 + 7x^2 + 7x + 7	\( -\,3^{5}\cdot 7^{2}\cdot 1567^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.29703138048.1	x^10 - 4x^9 + 8x^8 - 10x^7 + 8x^6 - 2x^5 - 8x^3 + 16x^2 - 12x + 4	\( -\,2^{8}\cdot 3^{5}\cdot 691^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.32338268928.1	x^10 - 4x^9 + 13x^8 - 30x^7 + 59x^6 - 84x^5 + 91x^4 - 66x^3 + 31x^2 - 8x + 1	\( -\,2^{8}\cdot 3^{5}\cdot 7^{2}\cdot 103^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.33028128125.1	x^10 - 3x^9 + 2x^8 + 4x^6 - 4x^5 - 5x^4 + 6x^3 - x + 1	\( 5^{5}\cdot 3251^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.35163750400.1	x^10 - 4x^9 + 10x^8 - 16x^7 + 19x^6 - 22x^5 + 26x^4 - 26x^3 + 21x^2 - 10x + 2	\( -\,2^{14}\cdot 5^{2}\cdot 293^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.42179301376.1	x^10 - 4x^9 + 7x^8 - 6x^7 + 3x^6 - 4x^5 + 4x^4 + 2x^3 - 4x^2 + 2	\( -\,2^{12}\cdot 3209^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.42436001792.1	x^10 - x^6 + 8x^4 - 12x^3 + 12x^2 - 8x + 4	\( -\,2^{17}\cdot 569^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.42926115483.1	x^10 - 3x^9 + 2x^8 + 5x^7 - 17x^6 + 20x^5 + x^4 - 30x^3 + 42x^2 - 27x + 9	\( -\,3^{5}\cdot 13291^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.46091337728.1	x^10 - 7x^6 - 8x^5 - 10x^4 - 8x^3 - 2x^2 - 4x + 2	\( 2^{17}\cdot 593^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.46323879507.1	x^10 - 2x^9 - 2x^8 + 4x^7 + 6x^6 - 9x^5 - 9x^4 + 8x^3 + 9x^2 + 2x + 1	\( -\,3^{5}\cdot 13807^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.47010848283.1	x^10 - x^9 - 4x^8 + 6x^7 + 9x^6 - 9x^5 - 15x^4 + 7x^3 + 23x^2 + 9x + 1	\( -\,3^{5}\cdot 7^{2}\cdot 1987^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.48194406027.1	x^10 - 5x^8 - 5x^7 + 15x^6 + 15x^5 - 19x^4 - 18x^3 + 9x^2 + 7x + 1	\( -\,3^{5}\cdot 14083^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.51536628125.1	x^10 - x^9 - x^8 + 4x^7 - 2x^6 + 2x^5 - 2x^4 - 5x^3 + 9x^2 - 5x + 1	\( 5^{5}\cdot 31^{2}\cdot 131^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.55243801600.1	x^10 - 2x^9 + 5x^8 - 8x^7 + 11x^6 - 10x^5 + 4x^4 - 2x^3 + 5x^2 - 4x + 1	\( -\,2^{10}\cdot 5^{2}\cdot 13^{2}\cdot 113^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.66261038067.1	x^10 - x^9 + 6x^8 - 6x^7 + 19x^6 - 23x^5 + 31x^4 - 25x^3 + 15x^2 - 5x + 1	\( -\,3^{5}\cdot 7^{4}\cdot 337^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.66632941568.1	x^10 - 2x^9 - x^8 + 2x^7 + x^6 - 4x^5 + 4x^4 + 4x^3 - 2x^2 - 4x + 2	\( 2^{17}\cdot 23^{2}\cdot 31^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.69620000000.1	x^10 - 3x^9 + x^8 + 8x^7 - 13x^6 - 5x^5 + 37x^4 - 44x^3 + 23x^2 - 3x - 1	\( 2^{8}\cdot 5^{7}\cdot 59^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.71073003125.1	x^10 + x^8 - 2x^7 + 6x^6 - 10x^5 + 12x^4 - 9x^3 + 5x^2 + x - 1	\( 5^{5}\cdot 19^{2}\cdot 251^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.71252957167.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 14x^6 - 14x^5 + 10x^4 - 5x^3 + 2x^2 - x + 1	\( -\,7^{5}\cdot 29^{2}\cdot 71^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.72719062443.1	x^10 - 3x^9 - x^8 + 13x^7 - 4x^6 - 24x^5 + 14x^4 + 13x^3 - 7x^2 - 2x + 1	\( -\,3^{5}\cdot 17299^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.73833061923.1	x^10 - 2x^9 + 6x^8 - 8x^7 + 12x^6 - 7x^5 + 10x^4 + 4x^3 + 4x^2 + 4x + 1	\( -\,3^{5}\cdot 17431^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.74145753125.1	x^10 - 2x^9 + x^8 + x^7 - x^6 - 4x^5 - 2x^4 - 7x^2 - 5x - 1	\( 5^{5}\cdot 4871^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.75522050000.1	x^10 - 2x^8 - 4x^7 - x^6 + 2x^5 + x^4 - 4x^3 + 2x + 1	\( 2^{4}\cdot 5^{5}\cdot 1229^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.77914570752.1	x^10 - 2x^8 - 2x^7 - 3x^6 + 4x^5 + 7x^4 + 2x^3 - 2x^2 - 4x + 3	\( -\,2^{17}\cdot 3^{2}\cdot 257^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.78452312832.1	x^10 - 5x^9 + 13x^8 - 20x^7 + 18x^6 - 4x^5 - 8x^4 + 8x^3 + x^2 - 3x + 3	\( -\,2^{8}\cdot 3^{5}\cdot 1123^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.80420573952.1	x^10 - 4x^9 + 10x^8 - 14x^7 + 16x^6 - 14x^5 + 8x^4 - 12x^3 + 8x^2 + 4	\( -\,2^{8}\cdot 3^{7}\cdot 379^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.81271579392.1	x^10 - 2x^9 + 2x^8 - 4x^6 + 2x^5 - 4x^3 + 8x^2 - 4x + 4	\( -\,2^{8}\cdot 3^{9}\cdot 127^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.2.81408800000.1	x^10 - 3x^9 - x^8 + 8x^7 + x^6 - 7x^5 - 7x^4 + 2x^3 + 5x^2 + 5x + 1	\( 2^{8}\cdot 5^{5}\cdot 11^{2}\cdot 29^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial
10.0.81491689472.1	x^10 - 4x^9 + 8x^8 - 14x^7 + 17x^6 - 12x^5 + 17x^4 - 24x^3 + 17x^2 - 6x + 1	\( -\,2^{15}\cdot 19^{2}\cdot 83^{2} \)	$A_5 \wr C_2$ (as 10T40)	Trivial