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 6921)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.95820414976.1	x^10 - 3x^8 - 2x^7 + x^6 + 4x^5 + 6x^4 - 6x^2 - 2x - 1	\( 2^{15}\cdot 11^{3}\cdot 13^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.197544116224.1	x^10 - 2x^9 + x^8 - 9x^2 + 2x - 1	\( 2^{18}\cdot 7^{3}\cdot 13^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.485773018381.1	x^10 - x^9 - x^8 + 6x^7 - 2x^6 - x^5 + 6x^4 - 3x^3 + 2x^2 + 8x + 1	\( 7^{3}\cdot 1123^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.663676747776.1	x^10 - 4x^9 + 3x^8 + 6x^7 - 9x^6 + 12x^5 - 12x^3 + 12x^2 - 2x - 1	\( 2^{15}\cdot 3^{10}\cdot 7^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.828465164288.1	x^10 - 3x^8 - 4x^7 - 3x^6 + 10x^5 + 16x^4 + 2x^3 - 6x^2 - 8x - 3	\( 2^{12}\cdot 587^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.1289945088000.1	x^10 - 4x^9 + 6x^8 + 4x^7 - 19x^6 + 36x^5 - 38x^4 + 32x^3 - 18x^2 + 8x - 2	\( 2^{19}\cdot 3^{9}\cdot 5^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.1508214295232.1	x^10 - 3x^9 - 5x^8 + 22x^7 - 2x^6 - 47x^5 + 30x^4 + 31x^3 - 22x^2 - 24x + 17	\( -\,2^{6}\cdot 47^{3}\cdot 61^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.1680066179072.1	x^10 + 2x^8 - 9x^6 - 8x^5 - 17x^4 - 14x^3 + 4x^2 + 4x + 2	\( -\,2^{12}\cdot 743^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.2144692699136.1	x^10 - 2x^9 + 4x^8 - 6x^7 + 7x^6 - 4x^5 + 3x^4 - 6x^3 - 8x^2 - 8x - 2	\( 2^{15}\cdot 13^{3}\cdot 31^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.2653290315584.1	x^10 - 3x^9 - x^8 + 10x^7 - 2x^6 - 3x^5 + 8x^4 - 3x^3 - 6x^2 + 4x - 1	\( 2^{6}\cdot 3461^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.2.2714614890496.1	x^10 - 2x^9 + x^8 + 4x^7 + x^6 + 10x^5 + 15x^4 - 10x^2 - 8x - 2	\( 2^{19}\cdot 173^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.2907063451648.1	x^10 - 2x^9 - 4x^8 + 16x^7 + 4x^6 - 32x^5 + 10x^4 + 8x^3 - 8x^2 + 16x - 8	\( 2^{18}\cdot 223^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.2916851535872.1	x^10 - 4x^9 + 4x^8 + 6x^7 - 9x^6 - 2x^5 + 6x^4 + 16x^3 - 12x^2 - 24x + 8	\( 2^{12}\cdot 19^{3}\cdot 47^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.4.3045472337375.1	x^10 - 2x^9 - 8x^8 + 12x^7 + 21x^6 - 24x^5 - 31x^4 + 8x^3 + 13x^2 - 8x + 1	\( -\,5^{3}\cdot 13^{3}\cdot 223^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.3196661779891.1	x^10 - x^9 - 9x^8 + 7x^7 + 28x^6 - 13x^5 - 35x^4 + 19x^2 + 4x - 3	\( -\,14731^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.3210352427008.1	x^10 - 2x^9 + 2x^8 - 6x^7 + x^6 + 12x^5 + 3x^4 - 2x^3 - 8x^2 - 4x - 2	\( 2^{15}\cdot 461^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.3359232000000.1	x^10 - 4x^9 + 11x^8 - 28x^7 + 48x^6 - 64x^5 + 75x^4 - 58x^3 + 22x^2 - 4x + 2	\( 2^{15}\cdot 3^{8}\cdot 5^{6} \)	$S_{6}$ (as 10T32)	Trivial
10.2.3659442442069.1	x^10 - 4x^8 - 4x^7 + 4x^6 - x^5 + 4x^4 - 9x^3 + 9x^2 - 5x + 1	\( 41^{4}\cdot 109^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.2.3820559641137.1	x^10 - x^9 - 3x^8 - 6x^7 + 9x^6 + 3x^5 + 24x^4 - 3x^3 + 6x^2 - 8x - 1	\( 3^{12}\cdot 193^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.2.4145348870144.1	x^10 - 2x^9 - 6x^8 + 8x^7 + 6x^6 - 20x^5 + 10x^4 + 24x^3 - 16x^2 + 16	\( 2^{18}\cdot 251^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.4475809792000.1	x^10 - 2x^9 - 4x^8 + 6x^7 + 9x^6 - 4x^5 - 13x^4 - 6x^3 + 8x^2 + 8x + 2	\( 2^{15}\cdot 5^{3}\cdot 103^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.4644089101504.1	x^10 - 5x^9 + 8x^8 - x^7 - 5x^6 - 7x^5 + 27x^4 - 20x^3 - 24x^2 + 49x - 22	\( 2^{6}\cdot 43^{3}\cdot 97^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.5100326977536.1	x^10 - 2x^9 + 2x^8 - 8x^7 + 26x^6 - 20x^5 + 13x^4 - 30x^3 + 23x^2 + 20x - 19	\( 2^{15}\cdot 3^{3}\cdot 7^{8} \)	$S_{6}$ (as 10T32)	Trivial
10.2.5246255333376.1	x^10 - 4x^9 + 5x^8 + 4x^7 - 18x^6 + 8x^5 + 19x^4 - 18x^3 - 10x^2 + 8x - 2	\( 2^{15}\cdot 3^{3}\cdot 181^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.5785159315869.1	x^10 - 2x^9 + 3x^8 + 3x^7 - 3x^6 + 9x^3 + 33x^2 + x - 14	\( 3^{10}\cdot 461^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.6322388744771.1	x^10 - x^9 - 6x^8 + 19x^6 + 22x^5 - 29x^4 - 59x^3 - 7x^2 + 45x + 31	\( -\,11^{3}\cdot 41^{6} \)	$S_{6}$ (as 10T32)	Trivial
10.2.6850339647488.1	x^10 + 5x^8 - 6x^7 + 4x^6 - 14x^5 - 18x^4 - 14x^3 - 21x^2 - 14x - 3	\( 2^{12}\cdot 1187^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.7346640384000.1	x^10 - 2x^9 - 3x^8 + 10x^7 - 5x^6 - 18x^5 + 21x^4 + 18x^3 - 24x^2 - 16x + 26	\( 2^{12}\cdot 3^{15}\cdot 5^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.7522959753216.1	x^10 - 2x^9 + 3x^8 - 8x^7 + x^6 + 6x^5 + 5x^4 + 8x^3 - 6x^2 - 8x - 2	\( 2^{19}\cdot 3^{15} \)	$S_{6}$ (as 10T32)	Trivial
10.2.7864682820608.1	x^10 - 4x^9 + 7x^8 - 10x^7 + 10x^6 - 2x^5 - 6x^4 + 18x^3 - 43x^2 + 62x - 49	\( 2^{10}\cdot 1973^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.4.8057738350592.1	x^10 - 2x^9 - 4x^8 + 10x^7 - 2x^6 + 4x^5 - 5x^4 - 40x^3 + 43x^2 + 28x - 35	\( -\,2^{12}\cdot 7^{3}\cdot 179^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.8350600527872.1	x^10 - 4x^9 + 14x^8 - 24x^7 + 35x^6 - 36x^5 + 24x^4 - 20x^3 - 12x^2 - 8x - 4	\( 2^{18}\cdot 317^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.4.8776234231883.1	x^10 - 2x^9 - 2x^8 + 2x^7 + 5x^6 + 6x^5 - 27x^4 + 21x^3 + 25x^2 - 51x + 14	\( -\,20627^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.8813954560000.1	x^10 - 4x^9 - 2x^8 + 38x^7 - 82x^6 + 68x^5 - 7x^4 - 12x^3 - 9x^2 + 6x + 5	\( 2^{12}\cdot 5^{4}\cdot 151^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.9069459977216.1	x^10 - 4x^9 + x^8 + 8x^7 - 10x^5 - 28x^4 - 8x^3 - 5x^2 + 6x - 1	\( 2^{10}\cdot 2069^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.2.9921743286272.1	x^10 - 2x^9 - 6x^7 - 15x^6 - 16x^5 - 11x^4 - 44x^3 + 4x^2 - 8x + 8	\( 2^{12}\cdot 17^{3}\cdot 79^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.10903552000000.1	x^10 - 4x^9 + 8x^8 - 4x^7 + 3x^6 - 4x^5 - 22x^4 + 16x^3 - 12x^2 + 16x - 8	\( 2^{19}\cdot 5^{6}\cdot 11^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.11007962872832.1	x^10 - 4x^9 + x^8 + 18x^7 - 26x^6 - 10x^5 + 46x^4 - 42x^3 + 9x^2 + 38x - 47	\( -\,2^{10}\cdot 2207^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.4.11076145588171.1	x^10 - x^9 - 9x^8 + 5x^7 + 32x^6 - 5x^5 - 49x^4 - 6x^3 + 17x^2 + 10x + 9	\( -\,22291^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.11295211407453.1	x^10 - 12x^8 + 51x^6 - 3x^5 - 90x^4 + 18x^3 + 54x^2 - 24x + 9	\( 3^{12}\cdot 277^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.2.11678542364672.1	x^10 - 4x^9 + 11x^8 - 24x^7 + 40x^6 - 52x^5 + 45x^4 - 30x^3 + 26x^2 - 12x - 2	\( 2^{15}\cdot 709^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12397455648000.1	x^10 - 4x^9 + 9x^8 - 18x^7 + 36x^6 - 36x^5 + 54x^4 - 54x^3 + 27x^2 - 36x + 9	\( 2^{8}\cdot 3^{18}\cdot 5^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12532434748352.1	x^10 - x^9 - 6x^8 + 2x^7 + 21x^6 - 41x^4 - 9x^3 + 40x^2 + 10x - 19	\( 2^{6}\cdot 5807^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12694994583552.1	x^10 - 2x^9 - 12x^7 + 6x^6 + 21x^4 - 6x^3 - 9x^2 - 4x - 1	\( 2^{15}\cdot 3^{18} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12694994583552.2	x^10 - 4x^9 + 9x^8 - 18x^7 + 27x^6 - 36x^5 + 12x^4 - 12x^3 + 2x + 1	\( 2^{15}\cdot 3^{18} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12694994583552.3	x^10 - 2x^9 - 9x^6 + 18x^2 - 12x + 6	\( 2^{15}\cdot 3^{18} \)	$S_{6}$ (as 10T32)	Trivial
10.2.12938153594176.1	x^10 - x^9 + 10x^8 - 8x^7 + 32x^6 - 26x^5 + 34x^4 - 48x^3 - x^2 - 37x - 12	\( 2^{6}\cdot 5869^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.4.13669658484283.1	x^10 - x^9 - 8x^8 + 11x^7 + 13x^6 - 37x^5 + 39x^4 + 16x^3 - 110x^2 + 101x - 24	\( -\,17^{4}\cdot 547^{3} \)	$S_{6}$ (as 10T32)	Trivial
10.2.13741221777408.1	x^10 - 2x^9 + 9x^8 - 18x^7 + 20x^6 - 2x^5 + 3x^4 + 6x^3 - 2x^2 + 4x + 2	\( 2^{12}\cdot 3^{3}\cdot 499^{3} \)	$S_{6}$ (as 10T32)	$[2]$
10.4.13787743742739.1	x^10 - 9x^8 - x^7 + 29x^6 + 8x^5 - 39x^4 - 21x^3 + 18x^2 + 15x + 2	\( -\,3^{3}\cdot 7993^{3} \)	$S_{6}$ (as 10T32)	Trivial