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 101)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.104256800000.1	x^10 - 3x^9 + 7x^8 - 10x^7 + 11x^6 - 3x^5 - 5x^4 + 12x^3 - 10x^2 + 8x - 4	\( 2^{8}\cdot 5^{5}\cdot 19^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.109853253125.1	x^10 - 4x^9 + 12x^8 - 24x^7 + 41x^6 - 52x^5 + 51x^4 - 34x^3 + 22x^2 - 9x + 1	\( 5^{5}\cdot 7^{4}\cdot 11^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.179030503125.1	x^10 - 3x^9 + 6x^8 - 6x^7 + 6x^6 - 4x^5 + 3x^4 + 4x^3 + 4x^2 - x - 1	\( 3^{4}\cdot 5^{5}\cdot 29^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.187404800000.1	x^10 - x^9 + x^7 + 5x^6 - 10x^5 + 7x^4 + 7x^3 - 10x^2 + 3x + 1	\( 2^{12}\cdot 5^{5}\cdot 11^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.812952003125.2	x^10 - 4x^9 + 6x^8 - 2x^7 - 10x^6 + 28x^5 - 35x^4 + 20x^3 - 2x^2 - 2x + 1	\( 5^{5}\cdot 127^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.812952003125.4	x^10 - 2x^9 + x^8 - 5x^7 - 3x^6 + x^5 + 7x^4 + 15x^3 + 16x^2 + 13x + 11	\( 5^{5}\cdot 127^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1595351953125.1	x^10 - x^9 - 5x^8 + 2x^7 + 10x^6 + 4x^5 - 9x^4 - 10x^3 + 3x^2 + 5x - 5	\( 3^{5}\cdot 5^{8}\cdot 7^{5} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1811791397533.1	x^10 - 3x^9 + 3x^8 - 3x^7 + 4x^6 - 6x^5 + 24x^4 - 46x^3 + 37x^2 - 11x + 1	\( 13^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1811791397533.2	x^10 - x^9 + 4x^8 - 10x^7 + 15x^6 - 11x^5 - x^4 + 11x^3 - 4x^2 + 2x + 3	\( 13^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.3110400000000.1	x^10 - 2x^9 + 7x^8 - 6x^7 + 10x^6 - 6x^5 - x^4 + 6x^3 - 23x^2 + 20x - 2	\( 2^{15}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2$ (as 10T9)	Trivial
10.2.3110400000000.2	x^10 - 2x^9 + 5x^8 - 12x^7 + 23x^6 - 36x^5 + 53x^4 - 50x^3 + 28x^2 - 12x + 3	\( 2^{15}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2$ (as 10T9)	Trivial
10.2.3688067268608.1	x^10 - 2x^9 - x^8 + 2x^7 + 5x^6 - 4x^5 - 6x^4 + 2x^3 + 9x^2 - 6x + 1	\( 2^{15}\cdot 103^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.3688067268608.4	x^10 - 2x^9 - x^8 - 2x^7 + 15x^6 - 12x^5 - 2x^4 - 14x^3 + 41x^2 - 30x + 7	\( 2^{15}\cdot 103^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.0.26477528679424.2	x^10 - 2x^9 - 6x^8 + 2x^7 + 27x^6 + 54x^5 + 56x^4 + 36x^3 + 6x^2 - 6x + 1	\( -\,2^{10}\cdot 401^{4} \)	$D_5^2$ (as 10T9)	$[5]$
10.0.26477528679424.3	x^10 - 4x^9 + 5x^8 - x^6 - 36x^5 + 143x^4 - 286x^3 + 352x^2 - 254x + 85	\( -\,2^{10}\cdot 401^{4} \)	$D_5^2$ (as 10T9)	$[5]$
10.0.38032777053184.2	x^10 - 2x^9 + 10x^8 - 34x^7 + 67x^6 - 82x^5 + 60x^4 - 28x^3 + 2x^2 + 6x + 1	\( -\,2^{10}\cdot 439^{4} \)	$D_5^2$ (as 10T9)	$[5]$
10.0.38032777053184.3	x^10 - 2x^9 - 6x^8 + 24x^7 + 5x^6 - 114x^5 + 180x^4 - 70x^3 - 22x^2 - 20x + 25	\( -\,2^{10}\cdot 439^{4} \)	$D_5^2$ (as 10T9)	$[5]$
10.2.49766400000000.3	x^10 - 2x^9 - x^8 + 8x^7 - 20x^6 + 16x^5 - 34x^4 + 128x^3 - 144x^2 - 32	\( 2^{19}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2$ (as 10T9)	Trivial (GRH)
10.2.49766400000000.4	x^10 - 2x^9 - 5x^8 + 4x^7 + 24x^6 + 8x^5 - 32x^4 - 40x^3 + 4x^2 + 24x + 12	\( 2^{19}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2$ (as 10T9)	Trivial
10.2.60750000000000.1	x^10 - 10x^7 - 10x^6 + 28x^5 + 25x^4 + 50x^3 - 190x^2 + 130x - 47	\( 2^{10}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.60750000000000.6	x^10 + 10x^6 - 2x^5 - 75x^4 + 150x^3 - 110x^2 + 50x - 11	\( 2^{10}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.61798095703125.1	x^10 - 10x^8 + 35x^6 - x^5 - 50x^4 + 5x^3 + 25x^2 - 5x - 11	\( 3^{4}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.61798095703125.2	x^10 + 10x^8 + 35x^6 - 3x^5 + 50x^4 - 15x^3 + 25x^2 - 15x + 1	\( 3^{4}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.64732311309312.2	x^10 - 4x^9 + x^8 + 14x^7 - 19x^6 + 22x^4 - 36x^3 + 45x^2 - 36x + 9	\( 2^{10}\cdot 3^{5}\cdot 127^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.64732311309312.3	x^10 - 2x^9 - 4x^8 + 12x^7 + 5x^6 - 36x^5 + 20x^4 + 10x^3 + 10x^2 - 24x + 9	\( 2^{10}\cdot 3^{5}\cdot 127^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.128000000000000.2	x^10 - 20x^7 + 30x^6 - 20x^5 + 50x^4 - 100x^3 + 85x^2 - 20x + 2	\( 2^{19}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.128000000000000.8	x^10 + 10x^8 + 25x^6 - 8x^5 - 50x^4 - 40x^3 + 80x^2 - 16	\( 2^{19}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.195312500000000.1	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x - 16	\( 2^{8}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.195312500000000.3	x^10 + 10x^8 + 35x^6 - 2x^5 + 50x^4 - 10x^3 + 25x^2 - 10x - 4	\( 2^{8}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.310144849772544.1	x^10 - 2x^9 - 7x^8 + 20x^7 + 7x^6 - 52x^5 + 37x^4 - 14x^3 + 6x^2 + 12x + 1	\( 2^{15}\cdot 3^{5}\cdot 79^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.310144849772544.3	x^10 - 12x^8 - 6x^7 + 65x^6 + 48x^5 - 219x^4 - 36x^3 + 235x^2 + 54x - 135	\( 2^{15}\cdot 3^{5}\cdot 79^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.338376389437717.1	x^10 - 3x^9 + 3x^8 - 15x^7 - 9x^6 - 61x^5 - 39x^4 - 116x^3 - 118x^2 - 57x - 9	\( 37^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.338376389437717.2	x^10 + 4x^8 - 13x^7 - 10x^6 - 44x^5 - 69x^4 - 167x^3 - 204x^2 - 170x - 67	\( 37^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.499679334400000.1	x^10 - 2x^9 - 5x^8 + 14x^7 + 6x^6 - 24x^5 - 19x^4 + 50x^3 + 5x^2 - 50x + 25	\( 2^{15}\cdot 5^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	$[2]$
10.2.499679334400000.4	x^10 - 4x^9 + 6x^8 + 6x^7 - 48x^6 + 58x^5 + x^4 + 20x^3 + 84x^2 - 180x + 135	\( 2^{15}\cdot 5^{5}\cdot 47^{4} \)	$D_5^2$ (as 10T9)	$[2]$
10.2.648000000000000.2	x^10 - 10x^8 - 20x^7 - 45x^6 - 102x^5 - 100x^4 - 50x^3 - 50x^2 - 40x - 17	\( 2^{15}\cdot 3^{4}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.648000000000000.3	x^10 + 10x^8 - 20x^7 - 45x^6 - 6x^5 + 50x^4 + 90x^3 + 90x^2 + 40x + 7	\( 2^{15}\cdot 3^{4}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.997094970703125.1	x^10 - 15x^7 + 10x^6 - 4x^5 - 75x^4 - 75x^3 - 50x^2 - 20x - 17	\( 3^{5}\cdot 5^{12}\cdot 7^{5} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1608361479003125.2	x^10 - 3x^9 + 6x^8 - 44x^7 + 37x^6 - 81x^5 + 357x^4 + 253x^3 + 978x^2 + 464x + 661	\( 5^{5}\cdot 7^{4}\cdot 11^{8} \)	$D_5^2$ (as 10T9)	$[5]$
10.2.1831817626953125.1	x^10 - 10x^8 + 35x^6 - 11x^5 - 50x^4 + 55x^3 + 25x^2 - 55x - 31	\( 5^{17}\cdot 7^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1831817626953125.2	x^10 + 10x^8 + 35x^6 - 7x^5 + 50x^4 - 35x^3 + 25x^2 - 35x + 11	\( 5^{17}\cdot 7^{4} \)	$D_5^2$ (as 10T9)	Trivial
10.2.1944000000000000.2	x^10 - 10x^7 - 20x^6 - 38x^5 - 125x^4 - 200x^3 - 340x^2 - 100x - 23	\( 2^{15}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.2743793676800000.1	x^10 - x^9 + 9x^8 - 36x^7 + 35x^6 - 99x^5 + 443x^4 + 84x^3 - 400x^2 + 52x + 76	\( 2^{12}\cdot 5^{5}\cdot 11^{8} \)	$D_5^2$ (as 10T9)	$[5]$
10.2.3125000000000000.5	x^10 + 10x^8 + 35x^6 - 8x^5 + 50x^4 - 40x^3 + 25x^2 - 40x - 4	\( 2^{12}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.3125000000000000.8	x^10 - 10x^8 + 35x^6 - 4x^5 - 50x^4 + 20x^3 + 25x^2 - 20x - 76	\( 2^{12}\cdot 5^{17} \)	$D_5^2$ (as 10T9)	Trivial
10.2.4201750000000000.2	x^10 + 10x^8 - 10x^7 + 45x^6 - 28x^5 + 125x^4 + 10x^3 - 10x^2 + 220x - 131	\( 2^{10}\cdot 5^{12}\cdot 7^{5} \)	$D_5^2$ (as 10T9)	Trivial (GRH)
10.2.4201750000000000.3	x^10 - 10x^7 + 10x^6 - 4x^5 + 25x^4 - 50x^3 - 130x^2 - 300x - 108	\( 2^{10}\cdot 5^{12}\cdot 7^{5} \)	$D_5^2$ (as 10T9)	Trivial (GRH)
10.0.6582258418359375.1	x^10 - 3x^9 + 13x^8 - 34x^7 + 21x^6 + 15x^5 + 86x^4 - 111x^3 + 18x^2 + 38x + 211	\( -\,3^{5}\cdot 5^{8}\cdot 37^{5} \)	$D_5^2$ (as 10T9)	$[8]$
10.2.15552000000000000.3	x^10 - 10x^8 + 95x^6 - 52x^5 - 350x^4 + 260x^3 + 550x^2 - 200x - 296	\( 2^{18}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial
10.2.15552000000000000.19	x^10 - 10x^8 - 20x^7 + 10x^6 + 148x^5 + 250x^4 + 60x^3 - 255x^2 - 1260x - 2124	\( 2^{18}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2$ (as 10T9)	Trivial