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 116)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.1966899200000.1	x^10 - 2x^9 + 7x^8 - 8x^7 + 16x^6 - 12x^5 + 22x^4 - 8x^3 + 16x^2 + 4	\( -\,2^{18}\cdot 5^{5}\cdot 7^{4} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.3428696723823.1	x^10 - 3x^9 + 10x^7 - 8x^6 - 12x^5 + 11x^4 + 7x^3 - 3x^2 - 3x + 2	\( -\,3^{6}\cdot 7^{5}\cdot 23^{4} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.3768595808256.1	x^10 - 2x^9 - 3x^8 + 6x^7 + 4x^5 - x^4 - 14x^3 + 7x^2 - 6x - 25	\( 2^{15}\cdot 3^{4}\cdot 17^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.4000000000000.2	x^10 - 10x^8 + 35x^6 - 2x^5 - 50x^4 + 10x^3 + 25x^2 - 10x + 2	\( -\,2^{14}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.7290000000000.4	x^10 - 4x^9 + 21x^8 - 64x^7 + 146x^6 - 234x^5 + 271x^4 - 214x^3 + 111x^2 - 34x + 5	\( -\,2^{10}\cdot 3^{6}\cdot 5^{10} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.8012167578125.1	x^10 + 10x^8 + 35x^6 - x^5 + 50x^4 - 5x^3 + 25x^2 - 5x - 7	\( 5^{8}\cdot 29^{5} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.9957427200000.1	x^10 - 2x^9 + 2x^8 - 4x^7 + 6x^6 + 4x^5 + 16x^4 + 20x^3 + 21x^2 + 14x + 6	\( -\,2^{14}\cdot 3^{4}\cdot 5^{5}\cdot 7^{4} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.10028200950000.1	x^10 - 4x^9 + 12x^8 - 24x^7 + 48x^6 - 65x^5 + 82x^4 - 68x^3 + 68x^2 - 8x + 24	\( -\,2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 19^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[8]$
10.2.11706520660992.1	x^10 - 4x^9 - x^8 + 18x^7 - 12x^6 - 22x^5 + 23x^4 + 8x^3 + x^2 + 1	\( 2^{10}\cdot 3^{5}\cdot 19^{6} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.26214400000000.2	x^10 - 4x^9 + 5x^8 - 8x^6 + 8x^5 + 25x^2 + 20x + 5	\( -\,2^{26}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.27880796160000.1	x^10 - 2x^9 + 3x^8 - 2x^7 - x^6 + 4x^5 + 10x^4 + 2x^3 + x^2 - 2x + 1	\( -\,2^{15}\cdot 3^{4}\cdot 5^{4}\cdot 7^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[4]$
10.2.29326100878125.1	x^10 - 2x^9 + 3x^8 + 13x^7 - 16x^6 + 19x^5 + x^4 - 13x^3 + 16x^2 - 2x + 1	\( 3^{4}\cdot 5^{5}\cdot 41^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.39319091796875.2	x^10 + 10x^8 + 35x^6 - x^5 + 50x^4 - 5x^3 + 25x^2 - 5x + 3	\( -\,5^{12}\cdot 11^{5} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.42229815050000.1	x^10 - 4x^9 + 8x^8 - 8x^7 + 4x^6 + 17x^5 - 34x^4 + 34x^3 - 4	\( 2^{4}\cdot 5^{5}\cdot 61^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.2.59443723108352.1	x^10 - 2x^9 + x^8 - 4x^7 + 58x^6 - 196x^5 + 366x^4 - 416x^3 + 298x^2 - 116x + 14	\( 2^{25}\cdot 11^{6} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.64000000000000.4	x^10 - 10x^8 + 35x^6 - 8x^5 - 50x^4 + 40x^3 + 25x^2 - 40x + 20	\( -\,2^{18}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.64000000000000.9	x^10 - 4x^9 + 11x^8 - 4x^7 - 24x^6 + 96x^5 - 94x^4 - 24x^3 + 216x^2 - 264x + 100	\( -\,2^{18}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.74649600000000.2	x^10 - 4x^9 + 5x^8 + 8x^7 - 11x^6 - 48x^5 + 127x^4 - 40x^3 - 109x^2 + 8x + 145	\( -\,2^{18}\cdot 3^{6}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.83070153450000.1	x^10 - 2x^9 + 5x^8 - 8x^7 + 10x^6 - 23x^5 + 21x^4 - 30x^3 + 27x^2 - 13x + 6	\( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 29^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[4]$
10.0.93702400000000.1	x^10 - 4x^9 + 5x^8 + 20x^7 - 40x^6 - 16x^5 + 124x^4 - 160x^2 + 80	\( -\,2^{14}\cdot 5^{8}\cdot 11^{4} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.2.121850336730512.1	x^10 - 2x^9 - 3x^8 + 8x^7 + 2x^6 + 7x^5 - 17x^4 - 30x^3 + 35x^2 + 17x - 22	\( 2^{4}\cdot 13^{5}\cdot 29^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.182250000000000.9	x^10 - 10x^7 + 100x^6 - 192x^5 + 125x^4 - 40x^3 + 20	\( -\,2^{10}\cdot 3^{6}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.324000000000000.1	x^10 - 4x^9 + 13x^8 - 26x^7 + 102x^6 - 236x^5 + 426x^4 - 272x^3 + 284x^2 - 208x + 68	\( -\,2^{14}\cdot 3^{4}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.0.370872403061616.1	x^10 - 2x^9 + 5x^8 - 12x^7 + 15x^6 - 38x^5 + 41x^4 - 50x^3 + 196x^2 - 264x + 208	\( -\,2^{4}\cdot 3^{5}\cdot 157^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[16]$
10.2.494265241600000.1	x^10 - 4x^9 + 8x^8 - 8x^7 - 11x^6 + 34x^5 - 68x^4 + 78x^3 - 90x^2 + 60x - 31	\( 2^{15}\cdot 5^{5}\cdot 13^{6} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.655360000000000.1	x^10 - 2x^9 + 5x^8 - 24x^5 + 8x^4 + 25x^2 - 10x + 5	\( -\,2^{26}\cdot 5^{10} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.655360000000000.6	x^10 - 2x^9 + 9x^8 - 8x^7 + 46x^6 - 20x^5 + 110x^4 + 40x^3 + 245x^2 + 110x + 125	\( -\,2^{26}\cdot 5^{10} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.2.769311977450000.1	x^10 - 2x^9 + 5x^8 - 8x^7 + 102x^6 - 125x^5 + 215x^4 - 234x^3 + 75x^2 + 9x - 4	\( 2^{4}\cdot 5^{5}\cdot 109^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.1620000000000000.1	x^10 + 5x^8 + 30x^6 - 56x^5 + 110x^4 - 160x^3 + 165x^2 - 120x + 49	\( -\,2^{14}\cdot 3^{4}\cdot 5^{13} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.2.1760198519540736.1	x^10 - 4x^9 + 5x^8 + 2x^7 - 8x^6 - 12x^5 + 37x^4 - 16x^3 - 13x^2 + 8x + 1	\( 2^{10}\cdot 3^{6}\cdot 11^{9} \)	$D_5^2 : C_2$ (as 10T19)	$[5]$
10.0.2123366400000000.3	x^10 - 4x^9 + 13x^8 - 8x^7 + 78x^6 - 80x^5 + 342x^4 + 616x^3 + 1049x^2 + 596x + 101	\( -\,2^{26}\cdot 3^{4}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.2916000000000000.19	x^10 - 10x^7 - 5x^6 - 60x^5 + 50x^4 - 160x^3 + 585x^2 + 150x + 986	\( -\,2^{14}\cdot 3^{6}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.3145527343750000.1	x^10 - 5x^9 + 25x^8 - 65x^7 + 135x^6 - 193x^5 + 210x^4 - 290x^3 + 250x^2 - 80x + 166	\( -\,2^{4}\cdot 5^{13}\cdot 11^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[4]$
10.0.3185049600000000.1	x^10 - 2x^9 + x^8 + 12x^7 - 6x^6 - 52x^5 + 46x^4 - 48x^3 + 114x^2 + 108x + 22	\( -\,2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.0.3185049600000000.2	x^10 - 2x^9 + 17x^8 - 32x^7 + 70x^6 - 76x^5 + 38x^4 + 32x^3 - 47x^2 + 30x + 33	\( -\,2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.0.3185049600000000.4	x^10 - 4x^9 - 2x^8 + 24x^7 - 28x^6 - 48x^5 + 184x^4 + 192x^3 - 104x^2 - 32x + 112	\( -\,2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.3185049600000000.5	x^10 - 4x^8 - 20x^7 - 20x^6 + 20x^5 + 160x^4 + 292x^3 + 425x^2 + 300x + 196	\( -\,2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.2.3185049600000000.1	x^10 - 2x^9 + 3x^8 - 12x^7 - 2x^6 - 4x^5 + 22x^4 - 8x^3 - 18x^2 - 28x - 2	\( 2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.3185049600000000.9	x^10 + 20x^6 - 48x^5 + 100x^2 - 480x + 192	\( 2^{25}\cdot 3^{5}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.8192000000000000.6	x^10 + 10x^6 - 40x^5 - 100x^4 + 40x^3 + 450x^2 + 760x + 408	\( -\,2^{25}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial
10.2.8774784915636224.1	x^10 - 2x^9 + 3x^8 + 40x^7 + 35x^6 + 8x^5 + 89x^4 + 94x^3 + 10x^2 + 52x + 55	\( 2^{15}\cdot 193^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$
10.0.12500000000000000.1	x^10 + 10x^8 + 35x^6 - 2x^5 + 50x^4 - 10x^3 + 25x^2 - 10x + 6	\( -\,2^{14}\cdot 5^{17} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.0.16384000000000000.9	x^10 - 40x^7 + 88x^5 + 400x^4 - 1135x^2 - 2400x + 4240	\( -\,2^{26}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)
10.0.19110297600000000.6	x^10 - 4x^9 + 5x^8 + 36x^6 - 96x^5 - 60x^4 + 900x^2 + 720x + 180	\( -\,2^{26}\cdot 3^{6}\cdot 5^{8} \)	$D_5^2 : C_2$ (as 10T19)	$[5]$ (GRH)
10.0.25920000000000000.1	x^10 - 40x^7 - 40x^6 + 112x^5 + 360x^4 + 240x^3 + 20x^2 + 16	\( -\,2^{18}\cdot 3^{4}\cdot 5^{13} \)	$D_5^2 : C_2$ (as 10T19)	$[10]$
10.2.26640056883642368.1	x^10 - 4x^9 + 14x^8 + 12x^7 + 13x^6 + 54x^5 + 38x^4 - 142x^3 + 162x^2 - 52x + 1	\( 2^{15}\cdot 241^{5} \)	$D_5^2 : C_2$ (as 10T19)	$[10]$
10.0.30181730444800000.1	x^10 + 33x^6 - 44x^5 + 121x^2 + 484x + 484	\( -\,2^{12}\cdot 5^{5}\cdot 11^{9} \)	$D_5^2 : C_2$ (as 10T19)	$[5, 20]$
10.0.31104000000000000.14	x^10 - 10x^8 - 40x^7 - 35x^6 + 176x^5 + 850x^4 + 1920x^3 + 2340x^2 + 1440x + 360	\( -\,2^{19}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.0.31104000000000000.21	x^10 - 10x^8 - 20x^7 - 35x^6 + 36x^5 + 550x^4 + 1520x^3 + 2260x^2 + 2160x + 1048	\( -\,2^{19}\cdot 3^{5}\cdot 5^{12} \)	$D_5^2 : C_2$ (as 10T19)	$[2]$ (GRH)
10.0.40000000000000000.5	x^10 - 20x^8 + 155x^6 - 4x^5 - 500x^4 - 100x^3 + 625x^2 + 500x + 200	\( -\,2^{18}\cdot 5^{16} \)	$D_5^2 : C_2$ (as 10T19)	Trivial (GRH)