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 19448)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.38305556224.1	x^10 - 3x^9 + 2x^8 - 2x^7 + 9x^6 - 7x^5 - 8x^3 + 8x^2 + 4x + 4	\( -\,2^{8}\cdot 13^{6}\cdot 31 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.50662187264.1	x^10 - x^9 - 2x^8 + 2x^7 + x^6 - 3x^5 + 2x^4 + 6x^3 + 2x^2 - 4x - 2	\( 2^{8}\cdot 13^{6}\cdot 41 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.68430008115.1	x^10 - 3x^9 + 4x^8 - 2x^7 + 3x^5 - x^4 - 6x^3 + 9x^2 - 5x + 1	\( -\,3^{4}\cdot 5\cdot 7\cdot 17^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.70000000000.1	x^10 + 5x^8 + 10x^6 - 4x^5 + 10x^4 + 5x^2 + 1	\( -\,2^{10}\cdot 5^{10}\cdot 7 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.72904123136.1	x^10 - 4x^9 + 9x^8 - 14x^7 + 20x^6 - 24x^5 + 22x^4 - 14x^3 + 11x^2 - 4x + 1	\( -\,2^{8}\cdot 13^{6}\cdot 59 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.95146059008.1	x^10 - 3x^9 + 3x^8 + 2x^7 - 3x^6 + 11x^5 - 3x^4 + 2x^3 + 3x^2 - 3x + 1	\( 2^{8}\cdot 7\cdot 11\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.98853048320.1	x^10 - x^8 - 4x^7 + 6x^6 - 6x^4 - 4x^3 + x^2 - 1	\( 2^{12}\cdot 5\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.105031363840.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - 3x^5 + x^4 + 2x^3 + x^2 - x - 1	\( 2^{8}\cdot 5\cdot 13^{6}\cdot 17 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.112445342464.1	x^10 - x^9 - x^8 + 2x^7 + 5x^6 + x^5 + 5x^4 + 2x^3 - x^2 - x + 1	\( -\,2^{8}\cdot 7\cdot 13^{7} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.113681005568.1	x^10 - 4x^9 + 6x^8 - 6x^7 + 6x^6 - 8x^5 + 10x^4 - 6x^3 + 8x^2 - 2x + 2	\( -\,2^{10}\cdot 13^{6}\cdot 23 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.117387994880.1	x^10 - x^9 + 2x^8 + 2x^7 + x^6 + x^5 - 4x^4 + 12x^3 - 8x + 8	\( -\,2^{8}\cdot 5\cdot 13^{6}\cdot 19 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.117500000000.1	x^10 - 5x^8 - 10x^7 + 10x^6 + 24x^5 + 20x^4 + 10x^3 + 5x^2 + 1	\( -\,2^{8}\cdot 5^{10}\cdot 47 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.120000000000.1	x^10 - 5x^8 + 10x^6 - 10x^4 + 5x^2 + 3	\( -\,2^{12}\cdot 3\cdot 5^{10} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.130000000000.1	x^10 - 5x^8 + 10x^6 - 2x^5 - 10x^4 + 10x^3 + 5x^2 - 10x + 3	\( 2^{10}\cdot 5^{10}\cdot 13 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.138394267648.1	x^10 - 2x^9 + 2x^8 - 2x^7 - 2x^6 + 4x^5 - 2x^4 - 2x^3 + 12x^2 - 8x + 10	\( -\,2^{12}\cdot 7\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.140380859375.1	x^10 + 5x^8 + 15x^6 - 6x^5 + 20x^4 - 15x^3 + 20x^2 - 20x + 7	\( -\,5^{14}\cdot 23 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.146484375000.1	x^10 - 5x^9 + 20x^8 - 45x^7 + 80x^6 - 90x^5 + 80x^4 - 45x^3 + 20x^2 - 5x + 1	\( -\,2^{3}\cdot 3\cdot 5^{14} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.147500000000.1	x^10 + 5x^8 + 10x^6 - 2x^5 + 5x^2 + 10x + 7	\( -\,2^{8}\cdot 5^{10}\cdot 59 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.154456304031.1	x^10 - 3x^9 + 9x^8 - 14x^7 + 27x^6 - 33x^5 + 44x^4 - 39x^3 + 33x^2 - 27x + 9	\( -\,3^{4}\cdot 17^{6}\cdot 79 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.170898437500.1	x^10 - 5x^9 + 10x^8 - 5x^7 - 15x^6 + 37x^5 - 45x^4 + 40x^3 - 25x^2 + 10x - 2	\( 2^{2}\cdot 5^{14}\cdot 7 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.172992834560.1	x^10 - 2x^9 - x^8 + 10x^7 - 12x^6 - 2x^5 + 24x^4 - 26x^3 + 11x^2 + 4x + 1	\( -\,2^{10}\cdot 5\cdot 7\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.176699823872.1	x^10 - 2x^9 + 4x^8 - 8x^7 + 14x^6 - 16x^5 + 24x^4 - 40x^3 + 40x^2 - 20x + 4	\( -\,2^{8}\cdot 11\cdot 13^{7} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.182500000000.1	x^10 - 5x^8 - 22x^5 - 10x^4 - 25x^2 - 10x - 1	\( 2^{8}\cdot 5^{10}\cdot 73 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.182878139392.1	x^10 - 4x^9 + x^8 + 8x^7 - 8x^6 + 4x^5 + 4x^4 - 4x^3 + 9x^2 - 6x + 5	\( 2^{10}\cdot 13^{6}\cdot 37 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.186585128704.1	x^10 - x^9 - 4x^8 + 2x^7 + 9x^6 + 9x^5 - 30x^4 - 8x^3 + 44x^2 - 24x + 4	\( -\,2^{8}\cdot 13^{6}\cdot 151 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.193559165811.1	x^10 - x^9 + x^8 + 4x^7 - 5x^6 + 10x^5 + 2x^4 - 21x^3 + 41x^2 - 30x + 7	\( -\,3^{6}\cdot 11\cdot 17^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.197469451989.1	x^10 - x^7 + 4x^6 - 3x^5 - 4x^4 - x^3 - 1	\( 3^{4}\cdot 17^{6}\cdot 101 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.201413085952.1	x^10 - 2x^9 - 2x^8 + 6x^7 - 4x^6 - 2x^5 + 4x^4 + 16x^2 + 4x + 4	\( -\,2^{8}\cdot 13^{6}\cdot 163 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.205290024345.1	x^10 - x^9 + 2x^8 - x^7 - 8x^5 + 4x^4 + 10x^3 - 6x^2 - x + 1	\( 3^{5}\cdot 5\cdot 7\cdot 17^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.207500000000.1	x^10 - 5x^9 + 15x^8 - 30x^7 + 55x^6 - 81x^5 + 75x^4 - 40x^3 + 15x^2 - 5x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 83 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.212534053888.1	x^10 - 2x^9 + 3x^8 - 2x^7 + 4x^6 + 2x^5 + 10x^3 + 11x^2 + 16x + 13	\( -\,2^{10}\cdot 13^{6}\cdot 43 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.213110596701.1	x^10 - x^9 + x^8 - 6x^7 + 3x^6 + 4x^5 + 12x^4 - 6x^3 - 7x^2 - 17x + 15	\( 3^{4}\cdot 17^{6}\cdot 109 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.217476706304.1	x^10 - 4x^9 + 5x^8 - 8x^7 + 18x^6 - 16x^5 + 18x^4 - 8x^3 + 5x^2 - 4x + 1	\( -\,2^{12}\cdot 11\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.217500000000.1	x^10 - 5x^8 - 10x^7 + 10x^6 + 34x^5 + 10x^4 - 30x^3 - 15x^2 + 10x + 7	\( -\,2^{8}\cdot 3\cdot 5^{10}\cdot 29 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.221183695616.1	x^10 - x^9 + 5x^8 + 2x^7 + 3x^6 + 11x^5 + 11x^4 + 4x^3 + 15x^2 + 7x + 1	\( -\,2^{8}\cdot 13^{6}\cdot 179 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.224841455235.1	x^10 - 2x^9 + 4x^8 - 3x^7 + 2x^6 + x^5 + 2x^4 - 3x^3 + 4x^2 - 2x + 1	\( -\,3^{4}\cdot 5\cdot 17^{6}\cdot 23 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.227500000000.1	x^10 - 5x^9 + 15x^8 - 20x^7 + 15x^6 - 5x^5 + 15x^4 - 20x^3 + 15x^2 - 5x + 1	\( -\,2^{8}\cdot 5^{10}\cdot 7\cdot 13 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.243425631488.1	x^10 - 5x^9 + 9x^8 - 6x^7 + x^6 - 3x^5 - x^4 - 6x^3 - 9x^2 - 5x - 1	\( 2^{8}\cdot 13^{6}\cdot 197 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.260724914944.1	x^10 - 5x^9 + 15x^8 - 28x^7 + 39x^6 - 37x^5 + 29x^4 - 8x^3 + 3x^2 + 3x + 1	\( -\,2^{8}\cdot 13^{6}\cdot 211 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.260724914944.2	x^10 - 4x^9 + 11x^8 - 18x^7 + 10x^6 + 4x^5 - 10x^3 + x^2 + 4x + 5	\( -\,2^{8}\cdot 13^{6}\cdot 211 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.262451171875.1	x^10 + 10x^6 - 6x^5 + 5x^4 + 15x^2 - 5x + 6	\( -\,5^{14}\cdot 43 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.271845882880.1	x^10 - 4x^9 + 11x^8 - 20x^7 + 16x^6 - 6x^5 + 16x^4 - 20x^3 + 11x^2 - 4x + 1	\( -\,2^{10}\cdot 5\cdot 11\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.290380829440.1	x^10 - x^9 + 3x^8 + 3x^6 + x^5 + 5x^4 - 4x^3 - x^2 + 3x + 1	\( -\,2^{8}\cdot 5\cdot 13^{6}\cdot 47 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.295323481856.1	x^10 - 5x^9 + 14x^8 - 26x^7 + 39x^6 - 47x^5 + 48x^4 - 38x^3 + 24x^2 - 10x + 2	\( -\,2^{8}\cdot 13^{6}\cdot 239 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.314778037329.1	x^10 - x^9 - 4x^8 - 2x^7 + 15x^6 + x^5 - 3x^4 - 14x^3 + x^2 - 4x + 1	\( 3^{4}\cdot 7\cdot 17^{6}\cdot 23 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.316329754624.1	x^10 + 2x^8 - 4x^6 + 8x^2 + 4	\( -\,2^{16}\cdot 13^{6} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.321272407040.1	x^10 - 2x^9 + x^8 - 8x^7 + 6x^6 - 16x^5 + 6x^4 - 8x^3 + x^2 - 2x + 1	\( 2^{10}\cdot 5\cdot 13^{7} \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.2.323486328125.1	x^10 - 5x^9 + 5x^8 + 10x^7 - 20x^6 + 4x^5 + 15x^4 - 15x^3 + 5x - 4	\( 5^{14}\cdot 53 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.331157711872.1	x^10 - 4x^9 + 9x^8 - 18x^7 + 36x^6 - 56x^5 + 68x^4 - 76x^3 + 79x^2 - 56x + 19	\( -\,2^{10}\cdot 13^{6}\cdot 67 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial
10.0.334329468219.1	x^10 + 2x^8 - 6x^7 - 9x^6 + 3x^5 + 12x^4 + 18x^3 - 9x^2 - 18x + 9	\( -\,3^{6}\cdot 17^{6}\cdot 19 \)	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	Trivial