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 450)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.467288576.1	x^9 - x^8 + x^6 - x^5 + x^4 + x^3 - 2x^2 + 2x - 1	\( 2^{9}\cdot 97^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.551368000.1	x^9 - 4x^8 + 9x^7 - 17x^6 + 23x^5 - 24x^4 + 20x^3 - 13x^2 + 5x - 1	\( 2^{6}\cdot 5^{3}\cdot 41^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.690807104.1	x^9 - x^8 + x^7 - 2x^6 + 2x^5 - x^4 + x^3 + x^2 - 2x + 1	\( 2^{6}\cdot 13^{3}\cdot 17^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.1749690125.1	x^9 - x^8 + 2x^6 - 3x^5 + x^4 + 2x^3 - x^2 + x - 1	\( 5^{3}\cdot 241^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.2191933899.1	x^9 - x^8 - 2x^6 - x^5 + 3x^4 + x^2 + x - 1	\( -\,3^{3}\cdot 433^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.2773505125.1	x^9 - x^8 - x^6 + x^5 + x^4 + 3x^3 + 2x^2 + 1	\( 5^{3}\cdot 281^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.2815166528.1	x^9 - 2x^8 + 2x^7 - 3x^6 - x^5 + 3x^4 - x^3 + 2x^2 + x - 1	\( -\,2^{6}\cdot 353^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.2858291712.1	x^9 - x^8 + 4x^7 - 5x^6 + 9x^5 - 5x^4 + 9x^3 - 2x^2 - 2x + 1	\( 2^{9}\cdot 3^{4}\cdot 41^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.3131359847.1	x^9 - 2x^7 - 4x^6 - x^5 + 3x^4 + 8x^3 + 9x^2 - x - 1	\( -\,7^{3}\cdot 11^{3}\cdot 19^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.3170044709.1	x^9 - x^8 + 2x^7 - 2x^6 - x^5 + 3x^4 + 2x^3 - 5x^2 + 3x - 1	\( 13^{3}\cdot 113^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.3186827264.1	x^9 - 2x^8 + 3x^7 + 2x^6 - x^5 + 4x^4 + 5x^3 + 6x^2 + 6x + 2	\( 2^{13}\cdot 73^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.3268147904.1	x^9 - x^8 + x^7 + 4x^6 - 2x^5 - x^4 + 5x^3 + x^2 - 10x + 3	\( -\,2^{6}\cdot 7^{3}\cdot 53^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.3491055413.1	x^9 + 4x^7 - 3x^6 + 4x^5 - 2x^4 + 6x^3 - 2x - 1	\( 37^{3}\cdot 41^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.4065356736.1	x^9 - 2x^8 + 2x^7 + x^6 - x^5 - x^4 + 3x^3 - 2x^2 + x - 1	\( 2^{6}\cdot 3^{3}\cdot 7^{3}\cdot 19^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.4467667023.1	x^9 - 6x^7 - 3x^6 + 9x^5 + 3x^4 - 10x^3 + 3x - 1	\( -\,3^{9}\cdot 61^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.4694808843.1	x^9 - 3x^8 + 6x^7 - 12x^6 + 18x^5 - 12x^4 - 3x^3 + 9x^2 - 6x + 1	\( -\,3^{10}\cdot 43^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.5030030016.1	x^9 + 6x^7 - 3x^6 + 9x^5 - 3x^4 + 3x^3 - 3x - 1	\( 2^{6}\cdot 3^{10}\cdot 11^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.5061868813.1	x^9 - 2x^8 + 4x^6 - 2x^5 - 4x^4 + 3x^3 + 4x^2 - 1	\( 17^{3}\cdot 101^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.5377771008.1	x^9 - 2x^8 + 2x^7 - 3x^6 + 3x^5 - x^4 - x^3 + x + 1	\( 2^{9}\cdot 3^{3}\cdot 73^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.5775106048.1	x^9 - x^8 - 2x^6 + 4x^5 - 2x^4 + 2x^3 + x + 1	\( 2^{13}\cdot 89^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.6219352719.1	x^9 - x^8 - x^7 - 3x^6 + 3x^5 + x^4 - x^3 + 3x^2 + x - 1	\( -\,3^{3}\cdot 613^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.6746163125.1	x^9 - x^8 - 4x^6 + 5x^5 - x^4 + 4x^3 - x^2 + x + 1	\( 5^{4}\cdot 13^{3}\cdot 17^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.7137811125.1	x^9 - x^8 + x^7 - 2x^6 + 9x^5 - 5x^4 + 6x^3 - 2x^2 + x + 1	\( 3^{4}\cdot 5^{3}\cdot 89^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.7361594368.1	x^9 - x^8 - 4x^6 + 4x^4 + 2x^3 + 2x^2 + x - 1	\( -\,2^{10}\cdot 193^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.7541066681.1	x^9 - x^8 + x^7 - 3x^6 + 3x^5 - x^4 + x^3 + 3x^2 + 3x + 1	\( 37^{3}\cdot 53^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.8048096064.1	x^9 - 2x^8 + 6x^7 - 5x^6 + 11x^5 - 11x^4 + 9x^3 - 2x^2 - 3x + 1	\( -\,2^{6}\cdot 3^{3}\cdot 167^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.9895523328.1	x^9 - 4x^8 + 3x^7 + 8x^6 - 19x^5 + 14x^4 + 9x^3 - 22x^2 + 12x - 4	\( -\,2^{10}\cdot 3^{3}\cdot 71^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.10463552512.1	x^9 - x^8 - 3x^7 + 5x^6 - 2x^5 - 8x^4 + 12x^3 + 2x^2 - 10x + 2	\( -\,2^{10}\cdot 7^{3}\cdot 31^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.11499840000.1	x^9 - 2x^8 + 2x^7 - 5x^6 - x^5 + 5x^4 + 3x^3 + 4x^2 + x - 1	\( -\,2^{9}\cdot 3^{3}\cdot 5^{4}\cdot 11^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.12487168000.1	x^9 - 3x^8 + 5x^7 - 5x^6 + x^5 + 5x^4 - 10x^3 + 2x^2 + 4x - 4	\( 2^{12}\cdot 5^{3}\cdot 29^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.12952921088.1	x^9 - 2x^8 + 2x^6 - 8x^5 + 4x^4 + 4x^3 + 8x - 8	\( -\,2^{10}\cdot 233^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.13178585088.1	x^9 - 3x^8 + 4x^6 + 6x^5 - 14x^4 + 4x^3 + 4x^2 - 8x + 8	\( -\,2^{14}\cdot 3^{3}\cdot 31^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.14047232000.1	x^9 - 2x^8 + 5x^7 - 10x^6 + 12x^5 - 18x^4 + 17x^3 - 14x^2 + 11x - 4	\( 2^{14}\cdot 5^{3}\cdot 19^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.14155776000.1	x^9 - 3x^8 + 6x^7 - 2x^6 - 3x^5 + 9x^4 - 12x^3 + 12x^2 - 6x + 2	\( 2^{22}\cdot 3^{3}\cdot 5^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.16915218263.1	x^9 + 2x^7 - 3x^6 + x^5 - x^4 - 5x^3 - x - 1	\( -\,17^{3}\cdot 151^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.17576000000.1	x^9 - x^8 - 3x^6 + x^5 + x^4 + 3x^3 + 2x^2 + 1	\( 2^{9}\cdot 5^{6}\cdot 13^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.17585676288.1	x^9 + x^7 - 4x^6 + x^5 - 6x^4 - 9x^3 - 4x^2 - 6x - 2	\( -\,2^{13}\cdot 3^{3}\cdot 43^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.18841337856.1	x^9 - 2x^8 + 2x^7 - 3x^5 + 2x^4 - 4x^3 + 4x - 8	\( 2^{19}\cdot 3^{3}\cdot 11^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.18970074963.1	x^9 - x^8 - 3x^7 - 2x^6 + 5x^5 - 3x^4 + 4x^2 + x - 1	\( -\,3^{3}\cdot 7^{3}\cdot 127^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.21064523776.1	x^9 - x^8 - 4x^7 - 2x^6 + 14x^5 - 10x^3 + 4x^2 + 3x - 1	\( -\,2^{13}\cdot 137^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.22407266304.1	x^9 - 3x^8 + 3x^7 + x^6 + 3x^3 + 9x^2 + 3x - 1	\( 2^{14}\cdot 3^{3}\cdot 37^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.22478848000.1	x^9 - x^8 + 2x^7 + 2x^6 - 4x^5 + 4x^4 + 12x^3 - 4x^2 - 12x - 4	\( -\,2^{19}\cdot 5^{3}\cdot 7^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.24187716288.1	x^9 - 2x^8 - 6x^6 + 4x^5 + 16x^4 - 12x^3 + 16x - 8	\( -\,2^{6}\cdot 3^{3}\cdot 241^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.24389000000.1	x^9 + x^7 - x^6 - 3x^5 - 2x^4 + 10x^3 + 13x^2 - 3x + 1	\( 2^{6}\cdot 5^{6}\cdot 29^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.25154560000.1	x^9 - x^8 + 6x^6 - 6x^4 + 14x^3 + 4x^2 + x + 1	\( 2^{13}\cdot 5^{4}\cdot 17^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.25233583104.1	x^9 - x^8 + 4x^6 - 4x^5 + 6x^3 - 2x^2 + x - 1	\( 2^{10}\cdot 3^{3}\cdot 97^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.25921093824.1	x^9 - 3x^8 + 3x^7 - 6x^6 + 12x^5 - 15x^4 + 15x^3 - 3x^2 + 3	\( -\,2^{6}\cdot 3^{10}\cdot 19^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.1.26677294272.1	x^9 - 2x^8 + 2x^7 - x^6 + 3x^5 - 3x^4 - x^3 + 2x^2 + x + 1	\( 2^{6}\cdot 3^{6}\cdot 83^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.27961796875.1	x^9 - 4x^8 + 7x^7 - 5x^6 - 2x^5 + 18x^4 - 22x^3 + 16x^2 - 1	\( -\,5^{7}\cdot 71^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial
9.3.29113459911.1	x^9 - 6x^7 - 3x^6 + 9x^5 + 3x^4 + 12x^3 + 3x - 1	\( -\,3^{10}\cdot 79^{3} \)	$S_3^2:C_2$ (as 9T16)	Trivial