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 )

Label	Polynomial	Discriminant	Galois group	Class group
9.1.7126573229.1	x^9 - x^8 + 5x^7 - 6x^6 + 5x^5 - 14x^4 - 3x^3 - 10x^2 - 3x - 1	\( 31^{3}\cdot 139\cdot 1721 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.8008148501.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 9x^5 - 11x^4 + 8x^3 + 5x + 1	\( 31^{3}\cdot 268811 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.8770691453.1	x^9 - 4x^8 + 13x^7 - 29x^6 + 54x^5 - 79x^4 + 93x^3 - 87x^2 + 58x - 19	\( 23^{3}\cdot 107\cdot 6737 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9194881741.1	x^9 - x^8 + 5x^7 - x^6 + 4x^5 + 11x^4 - 9x^3 + 35x^2 - 9x + 25	\( 23^{3}\cdot 733\cdot 1031 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9455991101.1	x^9 - 2x^8 + 4x^7 - 3x^6 - 6x^5 + 20x^4 - 22x^3 + 4x^2 + 4x + 1	\( 31^{3}\cdot 317411 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9483875477.1	x^9 - x^7 - x^6 - 9x^5 + 10x^4 + 15x^3 - 21x^2 + 8x - 1	\( 31^{3}\cdot 318347 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9501750077.1	x^9 - 2x^8 + 3x^7 - 3x^6 + 15x^4 - x^3 - 7x^2 + 2x + 1	\( 31^{3}\cdot 313\cdot 1019 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9613287581.1	x^9 - 3x^8 + 5x^7 - 6x^6 + 3x^5 - 6x^4 + x^3 - 6x^2 - 5x - 1	\( 31^{3}\cdot 523\cdot 617 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9653772313.1	x^9 - 4x^8 + 6x^7 - 3x^6 + x^5 + 11x^4 - 5x^3 - 20x^2 + 15x - 1	\( 23^{3}\cdot 793439 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.9750756928.1	x^9 + 2x^7 - 3x^6 + 2x^5 + 6x^4 + 7x^3 + 14x^2 - 8x + 1	\( 2^{6}\cdot 11^{3}\cdot 114467 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.10154128021.1	x^9 - 4x^7 + 4x^5 - 8x^4 + 23x^3 - 16x^2 - 1	\( 23^{3}\cdot 101\cdot 8263 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.10363595093.1	x^9 - 3x^8 + 7x^7 - 19x^6 + 26x^5 - 47x^4 + 43x^3 - 37x^2 + 15x - 11	\( 23^{3}\cdot 317\cdot 2687 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.10518099833.1	x^9 - x^8 - 2x^7 + 4x^6 + 3x^5 - 7x^4 + 7x^3 - 5x^2 - x + 9	\( 31^{3}\cdot 89\cdot 3967 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.10630233157.1	x^9 - 4x^8 + 10x^7 - 18x^6 + 17x^5 + 2x^4 - 16x^3 + 3x^2 + 5x + 1	\( 31^{3}\cdot 239\cdot 1493 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.10816986181.1	x^9 - x^8 - 4x^7 + 3x^6 + 10x^5 - 5x^4 - 24x^3 + 15x^2 + 29x - 25	\( 23^{3}\cdot 889043 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11015356949.1	x^9 - 2x^8 + 4x^6 - 3x^5 - 12x^4 + 10x^3 + 23x^2 + 13x + 1	\( 23^{3}\cdot 905347 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11075668189.1	x^9 - 3x^8 + 7x^7 - 14x^6 + 22x^5 - 27x^4 + 28x^3 - 26x^2 + 12x - 9	\( 31^{3}\cdot 371779 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11219329088.1	x^9 - x^8 + 5x^6 - 2x^5 - 3x^4 + 5x^3 - 4x^2 - 4x + 4	\( 2^{6}\cdot 11^{3}\cdot 131707 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11296852661.1	x^9 + 6x^7 - 2x^6 + 15x^5 - 5x^4 + 14x^3 - 5x^2 - 6x + 7	\( 23^{3}\cdot 59\cdot 15737 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11373578189.1	x^9 - 3x^8 + 8x^6 - 5x^5 - 11x^4 + 14x^3 + 7x^2 - 23x + 13	\( 31^{3}\cdot 293\cdot 1303 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11557323797.1	x^9 - 3x^8 + 10x^7 - 12x^6 + 19x^5 - 2x^4 + 6x^3 + 11x^2 + 6x - 1	\( 23^{3}\cdot 949891 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11669503537.3	x^9 - 5x^7 - 2x^6 + 10x^5 + 12x^4 - 17x^2 - 6x - 1	\( 23^{3}\cdot 661\cdot 1451 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11773611737.2	x^9 - x^8 - 4x^7 + 5x^6 + 3x^5 - 11x^4 + 21x^3 - 18x^2 + 4x - 1	\( 31^{3}\cdot 227\cdot 1741 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11833855373.1	x^9 - 2x^8 + x^7 + 2x^6 - 8x^5 - 9x^4 + 46x^3 - 40x^2 + 11x - 1	\( 23^{3}\cdot 37\cdot 97\cdot 271 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.11877802577.1	x^9 - x^8 - 3x^7 - 7x^6 + 7x^5 + 23x^4 + 7x^3 - 8x^2 - 12x - 8	\( 23^{3}\cdot 976231 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12016930669.1	x^9 - 3x^8 + 7x^7 - 6x^6 + 3x^5 + 3x^4 - 4x^2 + 2x + 1	\( 59^{3}\cdot 58511 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12039877412.1	x^9 - 2x^8 + x^7 + 9x^6 - 12x^5 + 10x^4 + 8x^3 + 2x + 1	\( 2^{2}\cdot 83\cdot 331^{3} \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12230548241.1	x^9 - 2x^8 - x^7 + 4x^5 - 8x^4 + 17x^3 + 6x^2 - 8x - 8	\( 23^{3}\cdot 1005223 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12307196541.1	x^9 - x^7 - 2x^6 - x^5 + x^4 + 6x^3 + 2x^2 + 4x - 1	\( 3\cdot 181\cdot 283^{3} \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12326618873.1	x^9 - 2x^8 - 2x^7 + x^5 + 2x^4 + 19x^3 + 42x^2 + 32x + 8	\( 23^{3}\cdot 907\cdot 1117 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12326890189.1	x^9 - 3x^8 + 6x^7 - 10x^6 + 7x^5 - 8x^4 + 8x^3 + 9x^2 + 1	\( 31^{3}\cdot 413779 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12503967893.2	x^9 - x^8 - x^7 + 7x^6 - x^4 + 13x^3 + 9x^2 + 11x + 9	\( 31^{3}\cdot 43^{2}\cdot 227 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12592200149.1	x^9 - x^8 + 2x^7 - 8x^6 + 9x^5 + 20x^4 - 56x^3 + 59x^2 - 36x + 11	\( 23^{3}\cdot 101\cdot 10247 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12702971773.1	x^9 - 2x^8 + 3x^7 - 3x^6 - 2x^5 + 10x^4 - 12x^3 + 12x^2 + x + 1	\( 31^{3}\cdot 577\cdot 739 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12711339413.1	x^9 - 4x^8 + 7x^7 - 13x^6 + 20x^5 - 13x^4 + 17x^3 - 7x^2 - 6x - 1	\( 23^{3}\cdot 1044739 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12772403776.1	x^9 - 4x^7 - 3x^6 + 8x^5 + 8x^4 - x^3 - 8x^2 - 4x - 1	\( 2^{6}\cdot 11^{3}\cdot 149939 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.12860995136.1	x^9 - 2x^8 + x^6 + 8x^4 - 11x^3 - 8x^2 + 14x + 1	\( 2^{6}\cdot 11^{3}\cdot 150979 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13121951329.1	x^9 - 3x^8 + 9x^7 - 11x^6 + 15x^5 - 5x^4 + 14x^3 - 6x^2 + 25x + 1	\( 23^{3}\cdot 937\cdot 1151 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13307035733.1	x^9 - 2x^8 - 4x^7 + 15x^6 - 4x^5 - 32x^4 + 44x^3 + 6x^2 - 46x + 23	\( 23^{3}\cdot 1093699 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13309141597.1	x^9 - 2x^8 + 2x^6 + 4x^5 - 14x^4 + 19x^3 - 14x^2 + 6x - 1	\( 331^{3}\cdot 367 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13494816553.1	x^9 - 3x^8 + 7x^7 - 12x^6 + 13x^5 - 14x^4 + 20x^3 - 6x^2 + 4x - 1	\( 31^{3}\cdot 452983 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13526820421.1	x^9 - 3x^8 + 8x^7 - 4x^6 + 7x^5 - 9x^4 + 34x^3 - 3x^2 + 11x + 1	\( 23^{3}\cdot 337\cdot 3299 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13600990453.1	x^9 + 6x^7 - 4x^6 + 18x^5 - 14x^4 + 23x^3 - 30x^2 + 18x - 1	\( 23^{3}\cdot 103\cdot 10853 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13647419725.1	x^9 - 2x^8 + 9x^7 - 13x^6 + 30x^5 - 28x^4 + 48x^3 - 20x^2 + 32x - 1	\( 5^{2}\cdot 23^{3}\cdot 44867 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.13954904149.2	x^9 - 2x^8 + x^7 - 4x^6 + 3x^5 + 9x^4 + 12x^3 - 28x^2 + 10x - 1	\( 23^{3}\cdot 1146947 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.14387952013.1	x^9 - x^8 + 9x^7 - 10x^6 + 32x^5 - 35x^4 + 54x^3 - 44x^2 + 36x - 7	\( 23^{3}\cdot 1182539 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.14472439661.1	x^9 - x^8 - x^7 - 3x^6 + 10x^5 + 7x^4 - 11x^3 + 9x^2 + 15x + 1	\( 23^{3}\cdot 1189483 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.14483054493.1	x^9 - 3x^8 + 2x^7 + 5x^6 - 14x^5 + 17x^4 - 12x^3 + 7x^2 - 3x + 1	\( 3^{2}\cdot 71\cdot 283^{3} \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.14488208093.1	x^9 - x^8 - 2x^7 + x^6 - 4x^5 + 11x^4 + 28x^3 + 5x^2 - 5x + 1	\( 23^{5}\cdot 2251 \)	$S_3\wr S_3$ (as 9T31)	$[2]$
9.1.14610438208.1	x^9 - 2x^8 + 11x^6 - 14x^5 - 4x^4 + 27x^3 - 20x^2 + 8x - 1	\( 2^{6}\cdot 19^{3}\cdot 83\cdot 401 \)	$S_3\wr S_3$ (as 9T31)	$[2]$

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