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 784)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.1272491584.1	x^9 - x^8 + x^7 - 2x^5 + 5x^4 - 11x^3 + 11x^2 - 2x - 1	\( -\,2^{6}\cdot 7^{6}\cdot 13^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.1384375783.1	x^9 - 4x^8 + 10x^7 - 15x^6 + 17x^5 - 16x^4 + 13x^3 - 8x^2 + 1	\( -\,7^{7}\cdot 41^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.1522731007.1	x^9 - 3x^8 + 7x^7 - 8x^6 + 5x^5 + 3x^4 - 8x^3 + 3x^2 + 2x - 1	\( -\,7^{7}\cdot 43^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.4146834123.1	x^9 - 3x^8 + 12x^6 - 24x^5 + 18x^4 - 3x^3 - 3x^2 + 1	\( -\,3^{15}\cdot 17^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.4478453307.1	x^9 + 3x^7 - x^6 + 3x^5 - 6x^4 - x^3 - 3x^2 - 6x + 1	\( -\,3^{13}\cdot 53^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.5179955427.1	x^9 - 3x^7 - 3x^6 + 9x^5 + 6x^4 - 3x^3 - 9x^2 + 6x - 1	\( -\,3^{15}\cdot 19^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.5673387727.1	x^9 - 4x^8 + 7x^7 - 8x^6 + x^5 + 13x^4 - 6x^3 - 7x^2 - 3x - 1	\( -\,7^{7}\cdot 83^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.13282925047.1	x^9 - 2x^8 + 7x^7 - 8x^6 + 4x^5 + 5x^4 + x^3 - 14x^2 + 8x - 1	\( -\,7^{7}\cdot 127^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.16012852443.1	x^9 - x^8 + 4x^7 - 7x^6 + 6x^5 - 15x^4 + 7x^3 - 10x^2 + 6x + 1	\( -\,3^{3}\cdot 7^{6}\cdot 71^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.17397345875.1	x^9 - 2x^8 - x^7 + 8x^6 - 14x^5 + 7x^4 + 14x^3 - 28x^2 + 21x - 7	\( -\,5^{3}\cdot 7^{7}\cdot 13^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.18253404027.1	x^9 - 3x^8 + 9x^7 - 11x^6 + 12x^5 - 3x^4 - 9x^3 + 9x^2 - 9x + 3	\( -\,3^{13}\cdot 107^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.18942151563.1	x^9 - 3x^8 + 3x^7 - 4x^6 - 6x^5 + 3x^4 - 2x^3 - 12x^2 + 3	\( -\,3^{13}\cdot 109^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.19643653683.1	x^9 - 3x^7 - 3x^6 + 9x^5 - 12x^4 + 15x^3 - 9x^2 + 6x - 1	\( -\,3^{15}\cdot 37^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.22967790727.1	x^9 - x^8 + 7x^7 + x^6 + 10x^5 + 9x^4 - x^3 + 8x^2 - 6x + 1	\( -\,7^{7}\cdot 167^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.26304786963.1	x^9 - x^8 + 2x^7 - 14x^4 - 7x^3 + 3x^2 + 4x - 1	\( -\,3^{3}\cdot 7^{8}\cdot 13^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.29488598208.1	x^9 - 3x^7 - 11x^6 - 15x^5 - 12x^4 + 9x^2 + 9x + 3	\( -\,2^{6}\cdot 3^{13}\cdot 17^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.36664957903.1	x^9 - 2x^8 + 4x^7 + x^6 - 3x^5 + 9x^4 - 13x^3 + 14x^2 + 3x - 1	\( -\,7^{7}\cdot 211^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.36835238592.1	x^9 - 3x^8 + 9x^7 - 20x^6 + 36x^5 - 51x^4 + 47x^3 - 33x^2 + 12x - 1	\( -\,2^{6}\cdot 3^{13}\cdot 19^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.37956390976.2	x^9 - 4x^8 + 5x^7 - 3x^6 - x^5 - 8x^4 + 12x^3 + 3x^2 + x + 1	\( -\,2^{6}\cdot 7^{6}\cdot 71^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.41389887175.1	x^9 - x^8 - 5x^7 + 3x^6 + 11x^5 - x^4 - 11x^3 - 6x^2 - 3x - 1	\( -\,5^{2}\cdot 7^{3}\cdot 13^{6} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.42359567787.1	x^9 - 3x^8 + 3x^7 - 7x^6 + 3x^5 - 6x^4 + 9x^3 - 9x^2 + 9x - 3	\( -\,3^{13}\cdot 163^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.43799715211.1	x^9 - 2x^8 - x^7 - 3x^6 + 9x^5 + 4x^4 - 9x^3 - x^2 + 4x - 1	\( -\,7^{2}\cdot 19^{7} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.46562734656.1	x^9 - 3x^8 + 6x^7 - 11x^6 + 9x^5 + 3x^4 - 9x^3 + 6x^2 + 6x + 1	\( -\,2^{6}\cdot 3^{12}\cdot 37^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.50658718208.1	x^9 + x^7 - 3x^6 - 16x^5 + 12x^4 - 12x^3 - 12x^2 + 8x - 8	\( -\,2^{9}\cdot 7^{6}\cdot 29^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.51234139467.1	x^9 - 2x^8 + 7x^7 - 11x^6 + 15x^5 - 24x^4 + 16x^3 + 10x^2 - 3x - 1	\( -\,3^{3}\cdot 7^{6}\cdot 127^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.51870973504.1	x^9 - 2x^8 + 6x^7 - 7x^6 + 13x^5 - 9x^4 + 5x^3 - 8x^2 - 7x + 1	\( -\,2^{6}\cdot 7^{6}\cdot 83^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.51884032543.1	x^9 - 3x^8 + 3x^7 - 6x^6 + 3x^5 + 2x^4 + 6x^3 + 8x^2 - 28x + 13	\( -\,7^{7}\cdot 251^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.52680152007.1	x^9 - 3x^8 + 6x^7 - 9x^6 - 9x^5 + 48x^4 - 53x^3 + 21x^2 - 3	\( -\,3^{12}\cdot 7^{3}\cdot 17^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.61783155200.1	x^9 - 2x^8 - x^7 + 5x^6 + 3x^5 - 26x^4 + 34x^3 - 15x^2 - 5x + 5	\( -\,2^{9}\cdot 5^{2}\cdot 13^{6} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.70700343007.2	x^9 + 5x^7 - 6x^6 + 27x^5 - 27x^4 + 27x^3 - 5x^2 - 8x - 1	\( -\,7^{7}\cdot 293^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.70845404224.1	x^9 - 2x^8 + 2x^7 - 11x^6 + 15x^5 - 13x^4 + 19x^3 - 30x^2 + 33x - 13	\( -\,2^{6}\cdot 7^{6}\cdot 97^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.71259528704.2	x^9 - 2x^8 + 4x^7 - x^6 - 5x^5 + 3x^4 + x^3 + 14x^2 + 21x + 7	\( -\,2^{9}\cdot 7^{7}\cdot 13^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.71943825375.1	x^9 - 3x^8 + 10x^6 - 18x^5 + 9x^4 + 7x^3 - 15x^2 + 9x - 3	\( -\,3^{13}\cdot 5^{3}\cdot 19^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.72332840187.1	x^9 - 3x^7 - 6x^6 + 9x^5 + 3x^4 - 3x^3 - 18x^2 + 24x - 8	\( -\,3^{15}\cdot 71^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.76465325403.1	x^9 - 3x^7 - 6x^6 + 18x^5 - 27x^4 + 30x^3 - 18x^2 + 9x - 3	\( -\,3^{15}\cdot 73^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.93528954967.1	x^9 - 2x^8 + x^6 - 15x^5 + x^4 + 6x^3 - 19x^2 + 11x + 29	\( -\,7^{7}\cdot 337^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.94143178827.1	x^9 - 3x^6 + 3	\( -\,3^{23} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.94143178827.2	x^9 - 3x^6 - 9x^3 + 3	\( -\,3^{23} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.94143178827.3	x^9 - 6x^6 + 9x^3 - 3	\( -\,3^{23} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.100397627200.1	x^9 - x^8 + 3x^6 - 3x^5 - 3x^4 + 5x^3 - 4x^2 - 4x + 5	\( -\,2^{6}\cdot 5^{2}\cdot 13^{7} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.104066070003.2	x^9 - 4x^8 + 12x^7 - 27x^6 + 42x^5 - 50x^4 + 34x^3 - 26x^2 + 16x + 1	\( -\,3^{3}\cdot 7^{6}\cdot 181^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.111376896512.1	x^9 - x^8 - 5x^6 - 7x^5 - 9x^4 - 15x^3 - 14x^2 - 14x - 7	\( -\,2^{9}\cdot 7^{6}\cdot 43^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.113468578083.1	x^9 - 7x^3 - 7	\( -\,3^{9}\cdot 7^{8} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.113468578083.2	x^9 - 7x^6 + 14x^3 - 7	\( -\,3^{9}\cdot 7^{8} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.113468578083.3	x^9 - 7x^6 + 7x^3 + 7	\( -\,3^{9}\cdot 7^{8} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.113657692347.1	x^9 - 3x^7 - 6x^6 - 9x^5 + 9x^4 + 21x^3 + 36x^2 + 36x + 24	\( -\,3^{15}\cdot 89^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.115366806603.1	x^9 - 3x^7 - 11x^6 - 6x^5 + 15x^4 + 45x^3 + 45x^2 + 18x + 3	\( -\,3^{13}\cdot 269^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.117088675443.1	x^9 - 3x^7 - 9x^6 + 18x^5 + 18x^4 - 6x^3 - 72x^2 + 54x - 9	\( -\,3^{13}\cdot 271^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.118294540063.1	x^9 - 3x^8 + 9x^7 - 13x^6 + 11x^5 + 2x^4 - 27x^3 + 28x^2 - 7	\( -\,7^{7}\cdot 379^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial
9.3.123277681107.1	x^9 - 5x^7 - 13x^6 - 8x^5 + 13x^4 + 11x^3 + 2x^2 + 8x - 8	\( -\,3^{3}\cdot 7^{6}\cdot 197^{2} \)	$(C_3^2:C_3):C_2$ (as 9T22)	Trivial