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 4282)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.846519025.1	x^9 - 3x^8 + 7x^7 - 9x^6 + 7x^5 - 7x^4 + 13x^3 - 6x^2 + x + 1	\( 5^{2}\cdot 11^{2}\cdot 23^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.1083199744.1	x^9 - x^8 - 2x^6 + 4x^4 + 6x^3 + 8x^2 + 5x + 1	\( 2^{8}\cdot 11^{4}\cdot 17^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.1186458025.1	x^9 - x^8 - x^7 + 3x^6 - x^5 - 2x^4 + 5x^3 - 4x^2 + x + 1	\( 5^{2}\cdot 83^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.1927824649.1	x^9 - 3x^8 + 7x^7 - 11x^6 + 15x^5 - 12x^4 + 9x^3 - 4x^2 - 2x - 1	\( 23^{4}\cdot 83^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.2021851225.1	x^9 - 3x^8 - x^7 + 7x^6 + x^5 - 8x^4 + x^3 + 6x^2 + 2x + 1	\( 5^{2}\cdot 17^{2}\cdot 23^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.2594170489.1	x^9 - 2x^8 + x^7 + 7x^6 - 20x^5 + 35x^4 - 36x^3 + 24x^2 - 8x + 1	\( 31^{4}\cdot 53^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.2702336256.1	x^9 - 2x^7 + 4x^5 - 2x^4 - 14x^3 - 16x^2 - 8x - 2	\( 2^{8}\cdot 3^{4}\cdot 19^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.3038765625.1	x^9 - x^8 + 2x^7 + 3x^5 + 7x^4 - 2x^3 + 4x^2 + 1	\( 3^{4}\cdot 5^{6}\cdot 7^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.3152148736.1	x^9 - 4x^8 + 4x^7 + 4x^6 - 4x^5 - 6x^4 + 2x^3 + 2x^2 + 2x - 2	\( 2^{8}\cdot 11^{4}\cdot 29^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.3401222400.1	x^9 - 3x^8 + 6x^7 - 6x^6 + 6x^5 - 6x^4 + 6x^3 - 3x + 1	\( 2^{8}\cdot 3^{12}\cdot 5^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.3573289729.1	x^9 - 4x^8 + 12x^7 - 25x^6 + 36x^5 - 41x^4 + 31x^3 - 12x^2 + 6x + 1	\( 23^{4}\cdot 113^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.5252335729.1	x^9 + x^7 - 8x^6 - 7x^5 - 27x^4 - 26x^3 - 23x^2 - 9x - 5	\( 23^{4}\cdot 137^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.5864802724.1	x^9 - 3x^8 + 8x^7 - 11x^6 + 15x^5 - 12x^4 + 13x^3 - 6x^2 + 4x + 2	\( 2^{2}\cdot 11^{2}\cdot 59^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.6212750041.1	x^9 - 3x^8 + 5x^7 - 4x^6 + 8x^5 - 15x^4 + 15x^3 + 9x^2 - 18x + 7	\( 23^{4}\cdot 149^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.6300549376.1	x^9 - 2x^8 + 6x^6 - 12x^5 - 2x^4 + 18x^3 - 6x^2 - 2x - 2	\( 2^{8}\cdot 11^{4}\cdot 41^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.7014397504.1	x^9 - 5x^6 + 6x^4 - x^3 + 6x^2 + 4x + 1	\( 2^{6}\cdot 19^{4}\cdot 29^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.9051429321.1	x^9 - x^8 + 3x^7 - 6x^6 + 10x^5 - 18x^4 + 26x^3 - 31x^2 + 24x - 9	\( 3^{4}\cdot 11^{2}\cdot 31^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.9558581824.1	x^9 - 2x^8 + x^7 - 2x^6 - x^5 + 6x^4 + 7x^3 + 10x^2 + 4x + 4	\( 2^{6}\cdot 11^{4}\cdot 101^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.9785759929.1	x^9 - 4x^8 + 3x^7 + 7x^6 - 2x^5 - 9x^4 - 2x^3 + 12x^2 + 12x + 5	\( 11^{2}\cdot 17^{2}\cdot 23^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.9829532736.1	x^9 - 3x^8 + 6x^7 - 9x^6 + 6x^5 - 3x^4 + 3x^3 - 2	\( 2^{6}\cdot 3^{12}\cdot 17^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.9940887616.1	x^9 - 2x^8 + 8x^7 - 9x^6 + 16x^5 - 6x^4 + 3x^3 + 12x^2 - 8x + 11	\( 2^{6}\cdot 11^{4}\cdot 103^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.10727987776.1	x^9 - 2x^8 + x^6 + 2x^5 + 3x^3 - 18x^2 + 6x - 1	\( 2^{6}\cdot 11^{4}\cdot 107^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.12890196225.1	x^9 - x^8 - x^7 + 3x^6 - 8x^4 + 10x^3 - 9x^2 + 3x - 3	\( 3^{6}\cdot 5^{2}\cdot 29^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.13107960100.1	x^9 - 2x^8 + 6x^7 - 5x^6 + 7x^5 + 2x^4 - x^3 + 10x^2 - 5x + 7	\( 2^{2}\cdot 5^{2}\cdot 107^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.14020454464.1	x^9 - 3x^8 + 6x^7 - 9x^6 + 8x^5 - x^4 - 5x^3 + 8x^2 - 8x + 4	\( 2^{6}\cdot 19^{4}\cdot 41^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.14526998784.1	x^9 - 3x^8 + 6x^7 - 8x^6 + 6x^5 - 6x^3 + 12x^2 - 9x + 3	\( 2^{8}\cdot 3^{10}\cdot 31^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.15587023104.1	x^9 - x^8 + 2x^6 - 2x^4 + 4x^3 + 4x^2 - x - 1	\( 2^{8}\cdot 3^{6}\cdot 17^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.16461916416.1	x^9 - 3x^8 + 6x^7 - 12x^6 + 18x^5 - 24x^4 + 18x^3 - 24x^2 + 9x - 1	\( 2^{8}\cdot 3^{12}\cdot 11^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.17333565649.1	x^9 - 7x^6 - 5x^5 + x^4 + 13x^3 + 20x^2 + 7x - 1	\( 31^{4}\cdot 137^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.17723064384.1	x^9 - x^8 + 2x^7 - 3x^6 + 3x^4 - 5x^3 + 10x^2 - 8x + 2	\( 2^{6}\cdot 3^{4}\cdot 43^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.19651834225.1	x^9 - x^8 - 6x^7 - x^6 + 19x^5 + 18x^4 - 11x^3 - 33x^2 - 22x - 7	\( 5^{2}\cdot 23^{4}\cdot 53^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.20834612964.1	x^9 - 3x^8 + 3x^7 - x^6 + 9x^4 - 3	\( 2^{2}\cdot 3^{16}\cdot 11^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.21162975625.1	x^9 - x^8 + x^7 - 5x^6 + 3x^5 - 3x^4 + 9x^3 - 8x^2 + 28x - 8	\( 5^{4}\cdot 11^{2}\cdot 23^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.21618703089.1	x^9 - 3x^8 + 3x^7 - x^6 + 5x^5 - x^4 + 5x^3 - 10x^2 - 4x - 8	\( 3^{4}\cdot 17^{2}\cdot 31^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.21880326400.1	x^9 - 2x^8 + 6x^7 - 6x^6 + 4x^5 + 2x^4 - 4x^3 + 2x^2 + 8x - 2	\( 2^{8}\cdot 5^{2}\cdot 43^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.23428588096.1	x^9 - x^8 - 2x^7 + x^6 + 2x^5 + 5x^4 - 13x^3 + 2x^2 + 4x + 4	\( 2^{6}\cdot 19^{4}\cdot 53^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.23459210896.1	x^9 - 2x^8 - 2x^7 + 8x^6 - 9x^5 + 18x^3 - 20x^2 + 7x - 2	\( 2^{4}\cdot 11^{2}\cdot 59^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.24895790656.1	x^9 - x^8 + 6x^7 - x^6 + 12x^5 + 7x^4 + 11x^3 + 10x^2 + 4	\( 2^{6}\cdot 11^{4}\cdot 163^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.25640335876.1	x^9 - 3x^8 + 3x^7 + 5x^6 - 10x^5 + 17x^3 - 7x^2 - 11x + 13	\( 2^{2}\cdot 23^{2}\cdot 59^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.25756077169.1	x^9 - x^8 - 2x^5 - 11x^4 + 18x^3 + 5x^2 - 2x - 9	\( 31^{4}\cdot 167^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.25820633344.1	x^9 - x^8 + 4x^7 - 4x^6 + 4x^5 - 4x^4 + 2x^3 - 2x^2 + 11x + 11	\( 2^{8}\cdot 11^{4}\cdot 83^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.26132662336.1	x^9 - 4x^8 + 6x^7 - 7x^6 + 6x^5 + 8x^4 - 11x^3 - 16x^2 + 4x - 1	\( 2^{6}\cdot 11^{4}\cdot 167^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.26244000000.1	x^9 - 3x^8 + 4x^7 - 8x^5 + 8x^4 - 6x^3 + 4x^2 + x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{6} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.26374734409.1	x^9 - 2x^8 - 3x^7 + 2x^6 + 11x^5 - 23x^4 + 11x^3 - 13x^2 - 8x - 1	\( 23^{4}\cdot 307^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.26374734409.2	x^9 - 3x^8 + x^7 + 15x^6 - 21x^5 + 3x^4 + 21x^3 - 14x^2 - 4x + 8	\( 23^{4}\cdot 307^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.26374734409.3	x^9 - x^8 + 6x^7 - 6x^6 + 2x^5 + 7x^4 - 11x^3 + 23x^2 - 19x + 5	\( 23^{4}\cdot 307^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.27950489856.1	x^9 - 3x^8 + 6x^7 - 6x^6 - 6x^5 + 18x^4 - 6x^3 - 18x^2 + 9x + 9	\( 2^{8}\cdot 3^{10}\cdot 43^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.29590536361.1	x^9 - 2x^8 + 6x^7 + 3x^6 - 13x^5 + 44x^4 - 39x^3 + 21x^2 - 5x + 1	\( 31^{4}\cdot 179^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial
9.1.29661450625.1	x^9 - 3x^8 + 3x^7 - 4x^6 + 14x^5 - 27x^4 + 26x^3 - 16x^2 + 13x - 8	\( 5^{4}\cdot 83^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	$[3]$
9.1.31037630625.1	x^9 - 3x^8 + 3x^7 - x^6 - 6x^5 + 15x^4 - 13x^3 + 12x^2 - 6x + 1	\( 3^{10}\cdot 5^{4}\cdot 29^{2} \)	$(C_3^3:C_3):C_2$ (as 9T21)	Trivial