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 1096)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.671898241.1	x^9 - 3x^8 + 3x^7 - 3x^6 + 8x^5 - 15x^4 + 17x^3 - 8x^2 - 4x + 5	\( 7^{4}\cdot 23^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.887503681.1	x^9 - x^7 - 2x^6 + 3x^5 + x^4 + 2x^3 - x^2 + x - 3	\( 31^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.6059221281.1	x^9 + 4x^7 - 3x^6 + 9x^5 - 13x^4 + 13x^3 - 15x^2 + 8x - 1	\( 3^{8}\cdot 31^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.8999178496.1	x^9 - 3x^8 + 6x^7 - 4x^6 + 8x^5 - 2x^4 + 4x^3 + 8x^2 + 3x + 1	\( 2^{8}\cdot 7^{4}\cdot 11^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.11019960576.1	x^9 + 6x^3 - 2	\( 2^{8}\cdot 3^{16} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.12043745536.1	x^9 - 2x^8 + 6x^7 - 6x^6 + 10x^5 - 4x^4 + 6x^3 + 4x^2 - 2x + 6	\( 2^{8}\cdot 19^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.18823840000.1	x^9 - x^8 + 2x^7 + 4x^2 + 3x + 1	\( 2^{8}\cdot 5^{4}\cdot 7^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.19770609664.1	x^9 - 3x^8 + 5x^7 - x^6 - x^5 + 5x^4 - 2x^3 + 3x + 1	\( 2^{12}\cdot 13^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.26376683281.1	x^9 - x^8 - 5x^7 - x^6 + 10x^5 + 9x^4 + 4x^3 - 17x^2 - 8x - 1	\( 13^{4}\cdot 31^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.26904200625.1	x^9 - 3x^8 + 3x^7 + 3x^6 - 6x^5 - 12x^4 + 36x^3 - 39x^2 + 21x - 5	\( 3^{16}\cdot 5^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.36469158961.1	x^9 + 2x^7 - 2x^6 - 2x^5 - 9x^4 + 6x^3 - 25x^2 + 35x - 17	\( 19^{4}\cdot 23^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.41764235769.2	x^9 - 2x^8 - 2x^7 + x^6 + 10x^5 + x^4 + 7x^3 - 11x^2 + 7x - 3	\( 3^{10}\cdot 29^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.45956640625.1	x^9 - 3x^8 + 4x^7 - 7x^6 + 21x^5 - 42x^4 + 56x^3 - 68x^2 + 64x - 27	\( 5^{8}\cdot 7^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.99179645184.2	x^9 - 2	\( 2^{8}\cdot 3^{18} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.99179645184.3	x^9 - 6x^6 + 6x^3 - 2	\( 2^{8}\cdot 3^{18} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.107049369856.1	x^9 - 3x^8 + 8x^7 - 14x^6 + 14x^5 - 16x^4 + 26x^3 - 6x^2 + 5x - 1	\( 2^{8}\cdot 11^{4}\cdot 13^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.119538913536.1	x^9 - x^8 + 2x^7 - 4x^2 - 3x - 1	\( 2^{8}\cdot 3^{4}\cdot 7^{8} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.139522419729.1	x^9 - 2x^8 + x^7 - 7x^5 + 7x^4 - 11x^2 + 15x - 11	\( 3^{4}\cdot 7^{6}\cdot 11^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.148718980881.1	x^9 - 13x^6 - 9x^5 + 9x^4 + 29x^3 + 45x^2 - 42x - 79	\( 3^{12}\cdot 23^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.148718980881.3	x^9 - 9x^7 + 27x^5 - 30x^3 + 9x - 25	\( 3^{12}\cdot 23^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.176319369216.1	x^9 + 9x^7 + 27x^5 + 24x^3 - 9x - 34	\( 2^{12}\cdot 3^{16} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.192699928576.1	x^9 - x^8 - x^7 + 11x^6 - 12x^5 - 10x^4 + 37x^3 - 35x^2 + 14x - 2	\( 2^{12}\cdot 19^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.208827064576.1	x^9 - 3x^8 + 4x^7 - 6x^6 + 3x^5 - x^4 - 7x^3 + x^2 + x - 1	\( 2^{8}\cdot 13^{8} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.218889236736.1	x^9 - 2x^7 - 6x^6 + 6x^5 - 8x^3 - 18x^2 + 10x - 6	\( 2^{8}\cdot 3^{8}\cdot 19^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.242137805625.1	x^9 + 9x^7 + 27x^5 + 30x^3 + 9x - 1	\( 3^{18}\cdot 5^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.314722122001.1	x^9 - 3x^8 + 5x^7 - 10x^6 + 20x^5 - 33x^4 + 52x^3 - 74x^2 + 69x - 28	\( 7^{4}\cdot 107^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.346083947521.1	x^9 - 3x^8 - 2x^7 + 12x^6 - 10x^4 - 60x^3 + 167x^2 - 160x + 59	\( 13^{4}\cdot 59^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.375878121921.2	x^9 + 9x^7 - 6x^6 + 27x^5 - 36x^4 + 24x^3 - 54x^2 - 9x - 1	\( 3^{12}\cdot 29^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.434734510336.1	x^9 - 3x^8 + x^7 + 9x^6 - 14x^5 + 2x^4 + 13x^3 - 31x^2 + 20x - 14	\( 2^{8}\cdot 7^{4}\cdot 29^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.488455618816.1	x^9 - 3x^8 + 8x^7 - 18x^6 + 50x^5 - 72x^4 + 60x^3 - 4x^2 + 11x - 11	\( 2^{8}\cdot 11^{4}\cdot 19^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.490796923761.3	x^9 - 9x^7 + 27x^5 - 30x^3 + 9x - 29	\( 3^{12}\cdot 31^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.524467088401.1	x^9 - 4x^8 + 8x^6 + 21x^5 - 16x^4 - 77x^3 - 121x^2 - 94x - 35	\( 23^{4}\cdot 37^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.629034575689.1	x^9 - x^8 - x^7 + 11x^6 - 11x^5 - x^4 + 31x^3 - 64x^2 + 47x - 25	\( 13^{6}\cdot 19^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.751274631121.1	x^9 - x^8 + 2x^7 + 14x^6 - 14x^5 - 21x^4 + 35x^3 - 11x^2 + 4x - 1	\( 7^{8}\cdot 19^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.860204310784.1	x^9 - x^8 - 4x^7 + 2x^6 - 2x^5 - 12x^4 + 12x^3 - 4x^2 - 17x - 9	\( 2^{8}\cdot 7^{6}\cdot 13^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.922368160000.1	x^9 - x^8 + 2x^7 + 7x^5 - 7x^4 + 7x^3 + 3x^2 - 3x - 1	\( 2^{8}\cdot 5^{4}\cdot 7^{8} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.952857108736.1	x^9 - 3x^8 + 6x^7 - 10x^6 + 28x^5 - 28x^4 - 10x^3 - 22x^2 + 3x - 1	\( 2^{8}\cdot 13^{4}\cdot 19^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.956720690641.1	x^9 - x^8 + 5x^7 + 9x^6 - 46x^5 + 153x^4 - 262x^3 + 363x^2 - 274x + 167	\( 23^{4}\cdot 43^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1229457398481.1	x^9 - 3x^8 + 3x^7 - 9x^6 + 12x^5 - 21x^4 + 18x^3 - 21x^2 + 12x - 11	\( 3^{16}\cdot 13^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1262548871424.2	x^9 - x^8 - 6x^7 + 4x^6 + 20x^5 - 38x^3 + 2x^2 + 15x + 21	\( 2^{8}\cdot 3^{10}\cdot 17^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1343677407241.1	x^9 - 4x^8 + 8x^7 - 16x^6 + 19x^5 - 32x^4 + 21x^3 - 33x^2 + 18x - 7	\( 13^{4}\cdot 19^{6} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1355457106081.1	x^9 - x^8 + 4x^7 - 5x^6 + 6x^5 + 18x^4 - 30x^3 + 100x^2 - 137x + 64	\( 13^{4}\cdot 83^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1375668606321.1	x^9 - 3x^8 + 4x^7 - x^6 - 9x^5 + 22x^4 - 7x^3 - 37x^2 + 49x - 18	\( 3^{4}\cdot 19^{8} \)	$(C_9:C_3):C_2$ (as 9T10)	$[9]$
9.1.1586874322944.7	x^9 + 9x^7 + 27x^5 + 30x^3 + 9x - 2	\( 2^{12}\cdot 3^{18} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1730827040881.1	x^9 - 3x^8 + 5x^6 + 7x^5 + 4x^4 - 54x^3 - 138x^2 - 124x - 39	\( 31^{4}\cdot 37^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial
9.1.1912622616576.2	x^9 - 4x^8 + 11x^7 - 14x^6 + 21x^5 - 28x^4 + 49x^3 - 30x^2 + 22x - 36	\( 2^{12}\cdot 3^{4}\cdot 7^{8} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.1991891886336.1	x^9 - 8x^6 - 36x^5 - 54x^4 - 106x^3 - 180x^2 - 96x - 38	\( 2^{8}\cdot 3^{12}\cdot 11^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.1991891886336.2	x^9 - 6x^7 - 4x^6 + 12x^4 + 70x^3 + 126x^2 + 114x + 34	\( 2^{8}\cdot 3^{12}\cdot 11^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.1991891886336.3	x^9 + 12x^7 - 4x^6 + 54x^5 + 12x^4 + 52x^3 + 126x^2 - 30x + 106	\( 2^{8}\cdot 3^{12}\cdot 11^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	$[3]$
9.1.2101386547456.1	x^9 - 3x^8 + 2x^7 + 4x^6 + 20x^5 - 26x^4 - 4x^3 + 24x^2 - x + 1	\( 2^{8}\cdot 7^{4}\cdot 43^{4} \)	$(C_9:C_3):C_2$ (as 9T10)	Trivial