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 870)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.9155562688.1	x^9 - x^7 - 5x^6 + x^5 + 2x^4 + 4x^3 - 3x^2 - x + 1	\( -\,2^{6}\cdot 523^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.16836267547.1	x^9 - 2x^8 + 2x^7 - x^6 + 3x^5 + 3x^4 - 14x^3 - 12x^2 + x + 2	\( -\,11^{3}\cdot 233^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.17256481947.1	x^9 - x^8 - 3x^7 + 3x^6 - 3x^5 + 6x^4 + 9x^3 - 18x^2 - 9x + 18	\( -\,3^{7}\cdot 53^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.17964142659.1	x^9 - 3x^8 + 7x^6 - 3x^5 - 12x^4 + 8x^3 + 3x - 2	\( -\,3^{9}\cdot 97^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.36889110963.1	x^9 + 3x^7 - 3x^6 + 6x^3 + 3x^2 - 9x - 5	\( -\,3^{9}\cdot 37^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.45537538411.1	x^9 - 3x^8 - 2x^7 + 8x^6 + 9x^5 - 10x^4 - 6x^3 + 9x^2 - x - 1	\( -\,3571^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.59273381699.1	x^9 - 3x^8 + 5x^7 - 5x^6 + 7x^5 + x^4 - 12x^3 + 10x^2 - 11x + 6	\( -\,7^{3}\cdot 557^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.67292260083.1	x^9 - 3x^8 + 7x^6 - 6x^5 + 6x^4 + 7x^3 - 6x^2 + 9x - 1	\( -\,3^{9}\cdot 43^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.69325227712.1	x^9 - 2x^8 - 5x^7 + 9x^6 + 11x^5 - 22x^4 + 6x^3 + 7x^2 - 9x + 1	\( -\,2^{6}\cdot 13^{3}\cdot 79^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.82556485632.1	x^9 - 4x^6 - 6x^5 + 12x^4 + 4x^3 - 12x^2 + 3x + 4	\( -\,2^{22}\cdot 3^{9} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.83702510811.1	x^9 - 2x^8 - 7x^7 + 13x^6 + 17x^5 - 26x^4 - 19x^3 + 13x^2 + 11x + 2	\( -\,3^{7}\cdot 337^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.98673100992.1	x^9 - 3x^8 + 3x^7 - 6x^6 + 12x^5 + 3x^4 - 21x^3 + 9x^2 + 1	\( -\,2^{6}\cdot 3^{7}\cdot 89^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.110522894399.1	x^9 - 3x^8 + 2x^7 - 5x^6 + 15x^5 - 11x^4 + 12x^3 - 31x^2 + 31x - 14	\( -\,4799^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.114162766875.1	x^9 - x^8 + x^7 - 7x^6 + 4x^5 + 5x^4 + 4x^3 - 13x^2 + x + 3	\( -\,3^{7}\cdot 5^{4}\cdot 17^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.127745014464.2	x^9 - x^8 - 7x^7 + 8x^6 + 8x^5 - x^4 - 25x^3 + 11x^2 + 8x + 1	\( -\,2^{6}\cdot 3^{7}\cdot 97^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.1.151803769808.1	x^9 - 2x^8 + 3x^7 - 10x^6 + 22x^5 - 21x^4 + 11x^3 - 11x^2 + 13x - 5	\( 2^{4}\cdot 29^{3}\cdot 73^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.176004726784.1	x^9 - 3x^8 + 2x^7 - 2x^6 + 4x^5 - 4x^4 + 4x^3 + 2x - 2	\( -\,2^{16}\cdot 139^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.193572384768.1	x^9 - 3x^8 + 10x^6 - 12x^5 - 12x^4 + 20x^3 - 12x + 4	\( -\,2^{12}\cdot 3^{9}\cdot 7^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.207773767683.1	x^9 - 3x^8 + 11x^6 - 18x^5 + 18x^4 - 33x^3 + 54x^2 - 27x - 9	\( -\,3^{13}\cdot 19^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.210082347387.1	x^9 - 3x^8 + 9x^6 + 3x^5 - 6x^3 - 12x^2 - 9x - 2	\( -\,3^{15}\cdot 11^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.213262572976.1	x^9 - 2x^8 - 3x^7 + 5x^6 + 2x^5 + 2x^3 - 12x^2 + 20x - 12	\( -\,2^{4}\cdot 2371^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.221788060119.1	x^9 - 4x^6 - 2x^5 - 19x^4 + 9x^3 + 8x^2 - 16x - 8	\( -\,3^{4}\cdot 1399^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.222742590768.1	x^9 - 3x^8 + 6x^7 - 3x^6 - 18x^4 + 6x^3 + 12x^2 + 12x - 4	\( -\,2^{4}\cdot 3^{9}\cdot 29^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.224201671875.2	x^9 - 3x^8 - 3x^7 + 8x^6 - 3x^5 - 3x^4 + 13x^3 + 9x + 9	\( -\,3^{15}\cdot 5^{6} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.225977811571.1	x^9 - x^8 + x^7 + 6x^6 + 14x^5 - 8x^4 + 13x^3 - 15x^2 + 2x + 1	\( -\,6091^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.1.241106407424.1	x^9 - 2x^8 + 4x^7 - 4x^6 + 8x^5 - 24x^4 + 4x^3 + 8x^2 + 20x + 8	\( 2^{12}\cdot 389^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.248028267187.1	x^9 - x^8 + 4x^6 + 3x^5 - 17x^4 - 18x^3 + 7x^2 + 25x + 11	\( -\,61^{3}\cdot 103^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.251559482544.1	x^9 - 3x^8 + 12x^7 - 21x^6 + 36x^5 - 30x^4 + 6x^3 + 12x^2 - 36x - 4	\( -\,2^{4}\cdot 3^{7}\cdot 193^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.255202035607.1	x^9 - 3x^8 + 4x^7 + x^6 - 15x^5 - 13x^4 + 10x^3 + 9x^2 - x - 2	\( -\,6343^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.260520451875.1	x^9 - x^8 - 5x^7 - 4x^6 + 34x^5 - 19x^4 - 11x^3 - 37x^2 + 67x - 24	\( -\,3^{6}\cdot 5^{4}\cdot 83^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.272527688403.1	x^9 - 3x^8 + 7x^6 + 3x^5 - 3x^4 - 14x^3 + 3x^2 + 9x - 7	\( -\,3^{9}\cdot 61^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.275513205843.1	x^9 - 3x^8 + 5x^6 - 3x^5 + 9x^4 - 2x^3 - 27x^2 + 9x + 13	\( -\,3^{9}\cdot 241^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.283722907411.1	x^9 - 6x^7 - 11x^6 - 3x^5 - 8x^4 + 9x^3 - 2x^2 + 7x + 5	\( -\,6571^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.293534171136.1	x^9 - 2x^8 + 4x^7 - 8x^6 + 14x^5 - 28x^4 + 20x^3 - 8x^2 - 23x + 14	\( -\,2^{27}\cdot 3^{7} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.295095094272.1	x^9 - 3x^8 + 6x^6 - 12x^3 + 6x^2 + 6x - 6	\( -\,2^{10}\cdot 3^{9}\cdot 11^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.299015684703.1	x^9 - 2x^8 + 9x^7 - 12x^6 + 8x^5 + 24x^4 - 14x^3 - 7x^2 + 12x + 5	\( -\,3^{6}\cdot 743^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.306045761419.1	x^9 + 4x^7 - 7x^6 + 3x^5 + 10x^4 + 4x^3 - 13x^2 + x + 1	\( -\,23^{3}\cdot 293^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.314928000000.2	x^9 + 6x^7 - 2x^6 - 26x^3 + 12x^2 - 15x + 2	\( -\,2^{10}\cdot 3^{9}\cdot 5^{6} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.321137672192.1	x^9 - 3x^8 + 4x^7 - 4x^6 + 14x^5 - 18x^4 - 44x^3 - 20x^2 - 3x + 1	\( -\,2^{18}\cdot 107^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.326086867387.1	x^9 - 4x^8 + 7x^7 + x^6 - 19x^5 + 30x^4 - 10x^3 - 12x^2 + 13x - 4	\( -\,6883^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.326086867387.2	x^9 - 4x^8 + 9x^7 - 16x^6 + 15x^5 + 7x^4 - 20x^3 + 4x^2 + 6x - 1	\( -\,6883^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.331841002867.1	x^9 - 3x^8 + 10x^7 - 16x^6 + 22x^5 - 20x^4 + 5x^3 - 3x^2 - 9x - 2	\( -\,11^{4}\cdot 283^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.334110914019.5	x^9 - 3x^8 + 6x^7 - 20x^6 + 39x^5 - 33x^4 + 13x^3 - 9x^2 + 3x + 2	\( -\,3^{9}\cdot 257^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.338171833063.1	x^9 - 4x^8 + 7x^7 + 4x^6 - 37x^5 + 77x^4 - 76x^3 + 33x^2 + 20x - 13	\( -\,6967^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.345450655424.1	x^9 - 2x^8 - 3x^7 + 3x^6 + 3x^5 - 6x^3 - 9x^2 - 5x + 1	\( -\,2^{6}\cdot 7^{4}\cdot 131^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.351353851875.1	x^9 - 3x^8 + x^6 + 6x^5 + 6x^4 - x^3 - 3x + 1	\( -\,3^{9}\cdot 5^{4}\cdot 13^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.352519065792.1	x^9 - 9x^7 - 15x^6 - 3x^5 + 18x^4 + 18x^3 - 9x^2 - 15x - 1	\( -\,2^{6}\cdot 3^{9}\cdot 23^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.359209479168.1	x^9 - 2x^8 + 2x^7 - 8x^6 + 8x^5 - 10x^4 + 2x^3 - 4x^2 - 6x + 4	\( -\,2^{10}\cdot 3^{4}\cdot 163^{3} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.409819132827.1	x^9 - 3x^8 + 3x^7 - 5x^6 + 27x^5 - 60x^4 + 38x^3 + 3x^2 - 27x + 8	\( -\,3^{15}\cdot 13^{4} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial
9.3.417942208512.1	x^9 - 3x^8 + 4x^6 + 12x^5 + 12x^4 - 8x^3 - 12x + 4	\( -\,2^{18}\cdot 3^{13} \)	$((C_3^2:Q_8):C_3):C_2$ (as 9T26)	Trivial