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 626)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.187570506627.1	x^9 - 3x^8 - 3x^7 + 12x^6 - 21x^5 + 36x^4 - 48x^3 + 45x^2 - 24x + 7	\( -\,3^{13}\cdot 7^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.204128387072.1	x^9 - 2x^8 - 8x^7 + 16x^6 + 28x^5 - 32x^4 - 24x^3 + 24x^2 + x - 2	\( -\,2^{24}\cdot 23^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.293534171136.1	x^9 - 2x^8 + 4x^7 - 8x^6 + 10x^5 - 20x^4 + 16x^3 - 32x^2 + 22x - 12	\( 2^{27}\cdot 3^{7} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.330225942528.1	x^9 - 3x^8 + 12x^5 + 12x^4 - 12x + 4	\( -\,2^{24}\cdot 3^{9} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.417942208512.2	x^9 - 6x^7 - 12x^6 + 12x^5 + 60x^4 + 6x^3 - 48x^2 + 9x + 8	\( -\,2^{18}\cdot 3^{13} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.419853238272.1	x^9 - 3x^8 + 6x^7 - 18x^6 + 12x^5 - 24x^4 + 24x^3 - 12x^2 + 6x - 2	\( 2^{18}\cdot 3^{6}\cdot 13^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.587068342272.1	x^9 - x^8 - 4x^7 - 4x^6 - 4x^5 - 4x^4 + 8x^3 + 8x^2 - 22x - 26	\( 2^{28}\cdot 3^{7} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.592815428352.1	x^9 + 3x^7 - 6x^6 - 24x^4 - 18x^3 - 48x^2 - 27x + 16	\( -\,2^{8}\cdot 3^{9}\cdot 7^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.736586891264.1	x^9 - 2x^8 + 8x^7 - 16x^6 + 28x^5 - 40x^4 + 40x^3 - 32x^2 + 18x - 4	\( 2^{31}\cdot 7^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.806215680000.1	x^9 - 6x^7 - 12x^6 - 12x^5 + 48x^4 + 84x^3 + 60x^2 + 30x + 8	\( -\,2^{16}\cdot 3^{9}\cdot 5^{4} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.832706445312.1	x^9 - 2x^8 - 2x^7 - 4x^6 - 8x^4 + 18x^3 - 7x + 2	\( -\,2^{18}\cdot 3^{3}\cdot 7^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.909193450176.1	x^9 - 2x^8 - x^7 + 7x^6 - 11x^5 - 4x^4 + 32x^3 - 37x^2 + 19x - 3	\( -\,2^{6}\cdot 3^{6}\cdot 11^{7} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.926004075723.1	x^9 - 9x^7 - 15x^6 - 3x^5 + 42x^4 + 138x^3 + 210x^2 + 153x + 35	\( -\,3^{9}\cdot 19^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.940369969152.4	x^9 - 3x^8 + 18x^5 + 18x^4 - 27x + 9	\( -\,2^{16}\cdot 3^{15} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1053894094848.1	x^9 - 4x^8 + 5x^7 + 14x^6 - 46x^5 + 26x^4 + 26x^3 - 28x^2 + 11x - 2	\( -\,2^{12}\cdot 3^{7}\cdot 7^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1146617856000.1	x^9 - 2x^8 - 2x^7 + 4x^6 + 13x^5 - 14x^4 - 38x^3 + 16x^2 + 43x + 6	\( -\,2^{22}\cdot 3^{7}\cdot 5^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.1303974703125.1	x^9 - 4x^7 - 4x^6 + 12x^5 + 2x^4 - 15x^3 + 2x^2 + 37x - 21	\( 3^{4}\cdot 5^{6}\cdot 101^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1318823395328.1	x^9 - 2x^8 - 16x^6 + 50x^5 - 68x^4 + 48x^3 - 16x^2 - x + 2	\( -\,2^{28}\cdot 17^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1391050107747.2	x^9 - 3x^8 - 2x^7 + 4x^6 + 7x^5 + 2x^4 - 4x^3 + 37x^2 + 53x + 17	\( -\,3^{3}\cdot 61^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1565515579392.1	x^9 - x^8 - 8x^7 + 8x^6 + 28x^5 - 28x^4 - 56x^3 + 56x^2 + 34x - 18	\( -\,2^{31}\cdot 3^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.1743862431744.1	x^9 - 4x^8 + 2x^7 + 8x^6 - 4x^5 + 8x^4 + 2x^3 - 4x^2 + 17x + 4	\( 2^{16}\cdot 3^{7}\cdot 23^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1940970550347.1	x^9 - x^8 - 12x^7 + 3x^6 + 33x^5 - 21x^4 - 69x^3 + 15x^2 + 18x + 3	\( -\,3^{7}\cdot 31^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.1941429671875.1	x^9 - 2x^8 + 6x^7 - 8x^6 - 6x^5 - 14x^4 + 15x^3 + 10x^2 + 25x + 25	\( -\,5^{6}\cdot 499^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.2209699390625.1	x^9 - 2x^8 + 3x^7 - 9x^6 + 10x^5 + 11x^4 + 13x^3 + 63x^2 - 19x + 70	\( 5^{6}\cdot 521^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.2474069078125.1	x^9 + 5x^7 - 5x^6 + 5x^5 - 19x^4 - 5x^3 - 20x^2 - 5x - 5	\( 5^{6}\cdot 541^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.2641807540224.1	x^9 - 3x^8 + 24x^6 - 18x^5 - 18x^4 + 24x^3 + 48x^2 - 3x + 1	\( 2^{27}\cdot 3^{9} \)	$(C_3^2:C_8):C_2$ (as 9T19)	$[3]$
9.3.2727580350528.1	x^9 - 4x^8 + 3x^7 - 3x^6 + 15x^5 - 24x^3 - 9x^2 - 27x - 21	\( -\,2^{6}\cdot 3^{7}\cdot 11^{7} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.3097158156288.1	x^9 - 6x^7 - 12x^6 + 24x^5 + 72x^4 + 90x^3 - 48x^2 - 75x - 16	\( -\,2^{16}\cdot 3^{9}\cdot 7^{4} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.3596615680000.1	x^9 - x^8 - 4x^7 + 20x^6 - 20x^5 - 44x^4 - 12x^3 + 12x^2 + x - 1	\( -\,2^{24}\cdot 5^{4}\cdot 7^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.3881196000000.1	x^9 - x^8 - 6x^6 + 14x^5 + 12x^4 - 17x^3 - 5x^2 - 57x - 47	\( -\,2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 11^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.3967389600768.1	x^9 - 3x^8 + 3x^7 + 3x^6 - 30x^4 + 87x^3 - 117x^2 + 81x - 41	\( 2^{10}\cdot 3^{7}\cdot 11^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.4121204000000.1	x^9 - 2x^8 + 3x^7 - 7x^5 - 2x^4 + 49x^3 - 26x^2 - 35x + 54	\( 2^{8}\cdot 5^{6}\cdot 101^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.4194304000000.1	x^9 - 3x^8 + 4x^7 - 12x^6 + 16x^5 - 8x^4 + 24x^3 + 8x^2 - 54x + 2	\( -\,2^{28}\cdot 5^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.4696546738176.1	x^9 - 2x^8 - 4x^7 + 16x^6 - 10x^5 - 20x^4 + 44x^3 - 32x^2 + 11x + 2	\( -\,2^{31}\cdot 3^{7} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.5150750736384.1	x^9 - 3x^8 + 6x^7 - 6x^6 + 12x^4 - 18x^3 + 6x^2 + 9x - 3	\( -\,2^{16}\cdot 3^{10}\cdot 11^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.5150750736384.2	x^9 - 3x^8 + 6x^7 + 6x^6 - 36x^5 + 48x^4 - 12x^3 - 12x^2 + 18x + 6	\( -\,2^{16}\cdot 3^{10}\cdot 11^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.5308416000000.1	x^9 - 2x^8 - 6x^7 + 12x^6 + 21x^5 - 14x^4 - 82x^3 + 64x^2 + 7x + 6	\( -\,2^{22}\cdot 3^{4}\cdot 5^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.6004750155776.1	x^9 - 2x^8 - 8x^7 + 16x^6 - 10x^5 - 4x^4 + 76x^3 + 80x^2 + 30x + 4	\( -\,2^{24}\cdot 71^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.6051948658688.1	x^9 - 2x^8 + 16x^7 - 16x^6 + 26x^5 - 20x^4 + 16x^3 - 32x^2 + x - 18	\( 2^{22}\cdot 113^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.6305990921875.1	x^9 - x^8 + 2x^7 - 9x^6 + 3x^5 + x^4 + 5x^3 + 60x^2 - 55x - 30	\( -\,5^{6}\cdot 739^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.6975449726976.1	x^9 - 24x^6 - 24x^5 - 48x^4 + 24x^3 + 48x^2 + 24x - 32	\( 2^{18}\cdot 3^{7}\cdot 23^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.7348698545643.1	x^9 - 4x^8 - 3x^7 + 33x^6 - 36x^5 - 24x^4 + 18x^3 + 33x^2 + 15x + 3	\( -\,3^{7}\cdot 7^{6}\cdot 13^{4} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.7504828453125.1	x^9 - 3x^8 + 7x^7 - 10x^6 + 51x^5 + 10x^4 + 33x^3 + 21x^2 + 11x + 5	\( 3^{4}\cdot 5^{6}\cdot 181^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.8502028075008.1	x^9 - 6x^7 - 12x^6 + 12x^5 + 60x^4 + 18x^3 - 96x^2 - 39x - 4	\( 2^{16}\cdot 3^{10}\cdot 13^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.1.8502028075008.2	x^9 - 24x^5 - 24x^4 + 24x^3 + 48x^2 + 120x + 32	\( 2^{16}\cdot 3^{10}\cdot 13^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.8951102171875.1	x^9 - x^8 - 13x^7 + 12x^6 + 55x^5 - 47x^4 - 73x^3 + 56x^2 - 29x - 25	\( -\,5^{6}\cdot 17^{4}\cdot 19^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.8957952000000.1	x^9 - 2x^8 + 2x^7 + 4x^6 - 28x^5 - 8x^4 + 38x^3 + 16x^2 - 7x + 2	\( -\,2^{18}\cdot 3^{7}\cdot 5^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.9009299354112.1	x^9 - 3x^8 + x^7 + 6x^6 - 15x^5 + 6x^4 + 67x^3 - 18x^2 - 134x - 63	\( -\,2^{9}\cdot 3^{6}\cdot 17^{6} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.9812134526976.1	x^9 - 3x^8 + 10x^7 - 26x^6 + 48x^5 - 76x^4 + 90x^3 - 102x^2 + 17x + 13	\( -\,2^{16}\cdot 3^{6}\cdot 59^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial
9.3.9903746546875.1	x^9 - 3x^8 - 5x^7 + 14x^6 + 21x^5 - 22x^4 - 43x^3 - x^2 + 25x + 8	\( -\,5^{6}\cdot 859^{3} \)	$(C_3^2:C_8):C_2$ (as 9T19)	Trivial