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 1259)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.562419575.1	x^9 - x^8 + 3x^6 + 3x^4 - x^3 - 2x^2 - 3x - 1	\( -\,5^{2}\cdot 23^{3}\cdot 43^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.3031561951.1	x^9 - 2x^8 - 2x^7 + 6x^6 - 4x^5 + x^4 - 2x^3 + 10x^2 - 6x - 1	\( -\,11^{2}\cdot 29^{2}\cdot 31^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.3303494199.1	x^9 - 3x^8 + 5x^7 - 7x^6 + 10x^4 - 19x^3 + 12x^2 - 3x + 3	\( -\,3^{4}\cdot 31^{3}\cdot 37^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.4616841152.1	x^9 - x^8 - 2x^7 + x^6 + x^5 + 7x^4 - 7x^3 + 10x^2 - 10x + 1	\( -\,2^{6}\cdot 7^{2}\cdot 11^{2}\cdot 23^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.4616841152.2	x^9 - x^8 - x^7 - 4x^6 + 4x^5 + 23x^4 - 35x^3 + 5x^2 + 6x + 1	\( -\,2^{6}\cdot 7^{2}\cdot 11^{2}\cdot 23^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.6276397671.1	x^9 - 4x^7 - 3x^6 + 9x^5 + 13x^4 - 5x^3 - 15x^2 - 8x - 1	\( -\,3^{6}\cdot 17^{2}\cdot 31^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.7497609575.1	x^9 - x^8 - 2x^7 + x^6 - 5x^5 + 2x^4 + 5x^3 - 7x^2 - 14x + 1	\( -\,5^{2}\cdot 23^{3}\cdot 157^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.8728715303.2	x^9 - 4x^8 + 2x^7 + 8x^6 - 8x^5 + 3x^4 - 2x^3 + 4x^2 - 14x + 5	\( -\,7^{2}\cdot 11^{4}\cdot 23^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.8885517056.1	x^9 - x^8 - 6x^7 + 11x^6 + 4x^5 - 15x^4 - x^3 + 18x^2 - 14x + 2	\( -\,2^{8}\cdot 13^{2}\cdot 59^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.9053014784.1	x^9 - x^8 - x^7 - 3x^6 - 6x^5 + 4x^4 - 2x^3 - 2x^2 + 4x + 2	\( -\,2^{8}\cdot 11^{3}\cdot 163^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.9502786304.1	x^9 - x^8 + 6x^6 - 2x^3 - 4x^2 - 7x - 1	\( -\,2^{8}\cdot 11^{3}\cdot 167^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.11488631031.1	x^9 + x^7 - 3x^6 - 6x^5 + 2x^4 - 5x^3 + 9x^2 - 7x - 1	\( -\,3^{6}\cdot 23^{2}\cdot 31^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.11661351647.1	x^9 - 3x^8 + x^6 + 7x^5 + 9x^4 - 21x^3 + 2x^2 - 20x + 25	\( -\,11^{2}\cdot 23^{3}\cdot 89^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.12859255359.1	x^9 - 2x^8 + 5x^6 - 11x^5 + 12x^4 - 25x^3 + 45x^2 - 27x + 3	\( -\,3^{4}\cdot 31^{3}\cdot 73^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.13089714176.1	x^9 - 2x^8 - 4x^7 + 4x^6 + 10x^5 + 12x^4 - 30x^3 - 16x^2 + 16x + 8	\( -\,2^{12}\cdot 7^{4}\cdot 11^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.5.14552404288.1	x^9 - 2x^8 + x^7 + x^6 - 5x^5 + 6x^4 - 2x^3 - 3x^2 + 5x - 1	\( 2^{6}\cdot 37^{3}\cdot 67^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.15289551047.1	x^9 - 4x^8 + 5x^7 + x^6 - 17x^5 + 43x^4 - 44x^3 + 11x^2 - 2x + 1	\( -\,19^{2}\cdot 23^{3}\cdot 59^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.16855297943.1	x^9 - 9x^7 - x^6 + 25x^5 - 9x^4 - 25x^3 + 2x^2 - 6x - 1	\( -\,11^{2}\cdot 23^{3}\cdot 107^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.18437397287.3	x^9 - x^8 - 8x^7 + 8x^6 + 23x^5 - 33x^4 - 65x^3 - 12x^2 + 9x - 1	\( -\,23^{3}\cdot 1231^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.19018604191.1	x^9 - 4x^8 + 7x^7 - 8x^6 + 2x^5 + 4x^4 + 12x^3 - 21x^2 - 13x + 11	\( -\,17^{2}\cdot 31^{3}\cdot 47^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.19163329175.1	x^9 - x^8 - 6x^7 - 2x^6 + 20x^5 + 22x^4 - 32x^3 - 30x^2 + 10x + 11	\( -\,5^{2}\cdot 23^{3}\cdot 251^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.19193880512.1	x^9 - 5x^7 - 7x^6 + 11x^5 + 22x^4 + 2x^3 - 31x^2 - 19x + 1	\( -\,2^{6}\cdot 23^{3}\cdot 157^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.20184371648.1	x^9 - x^8 - 2x^7 + x^6 + 9x^5 - 17x^4 - 3x^3 + 22x^2 - 22x + 1	\( -\,2^{6}\cdot 7^{2}\cdot 23^{5} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.21167672087.1	x^9 - x^8 + x^7 + 7x^6 - 14x^5 + 6x^4 - 10x^3 - 17x^2 - 7x - 1	\( -\,23^{3}\cdot 1319^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.21749352023.1	x^9 - 4x^8 + 2x^7 + 11x^6 - 19x^5 + 16x^4 - 17x^3 + 35x^2 - 53x + 23	\( -\,7^{2}\cdot 23^{3}\cdot 191^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.22637694896.1	x^9 - 3x^8 + 8x^6 - 10x^5 - 9x^4 + 16x^3 + 8x^2 - 8x - 4	\( -\,2^{4}\cdot 59^{3}\cdot 83^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.23650508871.1	x^9 - 4x^8 + 4x^7 - 3x^6 + 17x^5 - 20x^4 - 11x^3 + 10x^2 - 4x + 1	\( -\,3^{8}\cdot 11^{2}\cdot 31^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.24077115991.1	x^9 - 3x^7 - 3x^6 + 12x^5 - 33x^3 + 21x^2 - 7x - 1	\( -\,29^{2}\cdot 31^{5} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.24110756800.1	x^9 - 2x^8 - 3x^7 + 11x^6 - 9x^5 - 8x^4 + 20x^3 - 7x^2 - 5x - 1	\( -\,2^{6}\cdot 5^{2}\cdot 13^{3}\cdot 19^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.5.24112521369.1	x^9 + 3x^7 - 4x^6 - 6x^5 + 3x^4 - 10x^3 + 3x^2 + 6x + 1	\( 3^{9}\cdot 107^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.24303729344.1	x^9 - x^8 - 2x^7 + 8x^6 - 13x^5 + 14x^4 - 16x^3 + 12x^2 - 6x - 1	\( -\,2^{6}\cdot 43^{2}\cdot 59^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.25160316751.1	x^9 - x^8 - 6x^7 + 7x^6 + 7x^5 - 15x^4 + 11x^3 + 4x^2 - 18x + 9	\( -\,31^{3}\cdot 919^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.25175691584.1	x^9 - x^8 - 6x^7 + 5x^6 + 11x^5 - 11x^4 - 8x^3 + 5x^2 + 6x + 2	\( -\,2^{6}\cdot 29^{3}\cdot 127^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.27216950976.1	x^9 - x^8 - 5x^7 + 2x^6 + 14x^5 - 9x^4 - 11x^3 + 15x^2 - 4x - 3	\( -\,2^{6}\cdot 3^{2}\cdot 19^{3}\cdot 83^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.27229940672.1	x^9 - 2x^7 - 7x^6 + 3x^5 + 7x^4 + x^3 - 18x^2 - 17x + 5	\( -\,2^{6}\cdot 11^{2}\cdot 17^{2}\cdot 23^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.28027448576.1	x^9 - 3x^8 + x^7 + x^5 + 14x^4 - 27x^3 + 16x^2 - 2x + 1	\( -\,2^{8}\cdot 29^{3}\cdot 67^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.28407316928.1	x^9 - 3x^8 + 6x^7 - 5x^6 - 13x^5 + 35x^4 - 61x^3 + 46x^2 - 4x - 25	\( -\,2^{6}\cdot 23^{3}\cdot 191^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.30723115968.1	x^9 - 3x^8 + x^6 + 9x^5 - 9x^4 + 7x^3 - 6x^2 - 6x + 3	\( -\,2^{6}\cdot 3^{9}\cdot 29^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.30996752384.1	x^9 - 3x^8 + 3x^7 + 2x^6 - 7x^5 + 4x^4 + x^3 - 4x^2 + 1	\( -\,2^{11}\cdot 13^{3}\cdot 83^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.31177145439.1	x^9 - 3x^8 + 3x^7 - 7x^6 + 5x^5 + 3x^4 + 5x^3 - 4x^2 - 15x + 1	\( -\,3^{2}\cdot 11^{2}\cdot 31^{5} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.31728129984.1	x^9 - x^8 - 2x^7 + 3x^6 + 3x^5 - 13x^4 - 51x^3 - 80x^2 - 48x - 9	\( -\,2^{6}\cdot 3^{2}\cdot 31^{3}\cdot 43^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.33336714375.3	x^9 - 4x^8 + 15x^6 - 15x^5 - 9x^4 + 32x^3 - 11x^2 - 15x + 9	\( -\,3^{7}\cdot 5^{4}\cdot 29^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.33662906479.2	x^9 - 3x^8 + 7x^7 - 7x^6 - 4x^5 + 6x^4 - 19x^3 - 9x^2 - 10x + 1	\( -\,31^{3}\cdot 1063^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.34013870528.1	x^9 - 2x^8 + x^7 + x^6 - 13x^5 + 8x^4 + 16x^3 + 3x^2 - 17x + 1	\( -\,2^{6}\cdot 11^{2}\cdot 19^{2}\cdot 23^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.5.34373550825.1	x^9 - 3x^6 - 5x^5 + 5x^2 - 1	\( 3^{4}\cdot 5^{2}\cdot 257^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.5.34373550825.2	x^9 - 6x^7 - x^6 + 4x^5 - 9x^4 - x^3 + 17x^2 + 9x + 1	\( 3^{4}\cdot 5^{2}\cdot 257^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.34667968448.1	x^9 - 3x^8 + 5x^7 - 10x^6 + 2x^5 + 19x^4 - 29x^3 + 45x^2 - 49	\( -\,2^{6}\cdot 23^{3}\cdot 211^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.35403742700.1	x^9 - 6x^7 - x^6 + 11x^5 - 3x^4 - 13x^3 + 4x^2 + 4x - 2	\( -\,2^{2}\cdot 5^{2}\cdot 17^{2}\cdot 107^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.35994852800.1	x^9 - x^8 + 2x^7 - 15x^6 + 17x^5 + 7x^4 - 43x^3 + 40x^2 - 20x + 5	\( -\,2^{6}\cdot 5^{2}\cdot 23^{3}\cdot 43^{2} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial
9.3.36035099127.2	x^9 - 2x^7 - 3x^6 - 3x^5 + 4x^4 - 6x^3 + 3x^2 - 2x - 1	\( -\,3^{6}\cdot 367^{3} \)	$(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ (as 9T29)	Trivial