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 2959)

Label	Polynomial	Discriminant	Galois group	Class group
9.7.1904081383.1	x^9 - x^8 - 5x^7 + 6x^6 + 5x^5 - 11x^4 + 5x^3 + 6x^2 - 6x + 1	\( -\,37\cdot 51461659 \)	$S_9$ (as 9T34)	Trivial
9.7.2155688911.1	x^9 - 3x^8 - x^7 + 7x^6 - x^4 - 5x^3 - 4x^2 + 4x + 1	\( -\,337\cdot 6396703 \)	$S_9$ (as 9T34)	Trivial
9.7.2307632671.1	x^9 - 4x^7 + x^5 - 2x^4 + 5x^3 + 3x^2 - 2x - 1	\( -\,2307632671 \)	$S_9$ (as 9T34)	Trivial
9.7.2636091127.1	x^9 - 2x^8 - 2x^7 + 3x^6 + x^5 + 4x^4 - x^3 - 6x^2 + 1	\( -\,2791\cdot 944497 \)	$S_9$ (as 9T34)	Trivial
9.7.2668161671.1	x^9 - 7x^7 - 2x^6 + 14x^5 + 7x^4 - 8x^3 - 7x^2 + 1	\( -\,7^{6}\cdot 22679 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.2794474079.1	x^9 - 3x^8 + 4x^6 + 3x^4 - 4x^3 - 5x^2 + 2x + 1	\( -\,23\cdot 5569\cdot 21817 \)	$S_9$ (as 9T34)	Trivial
9.7.2964637151.1	x^9 - x^8 - 2x^7 - 3x^6 - 2x^5 + 12x^4 + 3x^3 - 8x^2 + 1	\( -\,7^{6}\cdot 113\cdot 223 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.3030520591.1	x^9 - x^8 - 2x^7 + 3x^6 - 6x^5 + x^4 + 13x^3 - 2x^2 - 7x - 1	\( -\,7^{6}\cdot 25759 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.3616883207.1	x^9 - x^8 - 5x^7 + 9x^6 + x^5 - 17x^4 + 15x^3 + 2x^2 - 5x + 1	\( -\,7^{6}\cdot 71\cdot 433 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.4475250311.1	x^9 - x^8 - 4x^7 + 4x^6 - 3x^4 + 12x^3 - 9x - 1	\( -\,7^{6}\cdot 38039 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.4591118799.1	x^9 - 3x^7 - 2x^6 - 3x^5 + 3x^4 + 8x^3 - 3x^2 - 3x + 1	\( -\,3^{12}\cdot 53\cdot 163 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.4664429903.1	x^9 - 3x^8 - 2x^7 + 13x^6 - 7x^5 - 13x^4 + 13x^3 + 5x^2 - 5x - 1	\( -\,7^{6}\cdot 41\cdot 967 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.4951022867.1	x^9 - x^8 - 5x^7 + 5x^6 + 6x^5 - 11x^4 - 3x^3 + 7x^2 + x - 1	\( -\,7^{6}\cdot 42083 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.5382559399.1	x^9 - 2x^8 - 4x^7 + 8x^6 + 5x^4 - 8x^3 - 6x^2 + 4x + 1	\( -\,7^{6}\cdot 45751 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.5520914623.1	x^9 - x^8 - 5x^7 + 2x^6 + 8x^5 + 4x^4 - 6x^3 - 5x^2 + 2x + 1	\( -\,7^{6}\cdot 167\cdot 281 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.5632916471.1	x^9 - x^8 - 6x^7 + 3x^6 + 10x^5 + 2x^4 - x^3 - 4x^2 - 4x - 1	\( -\,7^{6}\cdot 13\cdot 29\cdot 127 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.5975510359.1	x^9 - 2x^8 - 2x^7 - x^6 + 9x^5 + 7x^4 - 10x^3 - 5x^2 + 3x + 1	\( -\,7^{6}\cdot 13\cdot 3907 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6221161471.1	x^9 - 2x^8 - 5x^7 + 12x^6 + 3x^5 - 19x^4 + 7x^3 + 7x^2 - 2x - 1	\( -\,7^{6}\cdot 52879 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6225867431.1	x^9 - x^8 - 4x^7 - x^6 + x^5 + 7x^4 + 4x^3 - 6x^2 - x + 1	\( -\,7^{6}\cdot 52919 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6240926503.1	x^9 - 5x^7 - 2x^6 - x^5 + 2x^4 + 12x^3 - 4x^2 - 3x + 1	\( -\,7^{6}\cdot 53047 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6285162527.1	x^9 - 4x^8 + x^7 + 8x^6 - 2x^5 - 6x^3 - 3x^2 + 5x - 1	\( -\,7^{6}\cdot 41\cdot 1303 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6304927559.1	x^9 - x^8 - 6x^7 + 3x^6 + 17x^5 - 5x^4 - 22x^3 + 10x^2 + 3x - 1	\( -\,7^{6}\cdot 53591 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6370810999.1	x^9 - 2x^8 - 6x^7 + 6x^6 + 6x^5 - 8x^4 + 4x^3 + 4x^2 - 5x + 1	\( -\,7^{6}\cdot 54151 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6499283707.1	x^9 - 3x^8 - x^7 + 6x^6 + x^5 + x^4 - 6x^3 - 6x^2 + 5x + 1	\( -\,7^{6}\cdot 55243 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6606265867.1	x^9 - x^8 - 4x^7 + 2x^6 + 6x^3 + x^2 - 3x - 1	\( -\,641\cdot 10306187 \)	$S_9$ (as 9T34)	Trivial
9.7.6799053359.1	x^9 - x^8 - 5x^7 + 6x^6 + 3x^5 - 9x^4 + 11x^3 + 2x^2 - 10x + 1	\( -\,7^{6}\cdot 57791 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6833877463.1	x^9 - 3x^8 - x^7 + 10x^6 - 7x^5 - 8x^4 + 12x^3 - 4x + 1	\( -\,7^{6}\cdot 29\cdot 2003 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6868230971.1	x^9 - x^8 - 8x^7 + 8x^6 + 21x^5 - 18x^4 - 22x^3 + 11x^2 + 8x + 1	\( -\,7^{6}\cdot 58379 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.6884701831.1	x^9 - 3x^8 - 3x^7 + 15x^6 - 2x^5 - 24x^4 + 11x^3 + 13x^2 - 6x - 1	\( -\,7^{6}\cdot 139\cdot 421 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.7272002339.1	x^9 - 2x^8 - x^7 + 2x^6 - 6x^5 + 9x^4 + 12x^3 - 8x^2 - 7x - 1	\( -\,7^{6}\cdot 113\cdot 547 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.7609419671.1	x^9 - 3x^8 - 4x^7 + 17x^6 - x^5 - 24x^4 + 10x^3 + 4x^2 - 1	\( -\,7^{6}\cdot 64679 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.8218841491.1	x^9 - 4x^7 - 4x^6 + 3x^5 + 13x^4 + 4x^3 - 11x^2 - 4x + 1	\( -\,7^{6}\cdot 69859 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.8428256711.1	x^9 - 3x^8 + 3x^7 + 2x^6 - 13x^5 + 10x^4 + 10x^3 - 10x^2 + 1	\( -\,7^{6}\cdot 71\cdot 1009 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9072032039.1	x^9 - 3x^8 + 4x^7 - 5x^6 - 11x^5 + 22x^4 + 4x^3 - 14x^2 + 2x + 1	\( -\,7^{6}\cdot 29\cdot 2659 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9218857991.1	x^9 - x^8 - 4x^7 - 2x^6 + 11x^5 + 9x^4 - 11x^3 - 6x^2 + 3x + 1	\( -\,7^{6}\cdot 127\cdot 617 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9305918251.1	x^9 - x^8 - 7x^7 + 4x^6 + 15x^5 - 3x^4 - 6x^3 + 2x^2 - 3x - 1	\( -\,7^{6}\cdot 83\cdot 953 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9338859971.1	x^9 - 2x^8 - 5x^7 + 13x^6 + 4x^5 - 22x^4 + 2x^3 + 12x^2 - x - 1	\( -\,7^{6}\cdot 79379 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9437685131.1	x^9 - 2x^8 - 6x^7 + 9x^6 + 16x^5 - 12x^4 - 20x^3 + 4x^2 + 8x + 1	\( -\,7^{6}\cdot 97\cdot 827 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9487097711.1	x^9 - 5x^7 - x^6 + 6x^5 + 8x^4 - 3x^3 - 9x^2 + x + 1	\( -\,7^{6}\cdot 13\cdot 6203 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.9996282583.1	x^9 - 3x^8 - 4x^7 + 16x^6 + x^5 - 18x^4 - 4x^3 + 4x^2 + 7x + 1	\( -\,7^{6}\cdot 84967 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10000988543.1	x^9 - x^8 - 4x^7 + 6x^6 + x^5 - 21x^4 - 10x^3 + 8x^2 + 6x + 1	\( -\,7^{6}\cdot 13^{2}\cdot 503 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10214886592.1	x^9 - 2x^8 - 3x^7 + 9x^6 - 3x^5 - 12x^4 + 6x^3 + 7x^2 - x - 1	\( -\,2^{6}\cdot 23\cdot 37^{3}\cdot 137 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.7.10272993031.1	x^9 - x^8 - 4x^7 + 9x^6 - x^5 - 20x^4 + 11x^3 + 9x^2 - 4x - 1	\( -\,7^{6}\cdot 29\cdot 3011 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10336994087.1	x^9 - 2x^8 - 4x^7 + 13x^6 - 2x^5 - 23x^4 + 17x^3 + 7x^2 - 5x - 1	\( -\,7^{6}\cdot 41\cdot 2143 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10647587447.1	x^9 - 2x^8 - 6x^7 + 7x^6 + 14x^5 - 7x^3 - 8x^2 - 5x - 1	\( -\,7^{8}\cdot 1847 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10748765587.1	x^9 - 4x^8 + 4x^7 + 8x^6 - 26x^5 + 18x^4 + 13x^3 - 16x^2 + 2x + 1	\( -\,7^{6}\cdot 211\cdot 433 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10781707307.1	x^9 - 2x^8 - x^7 + 10x^6 - 5x^5 - 17x^4 + 6x^3 + 10x^2 - 1	\( -\,7^{6}\cdot 113\cdot 811 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10871591143.1	x^9 - 2x^8 - 3x^7 + x^6 + 18x^5 - 5x^4 - 34x^3 + 28x^2 - 4x - 1	\( -\,7^{7}\cdot 43\cdot 307 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10887120811.1	x^9 - 2x^8 - 6x^7 + 8x^6 + 15x^5 - 6x^4 - 22x^3 - x^2 + 11x + 1	\( -\,7^{6}\cdot 29\cdot 3191 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.7.10989240143.1	x^9 - 2x^8 - 3x^6 - 5x^5 + 16x^4 + 15x^3 - 3x^2 - 5x - 1	\( -\,7^{6}\cdot 93407 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial