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 6755)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.164590951.1	x^9 - 2x^8 + 3x^7 - x^6 - 2x^5 + 5x^4 - 4x^3 + 2x - 1	\( -\,7^{6}\cdot 1399 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.177767639.1	x^9 - 2x^8 + x^7 + 5x^6 - 9x^5 + 5x^4 + 4x^3 - 7x^2 + 4x - 1	\( -\,7^{6}\cdot 1511 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.186238367.1	x^9 - x^8 - x^7 + 4x^6 - 2x^5 - 4x^4 + 5x^3 - x^2 - 3x + 1	\( -\,7^{6}\cdot 1583 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.227180219.1	x^9 - x^8 - x^7 + x^6 + 3x^4 - x^3 - 3x^2 + x + 1	\( -\,7^{6}\cdot 1931 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.233768563.1	x^9 - x^8 + 4x^6 - 6x^5 + 4x^4 + x^3 - 5x^2 + 4x - 1	\( -\,7^{6}\cdot 1987 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.252121807.1	x^9 - x^8 - 2x^7 + 3x^5 + 3x^4 - 2x^3 - 4x^2 + 1	\( -\,7^{6}\cdot 2143 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.267314823.1	x^9 - 3x^8 + 3x^7 - 3x^5 + 3x^4 - x^3 - 1	\( -\,3^{12}\cdot 503 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.276592799.1	x^9 - x^8 + 3x^6 - 3x^5 + x^4 + 2x^3 - 2x^2 + x - 1	\( -\,7^{6}\cdot 2351 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.390477031.1	x^9 - 2x^8 - 2x^7 + 5x^6 + x^5 - 6x^4 + 3x^3 + 2x^2 - 2x + 1	\( -\,7^{6}\cdot 3319 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.391888819.1	x^9 - x^7 - 3x^6 - 2x^5 + 2x^4 + 4x^3 + 2x^2 - x - 1	\( -\,7^{6}\cdot 3331 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.449772127.1	x^9 - x^8 - x^7 - 3x^6 - 2x^5 + 3x^4 + 5x^3 + 6x^2 + 4x + 1	\( -\,7^{6}\cdot 3823 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.459654643.1	x^9 - 2x^8 + 5x^6 - 4x^5 - 4x^3 + 10x^2 - 6x + 1	\( -\,7^{6}\cdot 3907 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.467890073.1	x^9 - 2x^8 + x^7 + 2x^6 - 5x^5 + 2x^4 + x^3 - 3x^2 + x + 1	\( 7^{6}\cdot 41\cdot 97 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.470948947.1	x^9 - x^8 + x^7 - 3x^6 + x^4 - x^3 + 3x^2 - x + 1	\( -\,7^{6}\cdot 4003 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.474243119.1	x^9 - 2x^8 - 2x^7 + 6x^6 + 2x^5 - 7x^4 - 3x^3 + 2x^2 + 3x + 1	\( -\,7^{6}\cdot 29\cdot 139 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.489302191.1	x^9 - 2x^8 + 3x^7 - 4x^6 + 2x^5 - 2x^4 + x^2 + x + 1	\( -\,7^{6}\cdot 4159 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.502478879.1	x^9 - x^8 + x^7 - 5x^6 - x^5 - 4x^4 + 2x^3 + 2x^2 + 3x + 1	\( -\,7^{6}\cdot 4271 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.503890667.1	x^9 - 3x^7 - x^6 + 3x^5 + 2x^4 - 3x^3 - x^2 + 2x + 1	\( -\,7^{6}\cdot 4283 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.516029211.1	x^9 - 3x^8 + 6x^7 - 8x^6 + 6x^5 - 5x^3 + 3x^2 - 1	\( -\,3^{12}\cdot 971 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.532126427.1	x^9 - x^8 - 2x^6 - 2x^5 + 3x^3 + 5x^2 + 2x + 1	\( -\,7^{6}\cdot 4523 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.612598343.1	x^9 - x^8 - x^7 + x^6 - 4x^4 + 6x^3 - 3x^2 + x + 1	\( -\,7^{6}\cdot 41\cdot 127 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.624951488.1	x^9 - 2x^8 + x^7 - x^6 - x^5 + 6x^4 - 10x^3 + 11x^2 - 5x + 1	\( -\,2^{6}\cdot 7^{6}\cdot 83 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.668599267.1	x^9 - 4x^8 + 4x^7 + 2x^6 - 3x^5 - 6x^4 + 8x^3 + x^2 - 3x + 1	\( -\,7^{6}\cdot 5683 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.672128737.1	x^9 - x^8 - 4x^6 + 4x^5 + x^4 - 5x^3 + 5x^2 + x - 1	\( 7^{6}\cdot 29\cdot 197 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.689278977.1	x^9 - 3x^8 + 9x^6 - 9x^5 - 6x^4 + 11x^3 - 3x + 1	\( 3^{12}\cdot 1297 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.690246683.1	x^9 - x^8 - x^5 - x^4 + 2x^3 + x^2 - 3x + 1	\( -\,7^{6}\cdot 5867 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.696835027.1	x^9 - x^8 - 4x^7 + 4x^6 + 7x^5 - 10x^4 - 2x^3 + 7x^2 - 2x - 1	\( -\,7^{6}\cdot 5923 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.725541383.1	x^9 - x^8 + x^6 - 4x^5 + 2x^4 - x^3 + x^2 + x + 1	\( -\,7^{7}\cdot 881 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.741306349.1	x^9 - 4x^8 + 6x^7 - 8x^6 + 11x^5 - 7x^4 + 4x^3 - 3x^2 - 2x + 1	\( 7^{6}\cdot 6301 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.756130123.1	x^9 - 4x^8 + 8x^7 - 12x^6 + 14x^5 - 12x^4 + 5x^3 + 2x^2 - 4x + 1	\( -\,7^{6}\cdot 6427 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.760836083.1	x^9 - 2x^8 + 4x^7 - 3x^6 + 4x^4 - 8x^3 + 6x^2 - 4x + 1	\( -\,7^{6}\cdot 29\cdot 223 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.771659791.1	x^9 - x^8 - x^6 + 2x^5 - 4x^4 + x^3 + 2x - 1	\( -\,7^{7}\cdot 937 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.783071744.1	x^9 - 2x^8 + x^7 + x^6 + x^5 - 6x^4 + 6x^3 - x^2 - 3x + 1	\( -\,2^{9}\cdot 7^{6}\cdot 13 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.810248663.1	x^9 - 2x^8 + 2x^7 - x^6 - 3x^5 + 6x^4 - 5x^3 + 5x^2 - x - 1	\( -\,7^{6}\cdot 71\cdot 97 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.823660649.1	x^9 - x^8 + 4x^6 - 6x^5 - 3x^4 + 8x^3 + 2x^2 - 3x - 1	\( 7^{6}\cdot 7001 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.828601907.1	x^9 - 2x^8 + 4x^7 - 2x^6 + x^5 + 2x^3 - 3x^2 - x + 1	\( -\,7^{6}\cdot 7043 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.830248993.1	x^9 - x^8 - 2x^7 + 3x^6 + x^5 - 6x^4 - x^3 + 5x^2 - 1	\( 7^{6}\cdot 7057 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.897779519.1	x^9 - 3x^7 - 2x^6 + 3x^5 + 4x^4 - 2x^3 - 2x^2 + x + 1	\( -\,7^{6}\cdot 13\cdot 587 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.930721239.1	x^9 - 2x^8 + 5x^6 - 4x^5 + 3x^3 - 4x^2 + x + 1	\( -\,3^{3}\cdot 7^{6}\cdot 293 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.943897927.1	x^9 - 4x^8 + 7x^7 - 7x^6 + 3x^5 + 5x^4 - 12x^3 + 11x^2 - 6x + 1	\( -\,7^{6}\cdot 71\cdot 113 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.960133489.1	x^9 - 3x^8 + 2x^7 - x^5 + 4x^4 - 4x^3 - 2x^2 + 3x + 1	\( 7^{6}\cdot 8161 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.962721767.1	x^9 - x^8 + 2x^7 - 4x^2 + 4x - 1	\( -\,7^{8}\cdot 167 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.996604679.1	x^9 - 2x^8 + 2x^7 - 2x^6 + 3x^5 + 2x^4 - 2x - 1	\( -\,7^{6}\cdot 43\cdot 197 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.1014487327.1	x^9 - 2x^7 - 4x^6 - x^5 + 3x^4 + 4x^3 + 6x^2 + 5x + 1	\( -\,7^{6}\cdot 8623 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.1017781499.1	x^9 - 3x^8 + 6x^7 - 8x^6 + 8x^5 - 6x^4 + x^3 + x^2 - 2x + 1	\( -\,7^{6}\cdot 41\cdot 211 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1021310969.1	x^9 - x^8 + 3x^7 - 6x^6 + 2x^5 - 4x^4 + x^3 + 5x^2 - x - 1	\( 7^{6}\cdot 8681 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.1046605504.1	x^9 - 4x^8 + 8x^7 - 13x^6 + 19x^5 - 21x^4 + 15x^3 - 10x^2 + 5x - 1	\( -\,2^{6}\cdot 7^{6}\cdot 139 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.1047429047.1	x^9 - 2x^8 + 3x^6 - 6x^5 + 11x^4 - 5x^3 - 4x^2 + 4x - 1	\( -\,7^{6}\cdot 29\cdot 307 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1058958649.1	x^9 + 2x^7 - 4x^6 - x^5 - 3x^4 + 2x^3 + 6x^2 - 5x + 1	\( 7^{6}\cdot 9001 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.3.1075664807.1	x^9 - 3x^8 + 3x^7 - 5x^6 + 8x^5 - 4x^4 + 3x^3 - 3x^2 + 1	\( -\,7^{6}\cdot 41\cdot 223 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial