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 8932)

Label	Polynomial	Discriminant	Galois group	Class group
9.5.453771377.1	x^9 - x^8 - 3x^7 + 3x^6 + 2x^5 - x^4 - 3x^2 + 1	\( 453771377 \)	$S_9$ (as 9T34)	Trivial
9.5.455809769.1	x^9 - x^6 - 3x^5 + 4x^4 + x^3 - 4x^2 + 1	\( 109\cdot 4181741 \)	$S_9$ (as 9T34)	Trivial
9.5.460080721.1	x^9 - x^8 - 2x^7 + 2x^5 + x^4 - 5x^3 - x^2 + 3x + 1	\( 41\cdot 11221481 \)	$S_9$ (as 9T34)	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
9.5.507490937.1	x^9 - x^8 - 5x^7 + 5x^6 + 7x^5 - 8x^4 - 2x^3 + 4x^2 - x - 1	\( 507490937 \)	$S_9$ (as 9T34)	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
9.5.678717521.1	x^9 - x^8 - 2x^7 + 7x^6 - 5x^5 - 5x^4 + 9x^3 - x^2 - 3x + 1	\( 678717521 \)	$S_9$ (as 9T34)	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
9.5.710045729.1	x^9 - 3x^7 - 2x^6 + 3x^5 + 3x^4 - x^3 + x^2 - 1	\( 109\cdot 541\cdot 12041 \)	$S_9$ (as 9T34)	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
9.5.823660649.1	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
9.5.830248993.1	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
9.5.840423481.1	x^9 - 2x^8 - x^7 + 2x^6 - x^5 + 6x^4 - 4x^3 - x - 1	\( 2293\cdot 366517 \)	$S_9$ (as 9T34)	Trivial
9.5.865377817.1	x^9 - 2x^8 + 3x^6 - 5x^5 + 5x^3 + x^2 - x - 1	\( 865377817 \)	$S_9$ (as 9T34)	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
9.5.1021310969.1	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
9.5.1058958649.1	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
9.5.1087194409.1	x^9 - x^8 - 4x^7 - x^6 + 8x^5 + 7x^4 - 3x^3 - 6x^2 - x + 1	\( 7^{6}\cdot 9241 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1091048373.1	x^9 - 3x^7 - x^6 + 3x^5 - x^3 + 3x^2 - 1	\( 3^{12}\cdot 2053 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1149783677.1	x^9 - 2x^8 - 4x^7 + 8x^6 + 7x^5 - 9x^4 - 8x^3 + x^2 + 4x + 1	\( 7^{6}\cdot 29\cdot 337 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1209078773.1	x^9 - 2x^8 + 3x^6 - 6x^5 + 4x^4 + 2x^3 - 4x^2 + 4x - 1	\( 7^{6}\cdot 43\cdot 239 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1209078773.2	x^9 - 3x^8 + x^7 + x^6 + x^5 + 4x^4 - 5x^3 - 3x^2 + 3x + 1	\( 7^{6}\cdot 43\cdot 239 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1215667117.1	x^9 - x^8 - 4x^7 + 6x^6 + x^5 - 7x^4 + 4x^3 + x^2 - x + 1	\( 7^{6}\cdot 10333 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1238726321.1	x^9 - 2x^8 - 2x^7 + 6x^6 - 5x^5 + 4x^3 + 2x^2 - 4x + 1	\( 7^{6}\cdot 10529 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1263235257.1	x^9 - 2x^6 - 4x^3 + 3x + 1	\( 3^{12}\cdot 2377 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1274962213.1	x^9 - 2x^8 - 2x^7 + 8x^6 - 3x^5 - 9x^4 + 8x^3 + 3x^2 - 4x - 1	\( 7^{6}\cdot 10837 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1299958592.1	x^9 - 2x^8 - 3x^7 + 9x^6 - x^5 - 14x^4 + 10x^3 + 7x^2 - 7x + 1	\( 2^{6}\cdot 37^{3}\cdot 401 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.5.1330963137.1	x^9 - 2x^8 + 2x^7 + x^6 - 8x^5 + 14x^4 - 13x^3 + 2x^2 + 3x - 1	\( 3^{3}\cdot 7^{6}\cdot 419 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1512142597.1	x^9 - 2x^8 + x^7 - 2x^6 - 2x^5 + 5x^4 + 4x^3 - 3x - 1	\( 7^{6}\cdot 12853 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1610967757.1	x^9 - 4x^8 + 5x^7 + x^6 - 7x^5 + 6x^4 - x^3 - 5x^2 + 2x + 1	\( 7^{6}\cdot 13693 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1619909081.1	x^9 - x^8 + 2x^7 - 7x^6 + 7x^3 + 3x^2 - 3x - 1	\( 7^{8}\cdot 281 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1626740901.1	x^9 - 3x^7 - 4x^6 + 3x^5 + 9x^4 - 6x^2 + 1	\( 3^{12}\cdot 3061 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1630732789.1	x^9 + x^7 - x^6 - 2x^5 - 3x^4 - 3x^3 + 3x^2 + 4x + 1	\( 7^{6}\cdot 83\cdot 167 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1653791993.1	x^9 - 2x^7 - 3x^6 - x^5 + 4x^4 + 4x^3 + x^2 - 2x - 1	\( 7^{6}\cdot 14057 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1669812553.1	x^9 - 4x^5 + 3x - 1	\( 37\cdot 757\cdot 59617 \)	$S_9$ (as 9T34)	Trivial
9.5.1684851329.1	x^9 - 3x^8 + 3x^7 - 2x^6 - 5x^5 + 13x^4 - 2x^3 - 5x^2 + 1	\( 7^{6}\cdot 14321 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1699910401.1	x^9 - 4x^8 + 4x^7 + x^6 - 5x^5 + 4x^4 - x^3 + 5x^2 - 5x + 1	\( 7^{6}\cdot 14449 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1730969737.1	x^9 - x^8 - 3x^7 + 5x^6 - 2x^5 - 3x^4 + 7x^3 - 4x - 1	\( 7^{6}\cdot 14713 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1742734637.1	x^9 - x^8 - x^7 + 6x^6 - x^5 - 4x^4 + 3x^3 - 3x - 1	\( 7^{6}\cdot 14813 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1783676489.1	x^9 - 2x^8 + 2x^7 - 2x^6 - 4x^5 + 9x^4 - 7x^3 + 5x - 1	\( 7^{6}\cdot 15161 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1790264833.1	x^9 - 2x^8 + 2x^7 + 2x^6 - 7x^5 + 4x^4 - 2x^3 - 6x^2 + 6x + 1	\( 7^{6}\cdot 15217 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1837191537.1	x^9 - 3x^8 + 7x^6 - 6x^5 + 5x^3 - 6x^2 + 1	\( 3^{12}\cdot 3457 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1861324829.1	x^9 - x^8 + 4x^7 - x^6 + 2x^5 + 5x^4 - 12x^3 - x^2 + 5x - 1	\( 7^{6}\cdot 13\cdot 1217 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1890972377.1	x^9 - 2x^8 + x^7 + x^6 + x^5 + x^4 - 8x^3 - x^2 + 4x + 1	\( 7^{6}\cdot 16073 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.1928620057.1	x^9 - 4x^8 + 6x^7 - 4x^6 - 2x^5 + 5x^4 - 4x^3 - x^2 + 3x + 1	\( 7^{6}\cdot 13^{2}\cdot 97 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.2096622829.1	x^9 - x^8 + x^7 - 2x^6 - 3x^5 - 5x^3 + 2x^2 + 5x + 1	\( 7^{6}\cdot 71\cdot 251 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.2116387861.1	x^9 - 4x^8 + 5x^7 + 3x^6 - 17x^5 + 20x^4 - 7x^3 - 5x^2 + 4x + 1	\( 7^{6}\cdot 17989 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.2143301553.1	x^9 - 3x^7 + 3x^5 - 4x^3 + 3x - 1	\( 3^{12}\cdot 37\cdot 109 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial
9.5.2159425756.1	x^9 - x^8 + 2x^6 - 4x^5 + 4x^4 - 7x^2 + 2x + 2	\( 2^{2}\cdot 539856439 \)	$S_9$ (as 9T34)	Trivial
9.5.2165800441.1	x^9 - x^8 - 2x^6 - 2x^5 - 4x^3 - 2x^2 + 2x + 1	\( 7^{6}\cdot 41\cdot 449 \)	$S_3 \wr C_3 $ (as 9T28)	Trivial