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 146722)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.109880167.1	x^9 - 2x^8 + x^7 + x^6 - 3x^5 + x^4 + 3x^3 - 2x - 1	\( -\,367\cdot 299401 \)	$S_9$ (as 9T34)	Trivial
9.3.110852311.1	x^9 - x^8 - 4x^7 + 2x^6 + 8x^5 - x^4 - 8x^3 - 2x^2 + 3x + 1	\( -\,31^{3}\cdot 61^{2} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.111543479.1	x^9 - x^8 - x^7 + 3x^6 - 2x^5 - x^4 + 2x^3 - x^2 - 1	\( -\,111543479 \)	$S_9$ (as 9T34)	Trivial
9.3.112700719.1	x^9 - x^6 - x^5 + 3x^4 + 2x^3 - 3x^2 - x + 1	\( -\,7211\cdot 15629 \)	$S_9$ (as 9T34)	Trivial
9.3.112978759.1	x^9 - 3x^8 + 2x^7 + 3x^6 - 5x^5 + x^4 + 3x^3 - 3x^2 - x + 1	\( -\,43\cdot 2627413 \)	$S_9$ (as 9T34)	Trivial
9.3.112992391.1	x^9 - 2x^8 + x^7 + 3x^6 - 6x^5 + 3x^4 + 2x^3 - 4x^2 + 2x - 1	\( -\,112992391 \)	$S_9$ (as 9T34)	Trivial
9.3.113501567.1	x^9 - x^8 - x^7 + x^6 - 3x^4 + x^3 + 4x^2 - 1	\( -\,53\cdot 797\cdot 2687 \)	$S_9$ (as 9T34)	Trivial
9.3.113511599.1	x^9 - x^8 - 2x^7 + 2x^6 + 3x^5 - 5x^4 - 3x^3 + 4x^2 + x - 1	\( -\,193\cdot 727\cdot 809 \)	$S_9$ (as 9T34)	Trivial
9.3.113931487.1	x^9 - 2x^6 - x^5 - x^4 + 2x^2 + x + 1	\( -\,109\cdot 389\cdot 2687 \)	$S_9$ (as 9T34)	Trivial
9.3.114479303.1	x^9 - 3x^8 + 4x^7 - x^6 - 7x^5 + 11x^4 - 9x^3 + 3x^2 - x + 1	\( -\,23^{3}\cdot 97^{2} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.114807607.1	x^9 - x^7 - 2x^6 + x^5 + 4x^4 + 2x^3 - 2x^2 - 3x - 1	\( -\,29\cdot 3958883 \)	$S_9$ (as 9T34)	Trivial
9.3.115041127.1	x^9 - x^8 - 2x^7 + 3x^6 - 2x^4 - x^3 + 2x + 1	\( -\,97\cdot 229\cdot 5179 \)	$S_9$ (as 9T34)	Trivial
9.3.115270559.1	x^9 - 3x^8 + 3x^7 - 2x^6 + 2x^5 - 2x^4 - 2x^3 + 5x^2 - 4x + 1	\( -\,71\cdot 79\cdot 20551 \)	$S_9$ (as 9T34)	Trivial
9.3.115691111.1	x^9 + 2x^7 - x^6 + x^4 - 5x^3 + 2x^2 + 2x - 1	\( -\,47\cdot 67\cdot 36739 \)	$S_9$ (as 9T34)	Trivial
9.3.116188367.1	x^9 - 2x^7 - 3x^6 + x^5 + 3x^4 + x^3 - x^2 + 1	\( -\,116188367 \)	$S_9$ (as 9T34)	Trivial
9.3.118246927.1	x^9 - 4x^8 + 8x^7 - 12x^6 + 13x^5 - 10x^4 + 5x^3 - x^2 + 1	\( -\,31\cdot 3814417 \)	$S_9$ (as 9T34)	Trivial
9.3.118795951.1	x^9 - 2x^8 + x^7 + 2x^6 - 4x^5 + x^4 + 2x^3 - 3x^2 + 1	\( -\,167\cdot 711353 \)	$S_9$ (as 9T34)	Trivial
9.3.121510799.1	x^9 - 2x^7 - 3x^6 + x^5 + 5x^4 + 4x^3 - x^2 - 3x - 1	\( -\,2207\cdot 55057 \)	$S_9$ (as 9T34)	Trivial
9.3.129079703.1	x^9 - 3x^8 + 4x^7 - 5x^6 + 6x^5 - 7x^4 + x^3 + x + 1	\( -\,23^{3}\cdot 103^{2} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.131123051.1	x^9 - 2x^7 - 2x^6 + 4x^4 + 2x^3 - x^2 - 2x - 1	\( -\,131123051 \)	$S_9$ (as 9T34)	Trivial
9.3.133731799.1	x^9 - x^8 - 3x^7 + 4x^6 + 5x^5 - 5x^4 - 5x^3 + 2x + 1	\( -\,31^{3}\cdot 67^{2} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.134479871.1	x^9 + x^7 - 2x^6 - 2x^5 - x^4 - x^3 + 2x^2 + 1	\( -\,134479871 \)	$S_9$ (as 9T34)	Trivial
9.3.139751219.1	x^9 - 3x^8 + 4x^7 - 4x^6 + x^5 + 2x^4 - 3x^3 + 4x^2 - 2x + 1	\( -\,139751219 \)	$S_9$ (as 9T34)	Trivial
9.3.147184199.1	x^9 - 2x^8 - x^7 + 4x^6 - x^5 - 5x^4 + 5x^3 + 3x^2 - 4x - 1	\( -\,23^{3}\cdot 12097 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.157505216.1	x^9 - x^8 + x^7 - 2x^6 + 2x^5 + x^4 - 5x^3 + 3x^2 - 1	\( -\,2^{6}\cdot 11^{3}\cdot 43^{2} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
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
9.3.180181103.1	x^9 - 5x^7 + 8x^5 - 2x^4 - 4x^3 + x^2 - x + 1	\( -\,23^{3}\cdot 59\cdot 251 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.181543807.1	x^9 - 3x^8 + 3x^7 + 2x^6 - 7x^5 + 4x^4 + 2x^3 - 4x^2 + 1	\( -\,23^{3}\cdot 43\cdot 347 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.182350711.1	x^9 - 2x^8 - 2x^7 + 8x^6 - 4x^5 - 7x^4 + 7x^3 + 2x^2 - 3x - 1	\( -\,31^{3}\cdot 6121 \)	$S_3\wr S_3$ (as 9T31)	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
9.3.188795339.1	x^9 - 2x^8 + 2x^6 - 2x^5 + 6x^4 - 9x^3 + 4x^2 - 2x + 1	\( -\,23^{3}\cdot 59\cdot 263 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.195458751.1	x^9 - 4x^7 + 9x^5 - 5x^4 - 8x^3 + 6x^2 + x - 1	\( -\,3^{8}\cdot 31^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.197369219.1	x^9 - 3x^8 + 3x^7 - x^6 - 4x^5 + 7x^4 - 9x^3 + 7x^2 - 3x + 1	\( -\,31^{2}\cdot 59^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.203297472.1	x^9 - 3x^7 - x^6 + 3x^5 + 2x^4 + 4x^3 - x^2 - 5x + 1	\( -\,2^{6}\cdot 3^{3}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.215222063.1	x^9 - 2x^8 + 4x^7 - 5x^6 + 2x^4 - 5x^3 + 3x + 1	\( -\,7^{2}\cdot 19^{2}\cdot 23^{3} \)	$C_3 \wr S_3 $ (as 9T20)	Trivial
9.3.223836299.1	x^9 - 3x^7 - 3x^6 + 2x^5 + 6x^4 + 2x^3 - 2x^2 - 3x - 1	\( -\,23^{3}\cdot 18397 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.226999719.1	x^9 - x^8 - 2x^7 + 5x^6 - x^5 - 2x^4 - x^3 + 6x^2 - 5x + 1	\( -\,3^{3}\cdot 23^{3}\cdot 691 \)	$S_3\wr S_3$ (as 9T31)	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
9.3.227535067.1	x^9 - 2x^8 - x^7 + 3x^6 - 2x^5 + 2x^4 + 4x^3 - 4x^2 - 3x + 1	\( -\,23^{3}\cdot 18701 \)	$S_3\wr S_3$ (as 9T31)	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
9.3.240014927.1	x^9 - 2x^8 + 3x^4 - x^3 - x - 1	\( -\,31\cdot 7742417 \)	$S_9$ (as 9T34)	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
9.3.256589863.1	x^9 - 3x^8 + 4x^7 - 4x^6 - x^5 + 6x^4 - 8x^3 + 8x^2 - 5x + 1	\( -\,23^{3}\cdot 21089 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.257563223.1	x^9 - 3x^8 + x^7 + 6x^6 - 7x^5 - 2x^4 + 6x^3 - 2x^2 - 2x + 1	\( -\,23^{3}\cdot 21169 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.263858887.1	x^9 - 2x^8 + 4x^7 - 4x^6 - x^5 + 8x^4 - 9x^3 + 5x^2 - 4x + 1	\( -\,17\cdot 31^{3}\cdot 521 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.266372131.1	x^9 - x^8 + x^7 + x^6 - 7x^5 + 6x^4 - 5x^3 + 3x^2 + x - 1	\( -\,23^{3}\cdot 21893 \)	$S_3\wr S_3$ (as 9T31)	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
9.3.271366219.1	x^9 - x^7 - 3x^6 - 2x^5 + 2x^4 + 2x^3 + 2x^2 - x - 1	\( -\,31^{3}\cdot 9109 \)	$S_3\wr S_3$ (as 9T31)	Trivial
9.3.272097792.1	x^9 - 3x^8 + 7x^6 - 3x^5 - 9x^4 + 3x^3 + 6x^2 - 1	\( -\,2^{9}\cdot 3^{12} \)	$S_3\times C_3$ (as 9T4)	Trivial

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