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 )

Label	Polynomial	Discriminant	Galois group	Class group
9.1.9206560730304.2	x^9 - 17x^6 + 89x^3 - 1	\( 2^{6}\cdot 3^{4}\cdot 7^{3}\cdot 173^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[13]$
9.1.19171705120000.1	x^9 - 4x^8 + 7x^7 + 14x^6 - 57x^5 + 36x^4 + 70x^3 - 164x^2 + 160x - 64	\( 2^{8}\cdot 5^{4}\cdot 17^{3}\cdot 29^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[15]$
9.1.42108451158672.1	x^9 - 4x^8 + 13x^7 - 39x^6 + 65x^5 - 79x^4 + 231x^3 - 345x^2 + 238x - 153	\( 2^{4}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[12]$
9.1.50722851083913.1	x^9 - 4x^6 + 8x^3 + 1	\( 3^{12}\cdot 457^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[12]$
9.3.60272881070256.1	x^9 - 4x^8 + 7x^7 - 16x^6 + 32x^5 - 29x^4 + 11x^3 - 3x^2 + x + 1	\( -\,2^{4}\cdot 3^{3}\cdot 17^{3}\cdot 73^{4} \)	$C_3^2 : D_{6} $ (as 9T18)	$[12]$
9.1.63444813159104.1	x^9 - 17x^7 - 27x^6 + 79x^5 + 241x^4 + 582x^3 - 243x^2 - 740x - 664	\( 2^{6}\cdot 13^{6}\cdot 59^{3} \)	$S_3^2$ (as 9T8)	$[15]$
9.1.70328303784000.3	x^9 - 12x^7 - 3x^6 + 48x^5 + 195x^3 + 48x^2 + 12x + 1	\( 2^{6}\cdot 3^{10}\cdot 5^{3}\cdot 53^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.1.71931233000000.3	x^9 - 4x^8 + 10x^7 - 53x^6 + 138x^5 - 382x^4 - 203x^3 - 1292x^2 + 18x - 1	\( 2^{6}\cdot 5^{6}\cdot 11^{4}\cdot 17^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.1.72083387944512.1	x^9 - 3x^8 + 4x^7 + 7x^6 - 56x^5 - 21x^4 + 175x^3 + 226x^2 + 120x + 36	\( 2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 37^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.3.82103013853847.1	x^9 - 4x^8 + 18x^7 - 65x^6 + 164x^5 - 365x^4 + 557x^3 - 546x^2 + 240x + 104	\( -\,7^{6}\cdot 887^{3} \)	$S_3\times C_3$ (as 9T4)	$[13]$
9.3.111750324673463.1	x^9 - 4x^8 + 4x^7 + 27x^6 - 86x^5 + 101x^4 + 53x^3 - 132x^2 + 36x - 216	\( -\,7^{6}\cdot 983^{3} \)	$S_3\times C_3$ (as 9T4)	$[13]$
9.1.117278493945057.1	x^9 - 24x^6 + 246x^3 + 1	\( 3^{13}\cdot 419^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[12]$
9.1.134385470889984.1	x^9 - 3x^8 + 17x^7 - 65x^6 + 175x^5 - 347x^4 + 559x^3 - 447x^2 + 240x - 450	\( 2^{13}\cdot 3^{3}\cdot 157^{4} \)	$S_3^2$ (as 9T8)	$[35]$
9.1.135933466070016.2	x^9 - 22x^6 + 146x^3 - 512	\( 2^{10}\cdot 3^{10}\cdot 131^{3} \)	$S_3^2$ (as 9T8)	$[15]$
9.3.152093726358939.1	x^9 - 3x^8 + 9x^7 - 31x^6 - 3x^5 + 180x^4 - 483x^3 + 1557x^2 - 3159x + 2259	\( -\,3^{12}\cdot 659^{3} \)	$S_3\times C_3$ (as 9T4)	$[2, 6]$
9.1.156538373700096.1	x^9 - 14x^6 + 47x^3 - 64	\( 2^{9}\cdot 3^{10}\cdot 173^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[12]$
9.1.168433804634688.4	x^9 - x^8 + 11x^6 - 36x^5 + 25x^4 + 43x^3 - 308x^2 + 128x - 16	\( 2^{6}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[12]$
9.1.168433804634688.5	x^9 - x^8 - 18x^7 - 5x^6 + 80x^5 - 39x^4 + 337x^3 + 1244x^2 + 1920x + 612	\( 2^{6}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.3.168773156076447.2	x^9 - 20x^7 - 4x^6 + 103x^5 - 42x^4 + 87x^3 - 16x^2 + 132x + 40	\( -\,3^{3}\cdot 13^{6}\cdot 109^{3} \)	$S_3\times C_3$ (as 9T4)	$[2, 6]$
9.3.172315866325023.9	x^9 + 6x^7 - 15x^6 + 9x^5 - 15x^4 - 147x^3 - 75x - 125	\( -\,3^{15}\cdot 229^{3} \)	$S_3\times C_3$ (as 9T4)	$[2, 6]$
9.1.177792782538816.5	x^9 - 3x^8 + 6x^7 - 27x^6 + 84x^5 - 63x^4 + 111x^3 - 90x^2 + 108x + 216	\( 2^{6}\cdot 3^{10}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[18]$
9.1.229335107715072.1	x^9 - 3x^8 - 2x^7 + 6x^6 + 104x^5 - 352x^4 + 180x^3 + 1080x^2 - 2223x + 1521	\( 2^{14}\cdot 3^{4}\cdot 557^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[11]$
9.1.250994068000000.1	x^9 - x^8 - 11x^7 + 13x^6 + 70x^5 - 8x^4 - 233x^3 - 185x^2 + 333x + 437	\( 2^{8}\cdot 5^{6}\cdot 13^{7} \)	$S_3^2$ (as 9T8)	$[3, 6]$
9.1.253774260735625.1	x^9 - 3x^8 + 4x^7 + 21x^6 + 7x^5 - 35x^4 + 133x^3 - 68x^2 - 69x + 225	\( 5^{4}\cdot 7^{7}\cdot 79^{3} \)	$S_3\wr S_3$ (as 9T31)	$[18]$
9.1.256569916840000.1	x^9 - 2x^8 - 10x^7 + 29x^6 + 58x^5 + 30x^4 - 87x^3 + 46x^2 - 6x + 1	\( 2^{6}\cdot 5^{4}\cdot 283^{4} \)	$(C_3^3:C_3):C_2$ (as 9T21)	$[3, 6]$
9.1.262982299459441.3	x^9 - 3x^8 - 10x^7 + 13x^6 + 63x^5 + 40x^4 + 28x^3 - 256x^2 - 208x - 64	\( 4027^{4} \)	$C_3^2:C_2$ (as 9T5)	$[2, 6]$
9.3.270521872447536.1	x^9 - 3x^8 - 6x^7 - 14x^6 + 30x^5 + 120x^4 + 60x^3 + 12x^2 + 48	\( -\,2^{4}\cdot 3^{11}\cdot 457^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[12]$
9.1.310508782917696.5	x^9 - 3x^8 + 12x^7 - 39x^6 + 90x^5 - 57x^4 - 123x^3 + 120x^2 + 84x - 86	\( 2^{6}\cdot 3^{12}\cdot 11^{3}\cdot 19^{3} \)	$S_3^2$ (as 9T8)	$[2, 6]$
9.3.339002530743583.1	x^9 - x^8 - x^7 - 32x^6 + 106x^5 - 228x^4 + 609x^3 - 997x^2 + 751x - 209	\( -\,7^{6}\cdot 1423^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[3, 6]$
9.3.339002530743583.2	x^9 + 10x^7 - 16x^6 + 73x^5 - 200x^4 + 175x^3 - 1024x^2 - 64x + 512	\( -\,7^{6}\cdot 1423^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 6]$
9.3.341869344633467.1	x^9 + x^7 - 22x^6 + 19x^5 - 157x^4 + 116x^3 - 550x^2 + 942x + 1	\( -\,7^{6}\cdot 1427^{3} \)	$S_3\times C_3$ (as 9T4)	$[13]$
9.1.360695829930048.1	x^9 - 3x^8 + 12x^7 + 5x^6 - 12x^5 + 93x^4 - 235x^3 + 366x^2 + 30x + 706	\( 2^{6}\cdot 3^{10}\cdot 457^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.1.367123218156864.3	x^9 + 6x^7 - 12x^6 - 24x^5 + 24x^4 + 36x^3 - 24x^2 - 8	\( 2^{6}\cdot 3^{12}\cdot 13^{3}\cdot 17^{3} \)	$S_3^2$ (as 9T8)	$[12]$
9.1.376592059760400.1	x^9 - 3x^8 - 12x^7 + 48x^6 - 33x^5 - 81x^4 + 420x^3 - 936x^2 + 1173x - 529	\( 2^{4}\cdot 3^{12}\cdot 5^{2}\cdot 11^{6} \)	$(C_3^3:C_3):C_2$ (as 9T21)	$[2, 6]$
9.1.384441664409856.3	x^9 - 3x^8 - 6x^7 + 26x^6 + 69x^5 - 63x^4 + 53x^3 - 21x^2 + 15x + 1	\( 2^{8}\cdot 3^{12}\cdot 41^{4} \)	$C_3^2 : C_6$ (as 9T11)	$[27]$
9.1.387420489000000.19	x^9 - 6x^6 + 132x^3 - 8	\( 2^{6}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6]$
9.1.387420489000000.21	x^9 - 15x^6 + 75x^3 + 125	\( 2^{6}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6]$
9.3.400836216781872.1	x^9 - 3x^8 + 6x^7 + 82x^6 - 6x^5 - 216x^4 + 24x^3 + 420x^2 + 360x + 96	\( -\,2^{4}\cdot 3^{11}\cdot 521^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[15]$
9.1.402460112000000.1	x^9 - 2x^8 + 3x^7 - 4x^6 - 50x^5 - 20x^4 - 20x^3 - 600x^2 + 500x - 1000	\( 2^{10}\cdot 5^{6}\cdot 293^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[18]$
9.1.405017091000000.4	x^9 + 15x^7 - 13x^6 + 15x^5 + 75x^4 + 98x^3 + 885x^2 + 1350x + 1534	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 19^{3} \)	$S_3^2$ (as 9T8)	$[15]$
9.1.427222520357904.1	x^9 - 9x^6 + 12x^3 - 16	\( 2^{4}\cdot 3^{18}\cdot 41^{3} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[2, 6]$
9.1.456767897992641.1	x^9 - 2x^8 + 5x^7 - 29x^6 - x^5 - 95x^4 - 38x^3 + 27x^2 + 24x - 135	\( 3^{4}\cdot 23^{4}\cdot 67^{4} \)	$D_{9}$ (as 9T3)	$[19]$
9.3.480987324277551.1	x^9 - 4x^8 - 10x^7 + 143x^6 - 302x^5 - 401x^4 + 2771x^3 - 2282x^2 + 84x - 12488	\( -\,3^{3}\cdot 7^{6}\cdot 13^{3}\cdot 41^{3} \)	$S_3\times C_3$ (as 9T4)	$[19]$
9.3.481344381984375.3	x^9 - 3x^7 - 5x^6 - 72x^5 - 210x^4 - 441x^3 - 585x^2 - 585x - 455	\( -\,3^{12}\cdot 5^{6}\cdot 7^{3}\cdot 13^{2} \)	$C_3 \wr S_3 $ (as 9T20)	$[2, 6]$
9.1.482324159898000.2	x^9 + 6x^7 - 3x^6 + 36x^5 - 12x^4 - 3x^3 - 36x^2 - 12x - 1	\( 2^{4}\cdot 3^{15}\cdot 5^{3}\cdot 7^{5} \)	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[18]$
9.3.496885595535875.4	x^9 - x^8 - 30x^7 + 34x^6 + 384x^5 - 246x^4 - 2339x^3 - 191x^2 + 5460x + 4096	\( -\,5^{3}\cdot 7^{7}\cdot 13^{6} \)	$S_3\times C_3$ (as 9T4)	$[2, 6]$ (GRH)
9.3.528827395978651.1	x^9 - 7x^7 - 14x^6 - 161x^5 - 112x^4 - 868x^3 - 770x^2 - 189x - 56	\( -\,7^{8}\cdot 11^{3}\cdot 41^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[27]$
9.3.528827395978651.2	x^9 - 3x^8 + 4x^7 - 7x^6 + 42x^5 - 105x^4 + 70x^3 + 37x^2 - 41x + 1	\( -\,7^{8}\cdot 11^{3}\cdot 41^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[27]$
9.3.528827395978651.3	x^9 - 14x^7 - 7x^6 + 98x^5 + 105x^4 - 329x^3 - 161x^2 + 154x + 252	\( -\,7^{8}\cdot 11^{3}\cdot 41^{3} \)	$C_3 \wr S_3 $ (as 9T20)	$[27]$
9.1.540022788000000.1	x^9 - 3x^8 + 12x^7 - 46x^6 + 135x^5 - 261x^4 + 437x^3 - 891x^2 + 729x - 729	\( 2^{8}\cdot 3^{9}\cdot 5^{6}\cdot 19^{3} \)	$C_3^2 : D_{6} $ (as 9T18)	$[15]$

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