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 all 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.990677827584.1	x^9 - 3x^8 + 12x^7 - 12x^6 + 12x^5 - 12x^4 + 12x^3 - 12x^2 + 9x - 3	\( 2^{24}\cdot 3^{10} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.7644119040000.1	x^9 - 2x^8 - 4x^7 + 16x^6 + 10x^5 - 28x^4 + 20x^3 + 32x^2 - 23x + 6	\( 2^{24}\cdot 3^{6}\cdot 5^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.29721861554176.1	x^9 - 4x^8 + 16x^7 - 56x^6 + 118x^5 - 272x^4 + 452x^3 - 552x^2 + 686x - 440	\( 2^{24}\cdot 11^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.47775744000000.1	x^9 - x^8 + 4x^7 - 4x^6 + 36x^5 + 204x^4 + 304x^3 + 176x^2 + 16x - 16	\( 2^{22}\cdot 3^{6}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.47775744000000.2	x^9 - 3x^8 + 4x^7 - 12x^6 + 36x^5 - 84x^4 + 112x^3 - 96x^2 + 43x - 9	\( 2^{22}\cdot 3^{6}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.101240302206976.1	x^9 - 2x^8 + 8x^6 - 20x^5 + 8x^4 + 44x^3 + 88x^2 - 225x + 106	\( 2^{22}\cdot 17^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.108547746890625.2	x^9 - 3x^7 - 3x^6 - 24x^5 + 54x^4 - 3x^3 - 45x^2 + 474x + 499	\( 3^{10}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.151939915084881.1	x^9 - 3x^8 + 4x^7 - 23x^6 + 72x^5 - 7x^4 + 312x^3 - 408x^2 + 56x - 80	\( 3^{6}\cdot 7^{6}\cdot 11^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.343064484000000.1	x^9 - 30x^6 + 45x^5 + 126x^4 - 240x^3 - 90x^2 + 405x + 80	\( 2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.359729184374784.1	x^9 - 2x^8 - 2x^7 + 4x^6 + x^5 + 10x^4 - 14x^3 - 8x^2 + x + 18	\( 2^{22}\cdot 3^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.805005849390625.1	x^9 - 3x^8 + 16x^7 - 27x^6 + 34x^5 - 71x^4 - 40x^3 + 340x^2 + 320x + 80	\( 5^{6}\cdot 61^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.1438916737499136.1	x^9 - 2x^8 - 28x^5 + 112x^3 + 152x^2 + 81x + 14	\( 2^{24}\cdot 3^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.1686221298140625.1	x^9 + x^7 + 36x^5 - 30x^4 - 344x^3 - 750x^2 - 659x - 210	\( 3^{6}\cdot 5^{6}\cdot 23^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.2070185663499849.1	x^9 - 2x^8 + 5x^7 + 28x^6 + 55x^5 + 110x^4 + 113x^3 + 74x^2 + 31x + 12	\( 3^{6}\cdot 7^{6}\cdot 17^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.2378617464029184.1	x^9 - 3x^8 - 12x^7 + 36x^6 + 24x^5 - 96x^4 + 168x^3 + 120x^2 - 108x - 204	\( 2^{24}\cdot 3^{10}\cdot 7^{4} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.2379293284000000.1	x^9 - 4x^8 - 8x^7 + 34x^6 + 73x^5 - 26x^4 - 250x^3 - 540x^2 - 500x - 400	\( 2^{8}\cdot 5^{6}\cdot 29^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.2407470785888256.1	x^9 - 3x^8 - 4x^7 - 4x^6 + 18x^5 + 58x^4 - 60x^3 - 132x^2 + 198x - 90	\( 2^{24}\cdot 3^{4}\cdot 11^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[9]$
9.1.2871098559212689.1	x^9 - 3x^8 - 16x^7 + 22x^6 + 96x^5 - 28x^4 - 191x^3 - 77x^2 - 43x - 105	\( 13^{6}\cdot 29^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.3422620666036224.1	x^9 - 2x^8 + 24x^6 - 34x^5 + 36x^4 + 160x^3 - 616x^2 + 1305x - 34	\( 2^{24}\cdot 3^{6}\cdot 23^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.6011850680015625.1	x^9 - 12x^7 - 9x^6 + 71x^5 + 233x^4 + 488x^3 - 620x^2 - 4681x - 5977	\( 3^{4}\cdot 5^{6}\cdot 41^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.6499837226778624.1	x^9 - 24x^6 - 36x^5 - 288x^4 + 48x^3 - 1440x^2 + 225x - 2312	\( 2^{24}\cdot 3^{18} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.6499837226778624.2	x^9 - 48x^6 + 126x^5 + 72x^4 + 732x^3 - 1800x^2 + 1278x - 352	\( 2^{24}\cdot 3^{18} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.6499837226778624.3	x^9 - 24x^6 + 108x^5 - 288x^4 - 384x^3 + 1440x^2 + 1953x - 104	\( 2^{24}\cdot 3^{18} \)	$C_3^2:Q_8$ (as 9T14)	Trivial
9.1.7765332671265625.1	x^9 - 2x^8 - 6x^7 + 42x^6 - 44x^5 - 10x^4 + 575x^3 - 730x^2 + 155x + 1350	\( 5^{6}\cdot 89^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[6]$
9.1.8650464253968384.1	x^9 - 2x^8 - 16x^7 + 64x^6 - 22x^5 + 76x^4 - 1216x^3 + 3616x^2 - 4471x + 2222	\( 2^{24}\cdot 3^{6}\cdot 29^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.9437102258273001.1	x^9 - x^8 - 12x^7 - 14x^6 - 63x^5 + 76x^4 + 438x^3 - 321x^2 - 153x - 198	\( 3^{4}\cdot 13^{6}\cdot 17^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.14504514073657344.1	x^9 - 3x^8 + 84x^5 + 12x^4 + 264x^3 + 264x^2 + 81x + 21	\( 2^{24}\cdot 3^{10}\cdot 11^{4} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.28294749433626624.1	x^9 - 3x^8 - 12x^7 + 84x^6 - 132x^5 - 276x^4 + 1596x^3 - 3108x^2 + 2913x - 1075	\( 2^{24}\cdot 3^{10}\cdot 13^{4} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.29138063934357504.1	x^9 - 3x^8 + 12x^7 - 84x^6 + 108x^5 - 12x^4 - 72x^3 - 168x^2 - 45x - 33	\( 2^{22}\cdot 3^{10}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.9.136583925149390625.1	x^9 - 3x^8 - 48x^7 + 222x^6 + 57x^5 - 1149x^4 + 285x^3 + 2070x^2 - 330x - 1145	\( 3^{10}\cdot 5^{6}\cdot 23^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.9.700687604571439104.1	x^9 - 3x^8 - 60x^7 + 252x^6 + 612x^5 - 4356x^4 + 6756x^3 - 2820x^2 - 1023x + 661	\( 2^{24}\cdot 3^{10}\cdot 29^{4} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.712181767349390625.1	x^9 - 45x^7 - 45x^6 + 270x^5 - 954x^4 - 6975x^3 - 18945x^2 - 9900x - 7005	\( 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.712181767349390625.2	x^9 - 30x^6 - 225x^5 + 126x^4 + 4800x^3 - 11520x^2 + 7920x + 5120	\( 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.712181767349390625.3	x^9 + 9x^7 - 63x^6 - 198x^5 + 1386x^4 - 5085x^3 + 29169x^2 - 137448x + 230937	\( 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.9.768195266285705049.1	x^9 - 2x^8 - 35x^7 + 118x^6 - 24x^5 - 222x^4 + 160x^3 + 58x^2 - 59x + 4	\( 3^{6}\cdot 11^{6}\cdot 29^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.9.3496747289987252224.1	x^9 - 2x^8 - 60x^7 + 120x^6 + 980x^5 - 1808x^4 - 4012x^3 + 4936x^2 + 4673x - 1434	\( 2^{24}\cdot 7^{6}\cdot 11^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$
9.1.4062398266736640000.1	x^9 - 216x^6 + 684x^5 - 432x^4 + 4608x^3 - 6336x^2 - 3231x - 26472	\( 2^{24}\cdot 3^{18}\cdot 5^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.9.4062398266736640000.1	x^9 - 72x^7 - 24x^6 + 702x^5 + 72x^4 - 2076x^3 + 216x^2 + 1278x + 352	\( 2^{24}\cdot 3^{18}\cdot 5^{4} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.4062398266736640000.2	x^9 - 36x^7 - 48x^6 + 666x^5 + 144x^4 - 5100x^3 + 3600x^2 + 12825x - 17200	\( 2^{24}\cdot 3^{18}\cdot 5^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.4062398266736640000.3	x^9 - 120x^6 - 54x^5 + 2376x^4 + 1488x^3 - 13176x^2 - 30231x + 74216	\( 2^{24}\cdot 3^{18}\cdot 5^{4} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.25389989167104000000.1	x^9 - 72x^7 - 96x^6 + 2376x^5 + 4032x^4 - 33792x^3 - 23040x^2 + 448704x - 739328	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.9.25389989167104000000.2	x^9 - 90x^7 - 240x^6 + 1125x^5 + 3204x^4 - 5190x^3 - 11700x^2 + 10395x + 8020	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.9.25389989167104000000.3	x^9 - 90x^7 - 120x^6 + 2655x^5 + 6228x^4 - 24270x^3 - 73260x^2 + 29835x + 141860	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	Trivial (GRH)
9.1.25389989167104000000.4	x^9 - 18x^7 - 288x^6 - 1089x^5 - 2916x^4 - 6318x^3 + 7020x^2 + 73899x - 82476	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.25389989167104000000.9	x^9 - 120x^6 + 1710x^5 - 2304x^4 - 1320x^3 + 4320x^2 + 15660x + 20480	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.25389989167104000000.10	x^9 - 36x^7 - 480x^6 + 2916x^5 + 1440x^4 - 14136x^3 + 16920x^2 + 47331x + 29000	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.25389989167104000000.11	x^9 - 240x^6 + 630x^5 + 5904x^4 + 13440x^3 - 65520x^2 + 46980x + 50080	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)
9.1.25389989167104000000.12	x^9 - 54x^7 - 96x^6 + 2007x^5 + 4068x^4 - 35250x^3 - 114372x^2 + 500697x + 486076	\( 2^{22}\cdot 3^{18}\cdot 5^{6} \)	$C_3^2:Q_8$ (as 9T14)	$[3]$ (GRH)