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 546)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.24794911296.1	x^9 - 3x^6 + 3x^3 + 1	\( 2^{6}\cdot 3^{18} \)	$C_3^2:C_2$ (as 9T5)	Trivial
9.1.59049000000.1	x^9 - 7x^6 + 23x^3 + 1	\( 2^{6}\cdot 3^{10}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.315637217856.1	x^9 - 6x^7 - 9x^6 + 24x^5 + 18x^4 + 27x^3 + 6x^2 + 6x + 1	\( 2^{6}\cdot 3^{10}\cdot 17^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.444611571264.1	x^9 - 5x^6 + 27x^3 + 27	\( 2^{6}\cdot 3^{10}\cdot 7^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.497972971584.1	x^9 + 3x^7 - 6x^6 + 9x^5 + 6x^4 - 7x^3 - 54x^2 - 42x - 26	\( 2^{6}\cdot 3^{12}\cdot 11^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.568503936064.1	x^9 - 3x^8 + x^7 - 7x^6 + 20x^5 + 18x^4 - 40x^3 - 56x^2 + 96x - 36	\( 2^{6}\cdot 307^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.741536265625.1	x^9 - 4x^8 + 9x^7 - 9x^6 - 4x^5 + x^4 + 54x^3 - 160x^2 + 200x - 80	\( 5^{6}\cdot 83^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.845237519424.1	x^9 - 2x^8 + 6x^7 + 3x^6 - 6x^5 + 18x^4 - 13x^3 - 4x^2 + 12x - 33	\( 2^{6}\cdot 3^{4}\cdot 113^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.981256661056.1	x^9 - x^8 - 7x^7 + 11x^6 + 22x^5 - 52x^4 - 48x^3 + 156x^2 + 228x + 76	\( 2^{6}\cdot 7^{6}\cdot 19^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.1425595404289.1	x^9 - 4x^8 + 16x^7 - 32x^6 + 33x^5 - 10x^4 - 120x^3 + 306x^2 - 295x + 118	\( 7^{6}\cdot 59^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.3418801000000.2	x^9 - 2x^8 + 4x^7 - 11x^6 - 58x^4 + 139x^3 - 4x^2 - 56x - 27	\( 2^{6}\cdot 5^{6}\cdot 43^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.4432507043904.1	x^9 - 9x^7 - 4x^6 + 27x^5 + 24x^4 - 79x^3 - 36x^2 + 156x - 116	\( 2^{6}\cdot 3^{12}\cdot 19^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.5729665643584.2	x^9 - x^8 + 8x^7 - 17x^6 + 46x^5 - 81x^4 + 163x^3 - 202x^2 + 160x - 50	\( 2^{6}\cdot 547^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.6053445140625.1	x^9 - 6x^6 - 3x^3 - 8	\( 3^{18}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[2]$
9.1.6694969951296.1	x^9 - 3x^8 + 6x^7 + 3x^6 - 36x^5 + 27x^4 + 51x^3 - 60x^2 + 48x - 64	\( 2^{6}\cdot 3^{10}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.9529569000000.1	x^9 - 3x^8 + 4x^7 + 5x^6 - 38x^5 + 83x^4 - 111x^3 + 104x^2 - 24x + 6	\( 2^{6}\cdot 3^{4}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.10678935122496.3	x^9 - 3x^8 + 5x^6 + 6x^5 - 63x^4 + 145x^3 - 150x^2 + 96x + 12	\( 2^{6}\cdot 3^{10}\cdot 41^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.11065116586329.3	x^9 + 9x^7 - 12x^6 + 54x^5 - 36x^4 + 48x^3 + 81x^2 - 72x + 111	\( 3^{18}\cdot 13^{4} \)	$C_3^2:C_2$ (as 9T5)	Trivial
9.1.18241167657024.4	x^9 - 3x^8 + 6x^7 - 21x^6 + 60x^5 - 45x^4 + 51x^3 - 36x^2 + 48x + 64	\( 2^{6}\cdot 3^{10}\cdot 13^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.19937341265625.3	x^9 + 15x^7 - 2x^6 + 90x^5 - 30x^4 + 138x^3 - 45x^2 + 1	\( 3^{12}\cdot 5^{6}\cdot 7^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.20151121000000.1	x^9 - 3x^8 - 2x^7 + 5x^6 + 8x^5 - 39x^4 + 47x^3 + 58x^2 - 60x - 252	\( 2^{6}\cdot 5^{6}\cdot 67^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.20795424040000.2	x^9 - 3x^8 - 2x^7 + 23x^6 + 24x^5 - 35x^4 + 9x^3 - 82x^2 - 52x - 8	\( 2^{6}\cdot 5^{4}\cdot 151^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.22617481454656.1	x^9 - 3x^8 - 3x^7 - 9x^6 + 114x^5 + 150x^4 - 68x^3 - 372x^2 - 176x - 52	\( 2^{6}\cdot 11^{4}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.28455140560896.4	x^9 - 3x^8 + 3x^7 + 11x^6 - 3x^5 - 51x^4 + 181x^3 - 195x^2 + 42x + 78	\( 2^{12}\cdot 3^{10}\cdot 7^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.34012224000000.6	x^9 + 12x^7 - 12x^6 + 63x^5 - 96x^4 + 92x^3 - 432x^2 + 12x - 64	\( 2^{12}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$ (GRH)
9.1.43046721000000.2	x^9 - 18x^6 + 228x^3 - 216	\( 2^{6}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.43046721000000.3	x^9 - 9x^6 - 33x^3 - 27	\( 2^{6}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.43046721000000.4	x^9 - 9x^6 + 57x^3 - 27	\( 2^{6}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.45579633110361.5	x^9 - 6x^6 + 33x^3 - 8	\( 3^{18}\cdot 7^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.51039593640000.10	x^9 - 9x^7 - 16x^6 + 45x^5 + 162x^4 + 113x^3 - 36x^2 + 210x + 350	\( 2^{6}\cdot 3^{12}\cdot 5^{4}\cdot 7^{4} \)	$C_3^2:C_2$ (as 9T5)	$[9]$
9.1.65380565930625.1	x^9 - 3x^8 + 3x^7 + 5x^6 + 21x^5 + 39x^4 - 175x^3 - 276x^2 - 660x - 1400	\( 3^{10}\cdot 5^{4}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.67459939560000.2	x^9 - 13x^6 - 6x^5 + 156x^4 - 13x^3 - 234x^2 - 108x + 247	\( 2^{6}\cdot 3^{10}\cdot 5^{4}\cdot 13^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.69661074235041.6	x^9 - 6x^7 - 6x^6 + 36x^5 + 150x^4 + 137x^3 - 216x^2 - 564x - 512	\( 3^{12}\cdot 107^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.91219155960384.3	x^9 - 3x^8 + 6x^7 + 9x^6 - 60x^5 + 45x^4 + 111x^3 - 126x^2 + 108x - 216	\( 2^{6}\cdot 3^{10}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.107320814899776.1	x^9 - 6x^7 - 15x^6 - 6x^5 - 6x^4 + 45x^3 + 48x^2 - 54x - 299	\( 2^{6}\cdot 3^{10}\cdot 73^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.108547746890625.3	x^9 - 3x^8 + 6x^7 - 43x^6 + 78x^5 - 111x^4 + 85x^3 - 48x^2 + 12x - 48	\( 3^{10}\cdot 5^{6}\cdot 7^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.116281025423424.4	x^9 - 9x^7 - 40x^6 + 27x^5 + 240x^4 + 281x^3 - 360x^2 - 924x - 980	\( 2^{6}\cdot 3^{12}\cdot 43^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.118448417326801.7	x^9 - 3x^8 - 7x^7 + 41x^6 - 85x^5 + 123x^4 - 114x^3 + 16x^2 + 40x + 112	\( 3299^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.127052393149504.3	x^9 - 3x^8 + 2x^7 - 15x^6 + 32x^5 + 29x^4 - 73x^3 - 110x^2 + 260x - 124	\( 2^{6}\cdot 1187^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.131079601000000.3	x^9 - 3x^8 + 27x^7 - 73x^6 + 224x^5 - 410x^4 + 508x^3 - 248x^2 - 24x + 68	\( 2^{6}\cdot 5^{6}\cdot 107^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3]$
9.1.143496441000000.1	x^9 - 3x^8 + 4x^7 - 13x^6 + 58x^5 - 127x^4 + 93x^3 - 10x^2 + 60x - 90	\( 2^{6}\cdot 3^{4}\cdot 5^{6}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.160798833699904.3	x^9 - 3x^8 - 2x^7 - 5x^6 + 42x^5 - 7x^4 - 15x^3 - 4x^2 - 152x + 236	\( 2^{6}\cdot 1259^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.162388203244569.3	x^9 - 15x^7 - 18x^6 + 84x^5 + 192x^4 - 276x^3 - 771x^2 + 1062x - 347	\( 3^{10}\cdot 229^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.164924977505344.1	x^9 - 3x^8 + 4x^7 - 37x^6 + 68x^5 + 39x^4 - 73x^3 - 314x^2 + 756x - 504	\( 2^{6}\cdot 7^{4}\cdot 181^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$ (GRH)
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)	$[18]$
9.1.191374022440000.1	x^9 - 3x^8 + 19x^7 - 41x^6 + 56x^5 + 30x^4 - 112x^3 + 128x^2 + 120x - 180	\( 2^{6}\cdot 5^{4}\cdot 263^{4} \)	$C_3^2:C_2$ (as 9T5)	$[6]$
9.1.228886641000000.1	x^9 - 3x^8 - 13x^7 + 27x^6 + 144x^5 - 360x^4 - 172x^3 + 552x^2 + 1156x - 2052	\( 2^{6}\cdot 3^{4}\cdot 5^{6}\cdot 41^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$ (GRH)
9.1.230396455161856.5	x^9 - 4x^8 + 6x^7 + 16x^6 + 53x^5 + 92x^4 + 248x^3 + 136x^2 - 68x + 64	\( 2^{12}\cdot 487^{4} \)	$C_3^2:C_2$ (as 9T5)	$[9]$ (GRH)
9.1.237111461683776.5	x^9 + 12x^7 - 7x^6 + 36x^5 + 6x^4 + 95x^3 - 114x^2 - 96x + 133	\( 2^{6}\cdot 3^{10}\cdot 89^{4} \)	$C_3^2:C_2$ (as 9T5)	$[3]$
9.1.238130328086784.8	x^9 - 12x^6 + 81x^5 - 144x^4 + 30x^3 + 324x^2 - 504x + 336	\( 2^{8}\cdot 3^{18}\cdot 7^{4} \)	$C_3^2:C_2$ (as 9T5)	Trivial (GRH)