Global number field search results

Further refine search

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
9.3.22377849199125399.3	x^9 - 24x^7 - 12x^6 + 171x^5 + 66x^4 - 457x^3 - 432x^2 + 372x + 440	\( -\,3^{12}\cdot 7^{6}\cdot 71^{3} \)	$S_3\times C_3$ (as 9T4)	$[117]$
9.3.45370442231868096.9	x^9 - 3x^8 + 3x^7 - 18x^6 + 48x^5 - 39x^4 - 3x^3 + 15x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{16}\cdot 7^{4}\cdot 19^{3} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[6, 18]$
9.1.89296304144943168.1	x^9 - 3x^8 + 4x^7 + 7x^6 - 140x^5 - 105x^4 + 721x^3 + 1444x^2 + 1002x + 246	\( 2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 13^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 18]$
9.1.104608905489000000.2	x^9 - 3x^8 - 6x^7 - 25x^6 + 102x^5 - 147x^4 - 461x^3 + 24x^2 + 2856x - 3954	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6, 6]$ (GRH)
9.3.132798133404501799.3	x^9 - 2x^8 + 3x^7 + 475x^6 - 2252x^5 - 1772x^4 - 26904x^3 - 395552x^2 - 130176x + 1746432	\( -\,13^{6}\cdot 31^{7} \)	$S_3\times C_3$ (as 9T4)	$[3, 39]$ (GRH)
9.3.140558522604533019.7	x^9 - 3x^8 + 39x^7 + 138x^6 + 249x^5 + 258x^4 + 155x^3 + 48x^2 - 3x - 1	\( -\,3^{12}\cdot 7^{6}\cdot 131^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 36]$ (GRH)
9.3.145380128593826227.1	x^9 - 3x^8 + 4x^7 - 66x^6 - 250x^5 + 2536x^4 - 7387x^3 + 37441x^2 - 128324x + 142144	\( -\,283^{7} \)	$S_3\times C_3$ (as 9T4)	$[122]$
9.3.262552173266674368.13	x^9 - 3x^8 - 3x^7 - 52x^6 + 132x^5 - 285x^4 + 1833x^3 - 2037x^2 + 7518x - 12341	\( -\,2^{6}\cdot 3^{9}\cdot 7^{6}\cdot 11^{6} \)	$S_3\times C_3$ (as 9T4)	$[6, 18]$ (GRH)
9.3.279981688157042599.2	x^9 - 4x^8 - 42x^7 - 173x^6 - 259x^5 + 353x^4 + 1889x^3 + 2898x^2 + 2051x + 567	\( -\,7^{6}\cdot 13^{6}\cdot 79^{3} \)	$S_3\times C_3$ (as 9T4)	$[4, 36]$
9.1.285018244641000000.10	x^9 - 18x^6 + 14148x^3 - 216	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 13^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6, 6]$ (GRH)
9.1.285018244641000000.13	x^9 - 3x^8 + 69x^7 - 91x^6 + 1434x^5 + 48x^4 + 8868x^3 + 20520x^2 + 4356x + 25884	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 13^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 18]$ (GRH)
9.1.326830360514205681.1	x^9 - 3x^8 - 15x^7 + 20x^6 + 120x^5 + 456x^4 + 1807x^3 - 3009x^2 - 2445x - 1056	\( 3^{10}\cdot 7^{6}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[9, 18]$ (GRH)
9.3.329791532470972096.2	x^9 - 4x^8 + 18x^7 + 42x^6 - 336x^5 - 840x^4 - 560x^3 + 544x^2 - 608x - 2976	\( -\,2^{6}\cdot 7^{8}\cdot 19^{7} \)	$C_3 \wr S_3 $ (as 9T20)	$[6, 18]$
9.1.342413166234821184.1	x^9 - 3x^8 - 115x^6 + 240x^5 - 399x^4 + 8257x^3 - 8274x^2 + 17130x - 70966	\( 2^{6}\cdot 3^{9}\cdot 43^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 12]$ (GRH)
9.3.367638192988920000.5	x^9 + 21x^7 - 140x^6 + 315x^5 - 840x^4 - 525x^3 + 25200x^2 - 69300x + 52500	\( -\,2^{6}\cdot 3^{13}\cdot 5^{4}\cdot 7^{8} \)	$C_3 \wr S_3 $ (as 9T20)	$[6, 18]$ (GRH)
9.3.373943606076754623.5	x^9 - 86x^7 - 116x^6 + 2617x^5 + 6772x^4 - 23565x^3 - 118784x^2 - 185040x - 71616	\( -\,3^{3}\cdot 7^{6}\cdot 13^{6}\cdot 29^{3} \)	$S_3\times C_3$ (as 9T4)	$[129]$ (GRH)
9.3.374733943282472112.10	x^9 + 9x^7 - 162x^6 - 864x^5 + 3807x^4 + 11265x^3 + 70263x^2 - 431595x + 142325	\( -\,2^{4}\cdot 3^{19}\cdot 67^{4} \)	$C_3 \wr S_3 $ (as 9T20)	$[3, 39]$ (GRH)
9.1.405703886910977088.1	x^9 - 14x^7 - 31x^6 + 196x^5 + 1050x^4 + 717x^3 - 6076x^2 - 17892x - 17669	\( 2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 1259^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 3, 6]$ (GRH)
9.3.467691547524201567.9	x^9 - 3x^8 - 42x^7 + 278x^6 + 141x^5 - 4491x^4 + 14831x^3 + 3201x^2 - 71823x + 203131	\( -\,3^{12}\cdot 7^{3}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[3, 6, 6]$ (GRH)
9.3.530803525857667776.8	x^9 - 81x^7 - 75x^6 + 1809x^5 + 4050x^4 - 1554x^3 - 16875x^2 - 22275x - 15625	\( -\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 17^{3} \)	$S_3\times C_3$ (as 9T4)	$[6, 18]$ (GRH)
9.1.598488882256079424.2	x^9 - 51x^6 + 867x^3 + 4913	\( 2^{6}\cdot 3^{18}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 36]$ (GRH)
9.1.787656519800023104.1	x^9 - 9x^6 + 4185x^3 - 27	\( 2^{6}\cdot 3^{10}\cdot 7^{6}\cdot 11^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6, 6]$ (GRH)
9.3.806569710290630208.6	x^9 - 3x^8 + 9x^7 + 142x^6 - 1020x^5 + 2349x^4 - 4997x^3 - 19929x^2 - 19248x - 5617	\( -\,2^{6}\cdot 3^{12}\cdot 13^{6}\cdot 17^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 21]$ (GRH)
9.3.821824919051661504.15	x^9 - 3x^8 + 21x^7 - 10x^6 - 12x^5 + 159x^4 - 635x^3 - 2001x^2 - 1608x - 377	\( -\,2^{6}\cdot 3^{12}\cdot 7^{6}\cdot 59^{3} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 6, 6]$ (GRH)
9.3.821824919051661504.22	x^9 - 3x^8 + 21x^7 - 46x^6 + 312x^5 - 561x^4 + 337x^3 - 57x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{12}\cdot 7^{6}\cdot 59^{3} \)	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 6, 18]$ (GRH)
9.3.821824919051661504.23	x^9 - 3x^8 + 39x^7 + 198x^6 + 444x^5 + 603x^4 + 515x^3 + 273x^2 + 72x + 1	\( -\,2^{6}\cdot 3^{12}\cdot 7^{6}\cdot 59^{3} \)	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 9]$ (GRH)
9.3.827185934225070000.2	x^9 - 3x^8 + 18x^7 + 147x^6 + 378x^5 - 5670x^4 + 5040x^3 - 1188x^2 + 44388x - 36252	\( -\,2^{4}\cdot 3^{15}\cdot 5^{4}\cdot 7^{8} \)	$C_3 \wr S_3 $ (as 9T20)	$[3, 63]$ (GRH)
9.3.988941019347000000.1	x^9 - 123x^7 - 189x^6 + 3213x^5 + 2388x^4 - 37734x^3 + 16461x^2 + 153633x - 188677	\( -\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 41^{3} \)	$S_3\times C_3$ (as 9T4)	$[6, 18]$ (GRH)
9.1.1166498446237171776.5	x^9 - 57x^6 - 1083x^3 - 6859	\( 2^{6}\cdot 3^{18}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6, 18]$ (GRH)
9.1.1166498446237171776.7	x^9 - 42x^6 + 132x^3 - 2744	\( 2^{6}\cdot 3^{18}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[6, 18]$ (GRH)
9.3.1236937876870921408.1	x^9 - 67x^7 - 117x^6 + 1549x^5 + 5542x^4 - 7144x^3 - 66257x^2 - 121183x - 74171	\( -\,2^{6}\cdot 43^{3}\cdot 79^{6} \)	$S_3\times C_3$ (as 9T4)	$[21, 21]$ (GRH)
9.3.1287597438205439031.4	x^9 - 3x^8 + 36x^7 + 69x^6 + 201x^5 + 1071x^4 + 2055x^3 + 4182x^2 - 4913	\( -\,3^{15}\cdot 11^{6}\cdot 37^{3} \)	$S_3\times C_3$ (as 9T4)	$[117]$ (GRH)
9.3.1297978913113439283.2	x^9 - 48x^6 - 1041x^3 - 4096	\( -\,3^{15}\cdot 67^{6} \)	$S_3\times C_3$ (as 9T4)	$[126]$ (GRH)
9.1.1365414418584000000.2	x^9 + 9x^7 - 107x^6 + 27x^5 - 1287x^4 + 4130x^3 - 28053x^2 + 34884x - 75034	\( 2^{9}\cdot 3^{3}\cdot 5^{6}\cdot 43^{6} \)	$S_3^2$ (as 9T8)	$[3, 42]$ (GRH)
9.1.1425299311881000000.4	x^9 - 179x^6 + 49327x^3 - 27	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 17^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 6, 6]$ (GRH)
9.3.1443418037903955456.15	x^9 - 3x^8 + 4x^7 - 27x^6 - 23x^5 + 32x^4 + 200x^3 + 384x^2 + 64x - 512	\( -\,2^{9}\cdot 3^{3}\cdot 7^{6}\cdot 31^{6} \)	$S_3^2$ (as 9T8)	$[9, 27]$ (GRH)
9.3.1597657402133118656.2	x^9 - 32x^7 - 122x^6 + 124x^5 + 1516x^4 - 7288x^3 + 21472x^2 - 21480x - 88504	\( -\,2^{6}\cdot 11^{3}\cdot 163^{6} \)	$S_3\times C_3$ (as 9T4)	$[2, 162]$ (GRH)
9.3.1688134559643000000.104	x^9 - 21x^7 - 57x^6 + 1197x^5 - 4452x^4 - 15360x^3 + 156807x^2 - 395031x + 326341	\( -\,2^{6}\cdot 3^{15}\cdot 5^{6}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	$[6, 18]$ (GRH)
9.3.2070424448419852819.3	x^9 - 23x^7 - 32x^6 + 349x^5 + 1613x^4 + 802x^3 - 9248x^2 - 31222x - 37253	\( -\,7^{6}\cdot 19^{3}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[117]$ (GRH)
9.1.2143111299478636032.1	x^9 - 3x^8 + 4x^7 - 175x^6 + 406x^5 - 469x^4 + 5271x^3 + 1262x^2 - 4458x - 187032	\( 2^{9}\cdot 3^{4}\cdot 7^{7}\cdot 13^{7} \)	$S_3^2$ (as 9T8)	$[3, 3, 18]$ (GRH)
9.1.2146055133681216576.1	x^9 - 3x^8 + 6x^7 - 99x^6 + 372x^5 - 279x^4 + 2703x^3 - 2610x^2 + 2700x + 27000	\( 2^{6}\cdot 3^{10}\cdot 7^{6}\cdot 13^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 18]$ (GRH)
9.1.2237509978224568128.1	x^9 - 27x^7 - 60x^6 - 567x^5 + 162x^4 + 15633x^3 - 52290x^2 + 63504x - 28812	\( 2^{6}\cdot 3^{19}\cdot 311^{3} \)	$S_3^2$ (as 9T8)	$[6, 18]$ (GRH)
9.1.2367243417578765625.1	x^9 - 96x^6 + 8067x^3 - 32768	\( 3^{10}\cdot 5^{6}\cdot 37^{6} \)	$C_3^2:C_2$ (as 9T5)	$[2, 90]$ (GRH)
9.3.2414841170339528000.3	x^9 - 23x^7 - 11x^6 + 349x^5 + 2068x^4 + 3350x^3 - 3179x^2 - 23907x - 61039	\( -\,2^{6}\cdot 5^{3}\cdot 7^{6}\cdot 37^{6} \)	$S_3\times C_3$ (as 9T4)	$[117]$ (GRH)
9.3.2700223234725844672.1	x^9 - 4x^8 - 25x^7 - 145x^6 - 343x^5 - 352x^4 - 166x^3 - 43x^2 - 13x - 1	\( -\,2^{6}\cdot 13^{3}\cdot 79^{7} \)	$S_3\times C_3$ (as 9T4)	$[134]$ (GRH)
9.1.2778012227169000000.2	x^9 - 3x^8 - 6x^7 + 237x^6 - 1752x^5 + 6093x^4 - 11517x^3 + 12510x^2 - 7740x + 2520	\( 2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 19^{6} \)	$C_3^2:C_2$ (as 9T5)	$[3, 3, 18]$ (GRH)
9.3.3122592338962816083.6	x^9 - 39x^7 + 624x^5 - 2691x^4 + 5655x^3 + 5967x^2 - 42237x - 6864	\( -\,3^{13}\cdot 7^{4}\cdot 13^{8} \)	$C_3 \wr S_3 $ (as 9T20)	$[3, 63]$ (GRH)
9.3.3122592338962816083.8	x^9 - 3x^8 - 9x^7 + 228x^6 - 348x^5 - 612x^4 - 7989x^3 - 9801x^2 - 2547x + 2040	\( -\,3^{13}\cdot 7^{4}\cdot 13^{8} \)	$C_3 \wr S_3 $ (as 9T20)	$[6, 18]$ (GRH)
9.1.3196337928676458048.1	x^9 - 100x^6 + 2932x^3 - 13824	\( 2^{6}\cdot 3^{10}\cdot 7^{6}\cdot 193^{3} \)	$S_3^2$ (as 9T8)	$[3, 3, 18]$ (GRH)
9.3.3308743736900280000.2	x^9 - 21x^7 - 343x^6 + 2835x^5 - 5670x^4 - 78750x^3 + 212625x^2 + 212625x - 2310525	\( -\,2^{6}\cdot 3^{15}\cdot 5^{4}\cdot 7^{8} \)	$C_3 \wr S_3 $ (as 9T20)	$[3, 63]$ (GRH)

In order to download results, .