Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 50462 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.1.9206560730304.2	$x^{9} - 17 x^{6} + 89 x^{3} - 1$	$9$	[1,4]	$2^{6}\cdot 3^{4}\cdot 7^{3}\cdot 173^{3}$	$4$	$27.5711746399$	$120.5487453273571$				$C_3^2 : D_{6} $ (as 9T18)	$[13]$	$2$	$4$	$817.722229244$
9.1.19171705120000.1	$x^{9} - 4 x^{8} + 7 x^{7} + 14 x^{6} - 57 x^{5} + 36 x^{4} + 70 x^{3} - 164 x^{2} + 160 x - 64$	$9$	[1,4]	$2^{8}\cdot 5^{4}\cdot 17^{3}\cdot 29^{3}$	$4$	$29.9123954302$	$129.84745986823242$				$C_3^2 : D_{6} $ (as 9T18)	$[15]$	$2$	$4$	$643.317679341$
9.1.42108451158672.1	$x^{9} - 4 x^{8} + 13 x^{7} - 39 x^{6} + 65 x^{5} - 79 x^{4} + 231 x^{3} - 345 x^{2} + 238 x - 153$	$9$	[1,4]	$2^{4}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3}$	$4$	$32.64516045$	$96.85748364229387$				$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[12]$	$2$	$4$	$651.397515028$
9.1.50722851083913.1	$x^{9} - 4 x^{6} + 8 x^{3} + 1$	$9$	[1,4]	$3^{12}\cdot 457^{3}$	$2$	$33.3273211379$	$141.79696246379308$			✓	$C_3^2 : D_{6} $ (as 9T18)	$[12]$	$2$	$4$	$557.342010007$
9.3.60272881070256.1	$x^{9} - 4 x^{8} + 7 x^{7} - 16 x^{6} + 32 x^{5} - 29 x^{4} + 11 x^{3} - 3 x^{2} + x + 1$	$9$	[3,3]	$-\,2^{4}\cdot 3^{3}\cdot 17^{3}\cdot 73^{4}$	$4$	$33.9722773702$	$96.85748364229387$			✓	$C_3^2 : D_{6} $ (as 9T18)	$[12]$	$2$	$5$	$303.963856213$
9.1.63444813159104.1	$x^{9} - 17 x^{7} - 27 x^{6} + 79 x^{5} + 241 x^{4} + 582 x^{3} - 243 x^{2} - 740 x - 664$	$9$	[1,4]	$2^{6}\cdot 13^{6}\cdot 59^{3}$	$3$	$34.1664273894$	$84.93465030202505$				$S_3^2$ (as 9T8)	$[15]$	$2$	$4$	$517.094267184$
9.1.70328303784000.3	$x^{9} - 12 x^{7} - 3 x^{6} + 48 x^{5} + 195 x^{3} + 48 x^{2} + 12 x + 1$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{3}\cdot 53^{3}$	$4$	$34.5597041392$	$93.10029660430361$			?	$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$903.606305572$
9.1.71931233000000.3	$x^{9} - 4 x^{8} + 10 x^{7} - 53 x^{6} + 138 x^{5} - 382 x^{4} - 203 x^{3} - 1292 x^{2} + 18 x - 1$	$9$	[1,4]	$2^{6}\cdot 5^{6}\cdot 11^{4}\cdot 17^{3}$	$4$	$34.646350972$	$63.472772669544085$			?	$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$370.697940565$
9.1.72083387944512.1	$x^{9} - 3 x^{8} + 4 x^{7} + 7 x^{6} - 56 x^{5} - 21 x^{4} + 175 x^{3} + 226 x^{2} + 120 x + 36$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 37^{3}$	$4$	$34.6544863103$	$84.64406652482397$			?	$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$898.533968474$
9.3.82103013853847.1	$x^{9} - 4 x^{8} + 18 x^{7} - 65 x^{6} + 164 x^{5} - 365 x^{4} + 557 x^{3} - 546 x^{2} + 240 x + 104$	$9$	[3,3]	$-\,7^{6}\cdot 887^{3}$	$2$	$35.1592740938$	$108.98343779599615$				$S_3\times C_3$ (as 9T4)	$[13]$	$2$	$5$	$361.230225131$
9.3.111750324673463.1	$x^{9} - 4 x^{8} + 4 x^{7} + 27 x^{6} - 86 x^{5} + 101 x^{4} + 53 x^{3} - 132 x^{2} + 36 x - 216$	$9$	[3,3]	$-\,7^{6}\cdot 983^{3}$	$2$	$36.3845101746$	$114.7295928200602$				$S_3\times C_3$ (as 9T4)	$[13]$	$2$	$5$	$364.293700606$
9.1.117278493945057.1	$x^{9} - 24 x^{6} + 246 x^{3} + 1$	$9$	[1,4]	$3^{13}\cdot 419^{3}$	$2$	$36.580234624$	$106.36258740741502$			?	$C_3^2 : D_{6} $ (as 9T18)	$[12]$	$2$	$4$	$1960.16723152$
9.1.134385470889984.1	$x^{9} - 3 x^{8} + 17 x^{7} - 65 x^{6} + 175 x^{5} - 347 x^{4} + 559 x^{3} - 447 x^{2} + 240 x - 450$	$9$	[1,4]	$2^{13}\cdot 3^{3}\cdot 157^{4}$	$3$	$37.1378642281$	$86.81013765684283$				$S_3^2$ (as 9T8)	$[35]$	$2$	$4$	$2109.98429378$
9.1.135933466070016.2	$x^{9} - 22 x^{6} + 146 x^{3} - 512$	$9$	[1,4]	$2^{10}\cdot 3^{10}\cdot 131^{3}$	$3$	$37.1851552456$	$103.90834776745815$			?	$S_3^2$ (as 9T8)	$[15]$	$2$	$4$	$986.4289164139581$
9.3.152093726358939.1	$x^{9} - 3 x^{8} + 9 x^{7} - 31 x^{6} - 3 x^{5} + 180 x^{4} - 483 x^{3} + 1557 x^{2} - 3159 x + 2259$	$9$	[3,3]	$-\,3^{12}\cdot 659^{3}$	$2$	$37.652181585$	$111.0719458482692$			?	$S_3\times C_3$ (as 9T4)	$[2, 6]$	$2$	$5$	$700.16853703$
9.1.156538373700096.1	$x^{9} - 14 x^{6} + 47 x^{3} - 64$	$9$	[1,4]	$2^{9}\cdot 3^{10}\cdot 173^{3}$	$3$	$37.7728792946$	$134.03231195405488$				$C_3^2 : D_{6} $ (as 9T18)	$[12]$	$2$	$4$	$3663.17914026$
9.1.168433804634688.4	$x^{9} - x^{8} + 11 x^{6} - 36 x^{5} + 25 x^{4} + 43 x^{3} - 308 x^{2} + 128 x - 16$	$9$	[1,4]	$2^{6}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3}$	$4$	$38.0815276665$	$96.85748364229387$			?	$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[12]$	$2$	$4$	$2005.70249664$
9.1.168433804634688.5	$x^{9} - x^{8} - 18 x^{7} - 5 x^{6} + 80 x^{5} - 39 x^{4} + 337 x^{3} + 1244 x^{2} + 1920 x + 612$	$9$	[1,4]	$2^{6}\cdot 3^{4}\cdot 17^{4}\cdot 73^{3}$	$4$	$38.0815276665$	$96.85748364229387$				$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$2807.27447765$
9.3.168773156076447.2	$x^{9} - 20 x^{7} - 4 x^{6} + 103 x^{5} - 42 x^{4} + 87 x^{3} - 16 x^{2} + 132 x + 40$	$9$	[3,3]	$-\,3^{3}\cdot 13^{6}\cdot 109^{3}$	$3$	$38.0900450014$	$99.97761628235062$				$S_3\times C_3$ (as 9T4)	$[2, 6]$	$2$	$5$	$663.597105832$
9.3.172315866325023.9	$x^{9} + 6 x^{7} - 15 x^{6} + 9 x^{5} - 15 x^{4} - 147 x^{3} - 75 x - 125$	$9$	[3,3]	$-\,3^{15}\cdot 229^{3}$	$2$	$38.1780654939$	$100.37523353885224$				$S_3\times C_3$ (as 9T4)	$[2, 6]$	$2$	$5$	$704.420258553$
9.1.177792782538816.5	$x^{9} - 3 x^{8} + 6 x^{7} - 27 x^{6} + 84 x^{5} - 63 x^{4} + 111 x^{3} - 90 x^{2} + 108 x + 216$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 19^{6}$	$3$	$38.3110267925$	$40.722133961240765$			?	$C_3^2:C_2$ (as 9T5)	$[18]$	$2$	$4$	$824.370601768$
9.1.229335107715072.1	$x^{9} - 3 x^{8} - 2 x^{7} + 6 x^{6} + 104 x^{5} - 352 x^{4} + 180 x^{3} + 1080 x^{2} - 2223 x + 1521$	$9$	[1,4]	$2^{14}\cdot 3^{4}\cdot 557^{3}$	$3$	$39.4101273446$	$145.67215678608898$				$C_3^2 : D_{6} $ (as 9T18)	$[11]$	$2$	$4$	$5935.81941898$
9.1.250994068000000.1	$x^{9} - x^{8} - 11 x^{7} + 13 x^{6} + 70 x^{5} - 8 x^{4} - 233 x^{3} - 185 x^{2} + 333 x + 437$	$9$	[1,4]	$2^{8}\cdot 5^{6}\cdot 13^{7}$	$3$	$39.8072894214$	$49.57881307529992$				$S_3^2$ (as 9T8)	$[3, 6]$	$2$	$4$	$2888.59481975$
9.1.253774260735625.1	$x^{9} - 3 x^{8} + 4 x^{7} + 21 x^{6} + 7 x^{5} - 35 x^{4} + 133 x^{3} - 68 x^{2} - 69 x + 225$	$9$	[1,4]	$5^{4}\cdot 7^{7}\cdot 79^{3}$	$3$	$39.8560426187$	$100.58817171125796$			?	$S_3\wr S_3$ (as 9T31)	$[18]$	$2$	$4$	$926.650381413$
9.1.256569916840000.1	$x^{9} - 2 x^{8} - 10 x^{7} + 29 x^{6} + 58 x^{5} + 30 x^{4} - 87 x^{3} + 46 x^{2} - 6 x + 1$	$9$	[1,4]	$2^{6}\cdot 5^{4}\cdot 283^{4}$	$3$	$39.9045905755$	$78.0836101418872$			?	$(C_3^3:C_3):C_2$ (as 9T21)	$[3, 6]$	$2$	$4$	$636.92023427$
9.1.262982299459441.3	$x^{9} - 3 x^{8} - 10 x^{7} + 13 x^{6} + 63 x^{5} + 40 x^{4} + 28 x^{3} - 256 x^{2} - 208 x - 64$	$9$	[1,4]	$4027^{4}$	$1$	$40.0141925456$	$63.45864795282043$				$C_3^2:C_2$ (as 9T5)	$[2, 6]$	$2$	$4$	$3408.02133025$
9.3.270521872447536.1	$x^{9} - 3 x^{8} - 6 x^{7} - 14 x^{6} + 30 x^{5} + 120 x^{4} + 60 x^{3} + 12 x^{2} + 48$	$9$	[3,3]	$-\,2^{4}\cdot 3^{11}\cdot 457^{3}$	$3$	$40.1400623507$	$225.08864738092043$				$C_3 \wr S_3 $ (as 9T20)	$[12]$	$2$	$5$	$6987.09814873$
9.1.310508782917696.5	$x^{9} - 3 x^{8} + 12 x^{7} - 39 x^{6} + 90 x^{5} - 57 x^{4} - 123 x^{3} + 120 x^{2} + 84 x - 86$	$9$	[1,4]	$2^{6}\cdot 3^{12}\cdot 11^{3}\cdot 19^{3}$	$4$	$40.7596486869$	$105.54270389620275$			?	$S_3^2$ (as 9T8)	$[2, 6]$	$2$	$4$	$1181.16766907$
9.3.339002530743583.1	$x^{9} - x^{8} - x^{7} - 32 x^{6} + 106 x^{5} - 228 x^{4} + 609 x^{3} - 997 x^{2} + 751 x - 209$	$9$	[3,3]	$-\,7^{6}\cdot 1423^{3}$	$2$	$41.1592064882$	$138.03878988022086$			?	$C_3 \wr S_3 $ (as 9T20)	$[3, 6]$	$2$	$5$	$331.388928323$
9.3.339002530743583.2	$x^{9} + 10 x^{7} - 16 x^{6} + 73 x^{5} - 200 x^{4} + 175 x^{3} - 1024 x^{2} - 64 x + 512$	$9$	[3,3]	$-\,7^{6}\cdot 1423^{3}$	$2$	$41.1592064882$	$138.03878988022086$				$S_3\times C_3$ (as 9T4)	$[3, 6]$	$2$	$5$	$448.82699798$
9.3.341869344633467.1	$x^{9} + x^{7} - 22 x^{6} + 19 x^{5} - 157 x^{4} + 116 x^{3} - 550 x^{2} + 942 x + 1$	$9$	[3,3]	$-\,7^{6}\cdot 1427^{3}$	$2$	$41.1977360744$	$138.23266468065134$			?	$S_3\times C_3$ (as 9T4)	$[13]$	$2$	$5$	$710.573317035$
9.1.360695829930048.1	$x^{9} - 3 x^{8} + 12 x^{7} + 5 x^{6} - 12 x^{5} + 93 x^{4} - 235 x^{3} + 366 x^{2} + 30 x + 706$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 457^{3}$	$3$	$41.4438529994$	$122.26051691628487$			?	$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$1451.4565370876117$
9.1.367123218156864.3	$x^{9} + 6 x^{7} - 12 x^{6} - 24 x^{5} + 24 x^{4} + 36 x^{3} - 24 x^{2} - 8$	$9$	[1,4]	$2^{6}\cdot 3^{12}\cdot 13^{3}\cdot 17^{3}$	$4$	$41.5252664642$	$108.5303515945941$			?	$S_3^2$ (as 9T8)	$[12]$	$2$	$4$	$764.544094395$
9.1.376592059760400.1	$x^{9} - 3 x^{8} - 12 x^{7} + 48 x^{6} - 33 x^{5} - 81 x^{4} + 420 x^{3} - 936 x^{2} + 1173 x - 529$	$9$	[1,4]	$2^{4}\cdot 3^{12}\cdot 5^{2}\cdot 11^{6}$	$4$	$41.6429262576$	$105.58369734197706$				$(C_3^3:C_3):C_2$ (as 9T21)	$[2, 6]$	$2$	$4$	$1842.2738353$
9.1.384441664409856.3	$x^{9} - 3 x^{8} - 6 x^{7} + 26 x^{6} + 69 x^{5} - 63 x^{4} + 53 x^{3} - 21 x^{2} + 15 x + 1$	$9$	[1,4]	$2^{8}\cdot 3^{12}\cdot 41^{4}$	$3$	$41.7384883923$	$55.40941908037487$			?	$C_3^2 : C_6$ (as 9T11)	$[27]$	$2$	$4$	$1887.43856759$
9.1.387420489000000.19	$x^{9} - 6 x^{6} + 132 x^{3} - 8$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 5^{6}$	$3$	$41.7742995025$	$44.40336798307826$				$C_3^2:C_2$ (as 9T5)	$[3, 6]$	$2$	$4$	$2367.09044435$
9.1.387420489000000.21	$x^{9} - 15 x^{6} + 75 x^{3} + 125$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 5^{6}$	$3$	$41.7742995025$	$44.40336798307826$			?	$C_3^2:C_2$ (as 9T5)	$[3, 6]$	$2$	$4$	$893.735871646$
9.3.400836216781872.1	$x^{9} - 3 x^{8} + 6 x^{7} + 82 x^{6} - 6 x^{5} - 216 x^{4} + 24 x^{3} + 420 x^{2} + 360 x + 96$	$9$	[3,3]	$-\,2^{4}\cdot 3^{11}\cdot 521^{3}$	$3$	$41.9326089294$	$240.33352314477537$				$C_3 \wr S_3 $ (as 9T20)	$[15]$	$2$	$5$	$7141.31528807$
9.1.402460112000000.1	$x^{9} - 2 x^{8} + 3 x^{7} - 4 x^{6} - 50 x^{5} - 20 x^{4} - 20 x^{3} - 600 x^{2} + 500 x - 1000$	$9$	[1,4]	$2^{10}\cdot 5^{6}\cdot 293^{3}$	$3$	$41.9514506143$	$126.1209230589681$				$C_3^2 : D_{6} $ (as 9T18)	$[18]$	$2$	$4$	$2580.29921322$
9.1.405017091000000.4	$x^{9} + 15 x^{7} - 13 x^{6} + 15 x^{5} + 75 x^{4} + 98 x^{3} + 885 x^{2} + 1350 x + 1534$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 19^{3}$	$4$	$41.9809821225$	$91.83923613690506$				$S_3^2$ (as 9T8)	$[15]$	$2$	$4$	$4476.90692392$
9.1.427222520357904.1	$x^{9} - 9 x^{6} + 12 x^{3} - 16$	$9$	[1,4]	$2^{4}\cdot 3^{18}\cdot 41^{3}$	$3$	$42.2306958523$	$122.45158122838576$				$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[2, 6]$	$2$	$4$	$1705.60901287$
9.1.456767897992641.1	$x^{9} - 2 x^{8} + 5 x^{7} - 29 x^{6} - x^{5} - 95 x^{4} - 38 x^{3} + 27 x^{2} + 24 x - 135$	$9$	[1,4]	$3^{4}\cdot 23^{4}\cdot 67^{4}$	$3$	$42.5456402704$	$67.9926466612383$				$D_{9}$ (as 9T3)	$[19]$	$2$	$4$	$1848.94983597$
9.3.480987324277551.1	$x^{9} - 4 x^{8} - 10 x^{7} + 143 x^{6} - 302 x^{5} - 401 x^{4} + 2771 x^{3} - 2282 x^{2} + 84 x - 12488$	$9$	[3,3]	$-\,3^{3}\cdot 7^{6}\cdot 13^{3}\cdot 41^{3}$	$4$	$42.790580802$	$146.32647993022778$				$S_3\times C_3$ (as 9T4)	$[19]$	$2$	$5$	$718.832034117$
9.3.481344381984375.3	$x^{9} - 3 x^{7} - 5 x^{6} - 72 x^{5} - 210 x^{4} - 441 x^{3} - 585 x^{2} - 585 x - 455$	$9$	[3,3]	$-\,3^{12}\cdot 5^{6}\cdot 7^{3}\cdot 13^{2}$	$4$	$42.7941091158$	$301.55982900617937$			?	$C_3 \wr S_3 $ (as 9T20)	$[2, 6]$	$2$	$5$	$1931.02839318$
9.1.482324159898000.2	$x^{9} + 6 x^{7} - 3 x^{6} + 36 x^{5} - 12 x^{4} - 3 x^{3} - 36 x^{2} - 12 x - 1$	$9$	[1,4]	$2^{4}\cdot 3^{15}\cdot 5^{3}\cdot 7^{5}$	$4$	$42.8037789862$	$119.15955157499168$				$((C_3^3:C_3):C_2):C_2$ (as 9T24)	$[18]$	$2$	$4$	$1606.81948274$
9.3.496885595535875.4	$x^{9} - x^{8} - 30 x^{7} + 34 x^{6} + 384 x^{5} - 246 x^{4} - 2339 x^{3} - 191 x^{2} + 5460 x + 4096$	$9$	[3,3]	$-\,5^{3}\cdot 7^{7}\cdot 13^{6}$	$3$	$42.9454718274$	$62.56944033849911$				$S_3\times C_3$ (as 9T4)	$[2, 6]$	$2$	$5$	$8686.2165318$
9.3.528827395978651.1	$x^{9} - 7 x^{7} - 14 x^{6} - 161 x^{5} - 112 x^{4} - 868 x^{3} - 770 x^{2} - 189 x - 56$	$9$	[3,3]	$-\,7^{8}\cdot 11^{3}\cdot 41^{3}$	$3$	$43.243792199$	$119.75303495032989$				$C_3 \wr S_3 $ (as 9T20)	$[27]$	$2$	$5$	$1881.52091039$
9.3.528827395978651.2	$x^{9} - 3 x^{8} + 4 x^{7} - 7 x^{6} + 42 x^{5} - 105 x^{4} + 70 x^{3} + 37 x^{2} - 41 x + 1$	$9$	[3,3]	$-\,7^{8}\cdot 11^{3}\cdot 41^{3}$	$3$	$43.243792199$	$119.75303495032989$			?	$C_3 \wr S_3 $ (as 9T20)	$[27]$	$2$	$5$	$518.180219874$
9.3.528827395978651.3	$x^{9} - 14 x^{7} - 7 x^{6} + 98 x^{5} + 105 x^{4} - 329 x^{3} - 161 x^{2} + 154 x + 252$	$9$	[3,3]	$-\,7^{8}\cdot 11^{3}\cdot 41^{3}$	$3$	$43.243792199$	$119.75303495032989$				$C_3 \wr S_3 $ (as 9T20)	$[27]$	$2$	$5$	$2059.01204392$
9.1.540022788000000.1	$x^{9} - 3 x^{8} + 12 x^{7} - 46 x^{6} + 135 x^{5} - 261 x^{4} + 437 x^{3} - 891 x^{2} + 729 x - 729$	$9$	[1,4]	$2^{8}\cdot 3^{9}\cdot 5^{6}\cdot 19^{3}$	$4$	$43.3445677452$	$91.83923613690506$			?	$C_3^2 : D_{6} $ (as 9T18)	$[15]$	$2$	$4$	$2230.11782747$