Number field search results

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

Results (1-50 of 3463 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
9.1.479...000.1	$x^{9} - 3 x^{8} - 36 x^{7} - 1254 x^{6} + 5916 x^{5} + 33258 x^{4} + 548766 x^{3} - 719928 x^{2} + 759141 x + 95444679$	$9$	[1,4]	$2^{13}\cdot 3^{12}\cdot 5^{3}\cdot 7^{3}\cdot 137^{3}$	$5$	$198.569396085$	$1134.882869161268$			?	$S_3^2$ (as 9T8)	$[9, 216]$	$2$	$4$	$16901.915754085152$
9.3.961...744.1	$x^{9} - x^{8} - 69 x^{7} + 692 x^{6} - 3420 x^{5} + 9735 x^{4} - 16479 x^{3} + 16347 x^{2} - 8784 x + 1979$	$9$	[3,3]	$-\,2^{6}\cdot 17^{3}\cdot 163^{7}$	$3$	$214.499687208$	$456.4579703237679$			?	$S_3\times C_3$ (as 9T4)	$[2, 806]$	$2$	$5$	$6249.15485381864$
9.1.156...904.1	$x^{9} - 54 x^{6} - 1212 x^{3} - 5832$	$9$	[1,4]	$2^{6}\cdot 3^{16}\cdot 7^{6}\cdot 13^{6}$	$4$	$226.427839458$	$240.67809147708127$			?	$C_3^2:C_2$ (as 9T5)	$[3, 18, 54]$	$2$	$4$	$20292.121146119265$
9.3.244...875.5	$x^{9} - 108 x^{7} - 237 x^{6} + 3510 x^{5} + 14040 x^{4} - 25350 x^{3} - 228150 x^{2} - 456300 x - 333775$	$9$	[3,3]	$-\,3^{19}\cdot 5^{4}\cdot 7^{6}\cdot 13^{4}$	$4$	$237.8997278115839$	$639.3965908065919$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[6, 234]$	$2$	$5$	$34136.24361578262$
9.3.378...192.2	$x^{9} - 9 x^{7} - 25 x^{6} + 159 x^{5} + 216 x^{4} - 794 x^{3} - 3525 x^{2} - 75 x + 14299$	$9$	[3,3]	$-\,2^{6}\cdot 3^{9}\cdot 7^{4}\cdot 11^{6}\cdot 29^{4}$	$5$	$249.817871195$	$977.0585953813884$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 387]$	$2$	$5$	$12207.216264322764$
9.1.482...776.3	$x^{9} - 246 x^{6} + 181548 x^{3} - 551368$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 41^{7}$	$3$	$256.635432539$	$335.2914329244336$			?	$S_3^2$ (as 9T8)	$[3, 6, 84]$	$2$	$4$	$30642.778599587073$
9.3.643...123.3	$x^{9} - 174 x^{6} - 12651 x^{3} - 195112$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 19^{6}$	$3$	$264.94582246547594$	$281.62020645745537$				$S_3\times C_3$ (as 9T4)	$[2, 2, 2, 6, 36]$	$2$	$5$	$382780.2904583743$
9.3.866...504.1	$x^{9} - 3 x^{8} - 117 x^{7} - 1068 x^{6} - 5292 x^{5} - 15255 x^{4} - 26055 x^{3} - 25947 x^{2} - 13932 x - 3123$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{3}\cdot 31^{7}$	$4$	$273.864718034$	$487.24335268924307$			?	$S_3\times C_3$ (as 9T4)	$[3, 819]$	$2$	$5$	$10197.25168202796$
9.3.900...392.2	$x^{9} - 348 x^{6} - 50784 x^{3} - 1560896$	$9$	[3,3]	$-\,2^{6}\cdot 3^{13}\cdot 211^{6}$	$3$	$275.0321389248892$	$292.34130595343$			?	$S_3\times C_3$ (as 9T4)	$[2, 546]$	$2$	$5$	$48822.27920360761$
9.1.935...000.1	$x^{9} - 561 x^{6} + 867 x^{3} - 4913$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 5^{6}\cdot 17^{6}$	$4$	$276.190322415$	$293.57237980266905$				$C_3^2:C_2$ (as 9T5)	$[3, 6, 6, 12]$	$2$	$4$	$194065.38683133657$
9.3.994...448.1	$x^{9} - x^{8} - 93 x^{7} - 876 x^{6} - 4320 x^{5} - 12363 x^{4} - 21015 x^{3} - 20883 x^{2} - 11214 x - 2519$	$9$	[3,3]	$-\,2^{6}\cdot 7^{7}\cdot 19^{3}\cdot 31^{7}$	$4$	$278.089328719$	$612.5100831527393$			?	$S_3\times C_3$ (as 9T4)	$[4, 12, 156]$	$2$	$5$	$8156.370990731837$
9.1.115...000.3	$x^{9} - 72 x^{7} - 746 x^{6} + 1728 x^{5} + 35808 x^{4} + 168128 x^{3} - 429696 x^{2} - 4366848 x - 9021088$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 41^{7}$	$4$	$282.610854539$	$369.2280424450113$			?	$S_3^2$ (as 9T8)	$[3, 3, 270]$	$2$	$4$	$46392.20234039314$
9.3.115...875.3	$x^{9} - 675 x^{6} - 191250 x^{3} - 11390625$	$9$	[3,3]	$-\,3^{15}\cdot 5^{6}\cdot 61^{6}$	$3$	$282.7495901604568$	$339.56443188456166$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 54]$	$2$	$5$	$44382.293356941125$
9.1.123...000.1	$x^{9} - 275 x^{6} + 81675 x^{3} + 4492125$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{6}\cdot 7^{6}\cdot 11^{6}$	$5$	$284.74878364$	$302.669468387716$			?	$C_3^2:C_2$ (as 9T5)	$[3, 3, 3, 9, 36]$	$2$	$4$	$12266.667881941805$
9.1.135...000.1	$x^{9} - 810 x^{6} + 210060 x^{3} - 19683000$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 5^{7}\cdot 3581^{3}$	$4$	$287.82786413$	$1308.5951059473357$			?	$S_3^2$ (as 9T8)	$[3, 6, 72]$	$2$	$4$	$90522.28133274747$
9.3.140...952.1	$x^{9} - 273 x^{7} - 1001 x^{6} + 26208 x^{5} + 197652 x^{4} - 516516 x^{3} - 10434060 x^{2} - 41140008 x - 54787096$	$9$	[3,3]	$-\,2^{9}\cdot 3^{12}\cdot 7^{7}\cdot 13^{7}$	$4$	$288.995133334$	$525.0989623251638$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 12, 12]$	$2$	$5$	$29993.874000856085$
9.1.147...944.1	$x^{9} - 3 x^{8} + 6 x^{7} - 405 x^{6} + 1596 x^{5} - 1197 x^{4} + 52275 x^{3} - 51876 x^{2} + 52272 x + 2299968$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 397^{6}$	$3$	$290.635322766$	$308.92647726866056$			?	$C_3^2:C_2$ (as 9T5)	$[6, 18, 18]$	$2$	$4$	$70571.57897443848$
9.1.182...000.2	$x^{9} - 195 x^{6} - 15825 x^{3} - 274625$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 5^{6}\cdot 19^{6}$	$4$	$297.448358619$	$316.1682920120243$			?	$C_3^2:C_2$ (as 9T5)	$[3, 3, 9, 54]$	$2$	$4$	$29729.94131009686$
9.1.229...000.2	$x^{9} - 120 x^{6} + 266160 x^{3} - 64000$	$9$	[1,4]	$2^{13}\cdot 3^{10}\cdot 5^{7}\cdot 7^{3}\cdot 11^{6}$	$5$	$305.182977445$	$642.4148965262254$			?	$S_3^2$ (as 9T8)	$[3, 3, 126]$	$2$	$4$	$687277.8098318914$
9.1.283...664.1	$x^{9} - 3 x^{8} + 6 x^{7} + 245 x^{6} - 498 x^{5} + 207 x^{4} + 37955 x^{3} - 37842 x^{2} - 19236 x + 607446$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 13^{6}\cdot 307^{3}$	$5$	$312.46458564$	$974.6396466599571$			?	$S_3^2$ (as 9T8)	$[3, 3, 9, 18]$	$2$	$4$	$235895.95407725568$
9.3.421...875.2	$x^{9} - 36 x^{7} - 147 x^{6} + 3942 x^{5} - 10512 x^{4} - 122640 x^{3} + 575532 x^{2} - 767376 x - 5329$	$9$	[3,3]	$-\,3^{9}\cdot 5^{6}\cdot 13^{6}\cdot 73^{4}$	$4$	$326.492833169$	$1017.3388002320779$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 3, 126]$	$2$	$5$	$497055.8369150121$
9.1.461...088.1	$x^{9} - 931 x^{6} + 212268 x^{3} + 18821096$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 7^{6}\cdot 13^{6}\cdot 19^{6}$	$5$	$329.8048800623091$	$499.02306411240914$				$S_3^2$ (as 9T8)	$[3, 9, 54]$	$2$	$4$	$377974.07044676115$
9.3.465...883.6	$x^{9} - 3 x^{8} - 18 x^{7} + 870 x^{6} + 7113 x^{5} + 25632 x^{4} - 889296 x^{3} - 7178295 x^{2} + 3165336 x + 26712685$	$9$	[3,3]	$-\,3^{15}\cdot 7^{4}\cdot 13^{6}\cdot 23^{4}$	$4$	$330.0976960932966$	$1085.3129368487594$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 6, 126]$	$2$	$5$	$172477.7892431703$
9.1.585...000.1	$x^{9} - 3 x^{8} + 4 x^{7} + 77 x^{6} + 28 x^{5} + 1813 x^{4} + 4053 x^{3} - 14530 x^{2} - 14650 x + 32250$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 5^{6}\cdot 7^{7}\cdot 1381^{3}$	$5$	$338.63885470902704$	$1512.0720996870987$			?	$S_3^2$ (as 9T8)	$[3, 9, 45]$	$2$	$4$	$350723.1197531524$
9.1.629...568.1	$x^{9} - 1243 x^{6} - 55869 x^{3} - 2924207$	$9$	[1,4]	$2^{6}\cdot 3^{9}\cdot 11^{7}\cdot 37^{6}$	$4$	$341.387663301$	$468.40678928423944$			?	$S_3^2$ (as 9T8)	$[3, 18, 36]$	$2$	$4$	$70498.23177891904$
9.3.742...024.1	$x^{9} - 287 x^{7} - 445 x^{6} + 25039 x^{5} + 96194 x^{4} - 488422 x^{3} - 2638405 x^{2} - 3176523 x - 10543679$	$9$	[3,3]	$-\,2^{6}\cdot 7^{6}\cdot 37^{7}\cdot 47^{3}$	$4$	$347.667233531$	$807.1775161036906$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 111]$	$2$	$5$	$42274.62992272048$
9.3.770...704.1	$x^{9} - x^{8} - 259 x^{7} + 2834 x^{6} - 15538 x^{5} + 59769 x^{4} - 127105 x^{3} + 190071 x^{2} - 166668 x + 114449$	$9$	[3,3]	$-\,2^{9}\cdot 7^{7}\cdot 109^{7}$	$3$	$349.135110249$	$713.9187285092299$			?	$S_3\times C_3$ (as 9T4)	$[6, 474]$	$2$	$5$	$43965.8605300168$
9.3.797...000.9	$x^{9} + 171 x^{7} - 117 x^{6} - 2043 x^{5} - 30258 x^{4} - 53364 x^{3} + 189027 x^{2} + 1403361 x + 5192551$	$9$	[3,3]	$-\,2^{6}\cdot 3^{19}\cdot 5^{6}\cdot 7^{4}\cdot 13^{4}$	$5$	$350.4351911606789$	$1014.9788208712644$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 6, 126]$	$2$	$5$	$120269.2958189724$
9.3.814...000.1	$x^{9} - 273 x^{7} - 101 x^{6} + 24570 x^{5} + 16380 x^{4} - 737370 x^{3} - 737100 x^{2} - 245700 x - 327300$	$9$	[3,3]	$-\,2^{4}\cdot 3^{15}\cdot 5^{4}\cdot 7^{6}\cdot 13^{6}$	$5$	$351.296748837$	$1014.9788208712644$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[3, 18, 126]$	$2$	$5$	$54719.480029397564$
9.1.856...128.2	$x^{9} + 54 x^{7} - 645 x^{6} + 972 x^{5} + 11934 x^{4} + 156225 x^{3} - 208980 x^{2} - 5061960 x - 11203919$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 31^{7}$	$4$	$353.238352784$	$506.2650021052413$			?	$S_3^2$ (as 9T8)	$[9, 9, 54]$	$2$	$4$	$88308.14598049654$
9.1.856...128.3	$x^{9} - 3 x^{8} - 209 x^{6} - 6 x^{5} + 645 x^{4} + 16283 x^{3} + 15624 x^{2} - 16278 x + 390818$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 31^{7}$	$4$	$353.238352784$	$506.2650021052413$			?	$S_3^2$ (as 9T8)	$[3, 3, 9, 27]$	$2$	$4$	$281798.62230711465$
9.3.958...512.4	$x^{9} - 21 x^{7} - 978 x^{6} + 13167 x^{5} - 43596 x^{4} - 362895 x^{3} + 2433690 x^{2} - 3643164 x - 32428236$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 31^{6}$	$4$	$357.707937779$	$380.22031202922585$				$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 78]$	$2$	$5$	$323714.54160408437$
9.3.108...000.3	$x^{9} - 60 x^{6} - 251500 x^{3} - 8000$	$9$	[3,3]	$-\,2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 7^{6}\cdot 19^{6}$	$5$	$362.818159043$	$435.7217352042167$				$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 63]$	$2$	$5$	$330914.7085540995$
9.1.112...792.1	$x^{9} - 3 x^{8} - 49 x^{6} + 108 x^{5} - 573 x^{4} + 48859 x^{3} - 48606 x^{2} + 26328 x - 11292$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 11^{3}\cdot 13^{7}\cdot 71^{3}$	$5$	$364.282902007$	$1355.0014859526405$			?	$S_3^2$ (as 9T8)	$[3, 3, 3, 42]$	$2$	$4$	$315115.7569859473$
9.3.121...523.2	$x^{9} - 24 x^{6} - 1761 x^{3} - 512$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 31^{6}$	$3$	$367.194193276$	$390.3035856848673$				$S_3\times C_3$ (as 9T4)	$[3, 9, 90]$	$2$	$5$	$1828301.716579086$
9.3.121...523.3	$x^{9} - 153 x^{6} - 9774 x^{3} - 132651$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 31^{6}$	$3$	$367.1941932764816$	$390.3035856848673$			?	$S_3\times C_3$ (as 9T4)	$[3, 3, 3, 108]$	$2$	$5$	$32776.87828253766$
9.3.121...523.5	$x^{9} - 51 x^{6} - 1086 x^{3} - 4913$	$9$	[3,3]	$-\,3^{19}\cdot 7^{6}\cdot 31^{6}$	$3$	$367.1941932764816$	$390.3035856848673$			?	$S_3\times C_3$ (as 9T4)	$[6, 6, 90]$	$2$	$5$	$31570.346278180034$
9.3.127...875.1	$x^{9} - 108 x^{7} - 195 x^{6} + 3888 x^{5} + 14040 x^{4} - 36711 x^{3} - 252720 x^{2} - 358020 x - 42120$	$9$	[3,3]	$-\,3^{15}\cdot 5^{6}\cdot 7^{6}\cdot 13^{6}$	$4$	$369.155793821$	$639.3965908065919$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[6, 234]$	$2$	$5$	$374575.2084172953$
9.1.129...752.1	$x^{9} - 48 x^{6} - 956 x^{3} - 4096$	$9$	[1,4]	$2^{10}\cdot 3^{9}\cdot 431^{6}$	$3$	$369.757683892$	$518.0038307980768$			?	$S_3^2$ (as 9T8)	$[2, 2, 2, 12, 24]$	$2$	$4$	$118114.54856413984$
9.1.147...328.1	$x^{9} - 3 x^{8} + 18 x^{7} - 1531 x^{6} + 3090 x^{5} + 5391 x^{4} + 1083109 x^{3} - 1120128 x^{2} - 7085514 x - 121416404$	$9$	[1,4]	$2^{9}\cdot 3^{3}\cdot 523^{7}$	$3$	$375.370912721$	$902.6589547946423$				$S_3^2$ (as 9T8)	$[3, 3, 135]$	$2$	$4$	$288276.90188896947$
9.1.165...952.1	$x^{9} - 48 x^{6} - 926 x^{3} - 4096$	$9$	[1,4]	$2^{13}\cdot 3^{9}\cdot 7^{6}\cdot 11^{6}\cdot 17^{3}$	$5$	$379.972777526$	$958.1085888426854$			?	$S_3^2$ (as 9T8)	$[6, 6, 30]$	$2$	$4$	$423975.80438853556$
9.1.181...000.1	$x^{9} + 48 x^{7} - 135 x^{6} + 768 x^{5} - 5040 x^{4} + 16921 x^{3} - 34560 x^{2} + 129600 x - 70645$	$9$	[1,4]	$2^{6}\cdot 3^{9}\cdot 5^{6}\cdot 67^{3}\cdot 313^{3}$	$5$	$383.996826146$	$2421.6852725761564$			?	$S_3^2$ (as 9T8)	$[3, 6, 60]$	$2$	$4$	$571362.0994469885$
9.3.200...824.1	$x^{9} - 4 x^{8} - 129 x^{7} - 1167 x^{6} - 5805 x^{5} - 16800 x^{4} - 28764 x^{3} - 28677 x^{2} - 15399 x - 3449$	$9$	[3,3]	$-\,2^{9}\cdot 11^{3}\cdot 313^{7}$	$3$	$388.275350056$	$1126.8383456793752$			?	$S_3\times C_3$ (as 9T4)	$[9, 189]$	$2$	$5$	$63753.910140972286$
9.3.240...992.1	$x^{9} - 147 x^{7} - 759 x^{6} + 8721 x^{5} + 118404 x^{4} + 400242 x^{3} - 967725 x^{2} - 4041675 x - 94875$	$9$	[3,3]	$-\,2^{6}\cdot 3^{15}\cdot 11^{6}\cdot 23^{6}$	$4$	$396.249842338$	$421.1878540654572$			?	$(C_3^2:C_3):C_2$ (as 9T12)	$[9, 351]$	$2$	$5$	$65341.591954637915$
9.3.255...827.4	$x^{9} + 357 x^{7} - 168 x^{6} + 31752 x^{5} - 18522 x^{4} + 657237 x^{3} + 24696 x^{2} - 608139 x + 174930$	$9$	[3,3]	$-\,3^{15}\cdot 7^{6}\cdot 73^{6}$	$3$	$398.8559036454377$	$423.957928025228$				$S_3\times C_3$ (as 9T4)	$[3, 3, 9, 36]$	$2$	$5$	$2414336.5085325516$
9.1.259...696.1	$x^{9} - 3 x^{8} - 83 x^{6} - 6 x^{5} + 267 x^{4} + 3011 x^{3} + 2730 x^{2} - 3006 x + 30122$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 7^{7}\cdot 11^{3}\cdot 13^{7}$	$5$	$399.623617639$	$813.8773527198483$			?	$S_3^2$ (as 9T8)	$[9, 9, 54]$	$2$	$4$	$211502.74195413003$
9.1.268...096.1	$x^{9} + 48 x^{7} - 645 x^{6} + 768 x^{5} + 10608 x^{4} + 154489 x^{3} - 165120 x^{2} - 4499520 x - 10827207$	$9$	[1,4]	$2^{6}\cdot 3^{3}\cdot 7^{7}\cdot 19^{3}\cdot 31^{7}$	$5$	$401.074214852$	$1060.8985841687825$			?	$S_3^2$ (as 9T8)	$[3, 3, 180]$	$2$	$4$	$829950.8423150447$
9.1.273...712.6	$x^{9} - 18 x^{7} - 711 x^{6} + 2736 x^{5} + 7218 x^{4} - 2529 x^{3} + 250344 x^{2} + 1568340 x - 3346531$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 73^{7}$	$3$	$401.957639019$	$542.2567411113308$			?	$S_3^2$ (as 9T8)	$[3, 3, 18, 18]$	$2$	$4$	$253919.39161485436$
9.1.273...712.7	$x^{9} - 36 x^{7} - 267 x^{6} + 1746 x^{5} + 3780 x^{4} - 20013 x^{3} - 29250 x^{2} + 74880 x + 115113$	$9$	[1,4]	$2^{6}\cdot 3^{18}\cdot 73^{7}$	$3$	$401.957639019$	$542.2567411113308$			?	$S_3^2$ (as 9T8)	$[6, 18, 18]$	$2$	$4$	$131776.93121476186$
9.1.308...176.1	$x^{9} - 3 x^{8} + 24 x^{7} + 35 x^{6} + 12 x^{5} + 3603 x^{4} + 80571 x^{3} - 79218 x^{2} + 114300 x - 22500$	$9$	[1,4]	$2^{6}\cdot 3^{10}\cdot 43^{7}\cdot 67^{3}$	$4$	$407.36945085$	$1075.4475683785029$			?	$S_3^2$ (as 9T8)	$[3, 6, 6, 12]$	$2$	$4$	$529964.6112980747$