| 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 |
| 9.3.2228055232239.7 |
$x^{9} + 9 x^{7} - 36 x^{4} - 48 x^{3} + 27 x^{2} + 54 x + 17$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 71$ |
$2$ |
$23.5500466907$ |
$123.5735646798655$ |
|
|
|
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$5$ |
$715.474399893$ |
| 9.5.2290817351457.1 |
$x^{9} - 9 x^{6} - 27 x^{5} - 9 x^{4} - 3 x^{3} + 27 x^{2} + 18 x - 17$ |
$9$ |
[5,2] |
$3^{22}\cdot 73$ |
$2$ |
$23.6228489929$ |
$125.30195022263473$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$906.664289684$ |
| 9.5.9069126227001.1 |
$x^{9} - 9 x^{7} - 18 x^{6} + 27 x^{5} + 108 x^{4} + 42 x^{3} - 162 x^{2} - 207 x - 71$ |
$9$ |
[5,2] |
$3^{22}\cdot 17^{2}$ |
$2$ |
$27.5251373052$ |
$60.467339582680516$ |
|
|
? |
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25) |
trivial |
$2$ |
$6$ |
$1924.86925246$ |
| 9.5.11328562518849.2 |
$x^{9} - 9 x^{7} - 9 x^{6} + 27 x^{5} + 54 x^{4} - 12 x^{3} - 81 x^{2} - 45 x + 17$ |
$9$ |
[5,2] |
$3^{22}\cdot 19^{2}$ |
$2$ |
$28.2139483721$ |
$63.92536271398021$ |
|
|
|
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25) |
trivial |
$2$ |
$6$ |
$2531.1373598$ |
| 9.7.34142592854592.1 |
$x^{9} - 18 x^{7} + 81 x^{5} - 36 x^{4} - 75 x^{3} + 108 x^{2} - 64$ |
$9$ |
[7,1] |
$-\,2^{6}\cdot 3^{22}\cdot 17$ |
$3$ |
$31.8933112359$ |
$120.93467916536103$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$7$ |
$5591.94421569$ |
| 9.5.42960670604721.1 |
$x^{9} - 18 x^{7} - 9 x^{6} + 81 x^{5} + 135 x^{4} - 63 x^{3} - 324 x^{2} - 243 x + 9$ |
$9$ |
[5,2] |
$3^{22}\cdot 37^{2}$ |
$2$ |
$32.7179189665$ |
$89.20665656370325$ |
|
|
|
$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25) |
trivial |
$2$ |
$6$ |
$4178.77362564$ |
| 9.5.74310349154112.6 |
$x^{9} - 18 x^{7} - 18 x^{6} + 108 x^{4} + 504 x^{3} - 648 x^{2} - 1296 x + 1368$ |
$9$ |
[5,2] |
$2^{6}\cdot 3^{22}\cdot 37$ |
$3$ |
$34.7718422118$ |
$141.6067404717884$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$5160.6310219$ |
| 9.9.167229666656361.2 |
$x^{9} - 45 x^{7} - 54 x^{6} + 567 x^{5} + 1044 x^{4} - 1803 x^{3} - 3942 x^{2} + 584$ |
$9$ |
[9,0] |
$3^{22}\cdot 73^{2}$ |
$2$ |
$38.0511815733$ |
$256.16019224397155$ |
|
|
|
$C_3 \wr C_3 $ (as 9T17) |
trivial |
$2$ |
$8$ |
$25727.5581053$ |
| 9.3.1345462930735875.4 |
$x^{9} - 18 x^{7} - 45 x^{6} + 297 x^{4} + 477 x^{3} + 81 x^{2} - 1134 x - 2196$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$47.9717706349$ |
$86.76217340159114$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3]$ |
$2$ |
$5$ |
$10212.1884394$ |
| 9.3.1345462930735875.5 |
$x^{9} - 18 x^{7} - 36 x^{6} + 243 x^{4} + 288 x^{3} - 567 x^{2} - 2025 x - 1854$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$47.9717706349$ |
$86.76217340159114$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3]$ |
$2$ |
$5$ |
$79524.0668364$ |
| 9.3.1345462930735875.8 |
$x^{9} - 18 x^{7} - 9 x^{6} + 54 x^{4} + 18 x^{3} + 648 x^{2} - 1296 x - 315$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$47.9717706349$ |
$86.76217340159114$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
$[3]$ |
$2$ |
$5$ |
$9393.362476$ |
| 9.5.2008387814976000.3 |
$x^{9} - 18 x^{7} - 54 x^{6} + 81 x^{5} + 522 x^{4} + 357 x^{3} - 1080 x^{2} - 3564 x + 2008$ |
$9$ |
[5,2] |
$2^{9}\cdot 3^{22}\cdot 5^{3}$ |
$3$ |
$50.1552497726$ |
$155.99076676750158$ |
|
|
? |
$S_3 \wr C_3 $ (as 9T28) |
trivial |
$2$ |
$6$ |
$25182.0355995$ |
| 9.9.4089611069304489.1 |
$x^{9} - 72 x^{7} - 135 x^{6} + 1539 x^{5} + 5472 x^{4} - 5016 x^{3} - 48735 x^{2} - 77976 x - 39349$ |
$9$ |
[9,0] |
$3^{22}\cdot 19^{4}$ |
$2$ |
$54.2789370431$ |
$104.4236335758831$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$66816.604114$ |
| 9.9.58813158057863049.3 |
$x^{9} - 117 x^{7} - 9 x^{6} + 3996 x^{5} - 999 x^{4} - 45399 x^{3} + 160173 x + 121841$ |
$9$ |
[9,0] |
$3^{22}\cdot 37^{4}$ |
$2$ |
$72.9919463619$ |
$162.84117089348263$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$362195.809034$ |
| 9.9.891166893611747769.2 |
$x^{9} - 189 x^{7} - 315 x^{6} + 9855 x^{5} + 14454 x^{4} - 211116 x^{3} - 143883 x^{2} + 1678635 x - 580861$ |
$9$ |
[9,0] |
$3^{22}\cdot 73^{4}$ |
$2$ |
$98.7278987263$ |
$256.16019224397155$ |
|
|
|
$C_3 \wr C_3 $ (as 9T17) |
$[3]$ |
$2$ |
$8$ |
$588787.512342$ |
| 9.3.3230456496696835875.1 |
$x^{9} - 126 x^{6} + 378 x^{5} + 63 x^{4} - 4242 x^{3} + 6615 x^{2} - 18963 x - 58114$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$506430.869081$ |
| 9.3.3230456496696835875.3 |
$x^{9} - 63 x^{6} + 378 x^{5} + 1071 x^{4} - 7455 x^{3} - 22491 x^{2} - 28224 x - 18620$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$395088.319032$ |
| 9.3.3230456496696835875.4 |
$x^{9} - 63 x^{6} + 378 x^{5} - 1008 x^{4} - 7266 x^{3} + 29106 x^{2} - 28224 x - 1421$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$244105.73301$ |
| 9.3.323...875.10 |
$x^{9} - 63 x^{7} - 63 x^{6} + 1323 x^{5} + 2646 x^{4} - 5061 x^{3} - 27783 x^{2} - 88200 x + 98000$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$386610.364683$ |
| 9.3.323...875.11 |
$x^{9} - 63 x^{7} - 63 x^{6} + 1323 x^{5} + 2646 x^{4} - 5250 x^{3} - 27783 x^{2} - 84231 x + 109907$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
? |
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$75287.36925$ |
| 9.3.323...875.12 |
$x^{9} - 63 x^{7} - 126 x^{6} + 1323 x^{5} + 5292 x^{4} - 8652 x^{3} - 55566 x^{2} - 12789 x + 245980$ |
$9$ |
[3,3] |
$-\,3^{22}\cdot 5^{3}\cdot 7^{7}$ |
$3$ |
$113.916039481$ |
$165.97006698500886$ |
|
|
|
$C_3 \wr S_3 $ (as 9T20) |
$[3, 3]$ |
$2$ |
$5$ |
$1377951.94928$ |
| 9.9.4429692664637819049.4 |
$x^{9} - 216 x^{7} - 495 x^{6} + 14715 x^{5} + 57879 x^{4} - 300513 x^{3} - 1603935 x^{2} + 213858 x + 6213763$ |
$9$ |
[9,0] |
$3^{22}\cdot 109^{4}$ |
$2$ |
$117.982960187$ |
$334.642219781113$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$3015185.10042$ |
| 9.9.8163614486182905369.3 |
$x^{9} - 261 x^{7} - 891 x^{6} + 20574 x^{5} + 128016 x^{4} - 256413 x^{3} - 3048381 x^{2} - 3048381 x + 8725789$ |
$9$ |
[9,0] |
$3^{22}\cdot 127^{4}$ |
$2$ |
$126.275842977$ |
$370.53754041935434$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$3066060.83603$ |
| 9.1.200...000.40 |
$x^{9} - 36 x^{7} - 72 x^{6} + 432 x^{5} + 1728 x^{4} - 1200 x^{3} - 10368 x^{2} - 6336 x + 153856$ |
$9$ |
[1,4] |
$2^{13}\cdot 3^{22}\cdot 5^{7}$ |
$3$ |
$139.559961825$ |
$251.76946747483663$ |
|
|
|
$S_3\wr S_3$ (as 9T31) |
$[9]$ |
$2$ |
$4$ |
$1293615.74185$ |
| 9.9.221...449.1 |
$x^{9} - 333 x^{7} - 630 x^{6} + 30807 x^{5} + 123228 x^{4} - 600492 x^{3} - 4304178 x^{2} - 8369235 x - 5287231$ |
$9$ |
[9,0] |
$3^{22}\cdot 163^{4}$ |
$2$ |
$141.088264483$ |
$437.6109058848977$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$4200335.96176$ |
| 9.9.336...689.1 |
$x^{9} - 360 x^{7} - 1557 x^{6} + 34209 x^{5} + 244350 x^{4} - 549516 x^{3} - 7960923 x^{2} - 18280638 x - 10581803$ |
$9$ |
[9,0] |
$3^{22}\cdot 181^{4}$ |
$2$ |
$147.811798181$ |
$469.26206817515623$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$9972929.49103$ |
| 9.9.492...409.4 |
$x^{9} - 315 x^{7} - 702 x^{6} + 32238 x^{5} + 127161 x^{4} - 1030422 x^{3} - 5346135 x^{2} + 2138454 x + 24909029$ |
$9$ |
[9,0] |
$3^{22}\cdot 199^{4}$ |
$2$ |
$154.17319722$ |
$499.8792597608661$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
trivial |
$2$ |
$8$ |
$11715069.3768$ |
| 9.1.321...000.13 |
$x^{9} - 81 x^{7} - 18 x^{6} + 1917 x^{5} - 828 x^{4} - 13125 x^{3} + 58698 x^{2} + 160884 x + 97784$ |
$9$ |
[1,4] |
$2^{17}\cdot 3^{22}\cdot 5^{7}$ |
$3$ |
$189.911800476$ |
$448.6021916804156$ |
|
|
|
$S_3\wr S_3$ (as 9T31) |
$[9]$ |
$2$ |
$4$ |
$15851331.7352$ |
| 9.9.481...361.1 |
$x^{9} - 504 x^{7} - 2646 x^{6} + 75411 x^{5} + 745731 x^{4} - 1569666 x^{3} - 46805094 x^{2} - 210622923 x - 305471341$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{6}\cdot 19^{4}$ |
$3$ |
$198.623224256$ |
$382.11799860557556$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
$[3]$ |
$2$ |
$8$ |
$9335475.77181$ |
| 9.9.481...361.3 |
$x^{9} - 504 x^{7} - 2457 x^{6} + 75411 x^{5} + 687078 x^{4} - 1871310 x^{3} - 43461873 x^{2} - 180533934 x - 242816903$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{6}\cdot 19^{4}$ |
$3$ |
$198.623224256$ |
$382.11799860557556$ |
|
|
? |
$C_9:C_3$ (as 9T6) |
$[3]$ |
$2$ |
$8$ |
$10466762.7317$ |
| 9.9.474...001.4 |
$x^{9} - 657 x^{7} - 657 x^{6} + 143883 x^{5} + 287766 x^{4} - 10423524 x^{3} - 31510377 x^{2} - 17505765 x + 6613289$ |
$9$ |
[9,0] |
$3^{22}\cdot 73^{6}$ |
$2$ |
$256.160192244$ |
$256.16019224397155$ |
|
|
|
$C_3 \wr C_3 $ (as 9T17) |
$[3, 3]$ |
$2$ |
$8$ |
$14689322.6313$ |
| 9.9.147...289.22 |
$x^{9} - 819 x^{7} - 819 x^{6} + 105651 x^{5} + 14742 x^{4} - 2502318 x^{3} + 1938573 x^{2} + 5214573 x - 4850209$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{8}\cdot 13^{8}$ |
$3$ |
$808.47487326$ |
$808.4748732595972$ |
|
|
|
$C_9:C_3$ (as 9T6) |
$[3, 9]$ |
$2$ |
$8$ |
$1557459742.51$ |
| 9.9.147...289.23 |
$x^{9} - 819 x^{7} - 819 x^{6} + 135135 x^{5} + 280098 x^{4} - 300846 x^{3} - 656019 x^{2} + 104013 x + 309491$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{8}\cdot 13^{8}$ |
$3$ |
$808.47487326$ |
$808.4748732595972$ |
|
|
|
$C_9:C_3$ (as 9T6) |
$[3, 9]$ |
$2$ |
$8$ |
$1771130019.37$ |
| 9.9.147...289.32 |
$x^{9} - 819 x^{7} - 3276 x^{6} + 194103 x^{5} + 1199016 x^{4} - 13831545 x^{3} - 95085900 x^{2} + 299344500 x + 2144870000$ |
$9$ |
[9,0] |
$3^{22}\cdot 7^{8}\cdot 13^{8}$ |
$3$ |
$808.47487326$ |
$808.4748732595972$ |
|
|
|
$C_9:C_3$ (as 9T6) |
$[3, 9]$ |
$2$ |
$8$ |
$562994976933$ |
| 18.0.177...903.1 |
$x^{18} + 18 x^{16} - 36 x^{15} + 81 x^{14} - 693 x^{13} + 1299 x^{12} - 3672 x^{11} + 22167 x^{10} - 25679 x^{9} + 88533 x^{8} - 388035 x^{7} + 197658 x^{6} - 1441638 x^{5} + 4494087 x^{4} + 2545989 x^{3} + 21115836 x^{2} + 5593428 x + 3447793$ |
$18$ |
[0,9] |
$-\,3^{44}\cdot 23^{9}$ |
$2$ |
$70.3331904717$ |
$82.76466256650681$ |
|
|
? |
$C_3^2:C_{18}$ (as 18T82) |
$[9]$ |
$2$ |
$8$ |
$189495677.488$ |
| 18.6.799...904.1 |
$x^{18} - 279 x^{16} - 894 x^{15} + 36306 x^{14} + 190638 x^{13} - 2632323 x^{12} - 15552702 x^{11} + 80881875 x^{10} + 804737180 x^{9} - 417666807 x^{8} - 21953305296 x^{7} - 50695803237 x^{6} + 253594299600 x^{5} + 1405357004250 x^{4} + 693643929126 x^{3} - 11289381895908 x^{2} - 29208678187410 x - 5949099762173$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{40}\cdot 541^{6}$ |
$3$ |
$187.225589047$ |
|
|
|
|
$C_3\wr A_4$ (as 18T535) |
$[3]$ |
$2$ |
$11$ |
$27639164187500$ |
