| 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 |
| 9.1.173946175488.1 |
$x^{9} - 4 x^{8} + 8 x^{7} - 32 x^{5} + 80 x^{4} - 104 x^{3} + 80 x^{2} - 34 x + 8$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{4}$ |
$2$ |
$17.7392390888$ |
$25.412761497225222$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$462.796392768$ |
| 9.1.985223153873.1 |
$x^{9} - 4 x^{8} + 17 x^{6} - 17 x^{5} - 17 x^{4} + 34 x^{3} - 17 x + 17$ |
$9$ |
[1,4] |
$7^{4}\cdot 17^{7}$ |
$2$ |
$21.508739348$ |
$31.563984846697192$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$673.067545231$ |
| 9.1.1680747204608.1 |
$x^{9} - 3 x^{8} + 3 x^{7} - 11 x^{6} + 13 x^{5} - 23 x^{4} + 14 x^{3} - 6 x^{2} + 4 x - 4$ |
$9$ |
[1,4] |
$2^{12}\cdot 17^{7}$ |
$2$ |
$22.823863183$ |
$33.74331915933294$ |
|
|
|
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$1346.06817242$ |
| 9.1.33554432000000.1 |
$x^{9} - x^{8} + 12 x^{7} - 28 x^{6} + 50 x^{5} - 82 x^{4} + 132 x^{3} - 84 x^{2} + 121 x - 25$ |
$9$ |
[1,4] |
$2^{31}\cdot 5^{6}$ |
$2$ |
$31.8317927879$ |
$49.05900508138431$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$7776.97162299$ |
| 9.1.61334280470528.1 |
$x^{9} - 2 x^{8} + 40 x^{5} + 16 x^{4} + 8 x^{3} - 32 x^{2} - 98 x + 100$ |
$9$ |
[1,4] |
$2^{31}\cdot 13^{4}$ |
$2$ |
$34.0382348594$ |
$52.9008815613158$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$9790.60405402$ |
| 9.1.121721421175625.1 |
$x^{9} - x^{8} - 4 x^{7} + 9 x^{6} + 3 x^{5} - 39 x^{4} + 84 x^{3} - 129 x^{2} + 215 x - 166$ |
$9$ |
[1,4] |
$5^{4}\cdot 41^{7}$ |
$2$ |
$36.7316789184$ |
$57.632953563318466$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3]$ |
$2$ |
$4$ |
$2724.92791059$ |
| 9.1.218070794717793.1 |
$x^{9} - 9 x^{7} - 21 x^{6} + 72 x^{5} + 99 x^{4} - 99 x^{3} - 585 x^{2} + 549 x + 166$ |
$9$ |
[1,4] |
$3^{12}\cdot 17^{7}$ |
$2$ |
$39.1902018835$ |
$54.86700011448388$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$10929.5891081$ |
| 9.1.218070794717793.2 |
$x^{9} - 3 x^{8} + 6 x^{7} - 12 x^{6} + 39 x^{5} - 33 x^{4} - 135 x^{3} + 240 x^{2} - 102 x + 13$ |
$9$ |
[1,4] |
$3^{12}\cdot 17^{7}$ |
$2$ |
$39.1902018835$ |
$54.86700011448388$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$12733.5277839$ |
| 9.1.378956381627633.1 |
$x^{9} - 3 x^{8} + 12 x^{7} - 48 x^{6} + 122 x^{5} - 244 x^{4} + 435 x^{3} - 605 x^{2} + 503 x - 189$ |
$9$ |
[1,4] |
$17^{7}\cdot 31^{4}$ |
$2$ |
$41.6718947198$ |
$66.4237901889703$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3]$ |
$2$ |
$4$ |
$4448.56922195$ |
| 9.1.410338673000000.1 |
$x^{9} - 4 x^{8} + 5 x^{7} - 36 x^{6} + 139 x^{5} - 176 x^{4} + 315 x^{3} - 1064 x^{2} + 1496 x - 720$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{6}\cdot 17^{7}$ |
$3$ |
$42.0419154434$ |
$63.3223426132891$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$2189.2152425$ |
| 9.1.410338673000000.2 |
$x^{9} + 16 x^{7} - 3 x^{6} + 50 x^{5} - 200 x^{4} - 61 x^{3} - 242 x^{2} + 80 x - 7$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{6}\cdot 17^{7}$ |
$3$ |
$42.0419154434$ |
$63.3223426132891$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$2185.26900994$ |
| 9.1.949294310003793.1 |
$x^{9} - 2 x^{8} - 15 x^{7} + 31 x^{6} + 102 x^{5} - 212 x^{4} - 319 x^{3} + 489 x^{2} + 1318 x - 1905$ |
$9$ |
[1,4] |
$3^{4}\cdot 13^{4}\cdot 17^{7}$ |
$3$ |
$46.1482942474$ |
$74.50323141285185$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3]$ |
$2$ |
$4$ |
$10616.296287$ |
| 9.1.1141260857376768.1 |
$x^{9} + 12 x^{7} - 24 x^{6} + 18 x^{5} + 24 x^{4} - 60 x^{3} - 72 x^{2} - 33 x - 8$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}$ |
$2$ |
$47.1023710327$ |
$67.47760233783548$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$5560.17577237$ |
| 9.1.1980626399884457.1 |
$x^{9} - x^{8} + 6 x^{7} - 17 x^{6} + 49 x^{5} - 73 x^{4} - 19 x^{3} - 152 x^{2} + 304 x - 635$ |
$9$ |
[1,4] |
$13^{6}\cdot 17^{7}$ |
$2$ |
$50.0777409535$ |
$81.67710206860912$ |
|
|
|
$C_3^2:C_8$ (as 9T15) |
$[3]$ |
$2$ |
$4$ |
$8374.76136348$ |
| 9.1.6904624074435625.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 18 x^{6} + 108 x^{5} - 434 x^{4} + 1121 x^{3} - 1654 x^{2} + 1920 x - 608$ |
$9$ |
[1,4] |
$5^{4}\cdot 73^{7}$ |
$2$ |
$57.531334583$ |
$95.47562384622023$ |
|
|
|
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$170059.082386$ |
| 9.1.8268784250602433.1 |
$x^{9} - 4 x^{8} - 9 x^{7} + 4 x^{6} + 203 x^{5} + 401 x^{4} - 134 x^{3} - 1999 x^{2} - 3564 x - 2039$ |
$9$ |
[1,4] |
$17^{7}\cdot 67^{4}$ |
$2$ |
$58.6954759987$ |
$97.65178978680869$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$67632.1703188$ |
| 9.9.15056675074868288.1 |
$x^{9} - 26 x^{7} - 3 x^{6} + 236 x^{5} + 50 x^{4} - 889 x^{3} - 302 x^{2} + 1174 x + 629$ |
$9$ |
[9,0] |
$2^{6}\cdot 113^{7}$ |
$2$ |
$62.7372463982$ |
$99.34140587632257$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$531836.403896$ |
| 9.1.51835034729971712.1 |
$x^{9} - 4 x^{7} - 40 x^{6} + 62 x^{5} + 424 x^{4} + 332 x^{3} - 56 x^{2} + x - 8$ |
$9$ |
[1,4] |
$2^{31}\cdot 17^{6}$ |
$2$ |
$71.9747851406$ |
$97.0041945844675$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$32145.3937777$ |
| 9.1.51835034729971712.2 |
$x^{9} - 3 x^{8} + 8 x^{7} + 56 x^{6} - 64 x^{5} + 384 x^{4} - 576 x^{3} + 2528 x^{2} - 5192 x + 3864$ |
$9$ |
[1,4] |
$2^{31}\cdot 17^{6}$ |
$2$ |
$71.9747851406$ |
$97.0041945844675$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$31121.9065669$ |
| 9.9.57269713922998848.1 |
$x^{9} - 3 x^{8} - 23 x^{7} + 77 x^{6} + 78 x^{5} - 338 x^{4} - 12 x^{3} + 348 x^{2} - 16 x - 76$ |
$9$ |
[9,0] |
$2^{6}\cdot 3^{4}\cdot 73^{7}$ |
$3$ |
$72.7765842432$ |
$117.39640389563408$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$1441045.9779$ |
| 9.1.92442129447518208.1 |
$x^{9} - 3 x^{8} - 12 x^{7} + 36 x^{6} + 42 x^{5} - 174 x^{4} + 60 x^{3} - 84 x^{2} + 681 x - 715$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}$ |
$2$ |
$76.7532298601$ |
$103.44435526675392$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$364568.5526$ |
| 9.9.92442129447518208.1 |
$x^{9} - 36 x^{7} - 24 x^{6} + 378 x^{5} + 360 x^{4} - 1212 x^{3} - 1080 x^{2} + 801 x + 136$ |
$9$ |
[9,0] |
$2^{31}\cdot 3^{16}$ |
$2$ |
$76.7532298601$ |
$103.44435526675392$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$2272808.96352$ |
| 9.1.92442129447518208.4 |
$x^{9} - 3 x^{8} + 48 x^{6} - 108 x^{5} + 36 x^{4} + 432 x^{3} - 720 x^{2} - 324 x + 1164$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}$ |
$2$ |
$76.7532298601$ |
$103.44435526675392$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$429713.478834$ |
| 9.1.136294246698620625.1 |
$x^{9} - 3 x^{8} - 12 x^{7} + 60 x^{6} - 9 x^{5} - 288 x^{4} + 54 x^{3} - 1197 x^{2} - 1701 x - 2448$ |
$9$ |
[1,4] |
$3^{12}\cdot 5^{4}\cdot 17^{7}$ |
$3$ |
$80.1365858886$ |
$122.68634197747471$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$249728.185986$ |
| 9.1.136294246698620625.2 |
$x^{9} - 3 x^{8} - 102 x^{6} + 612 x^{5} - 969 x^{4} + 102 x^{3} + 306 x^{2} - 459 x - 816$ |
$9$ |
[1,4] |
$3^{12}\cdot 5^{4}\cdot 17^{7}$ |
$3$ |
$80.1365858886$ |
$122.68634197747471$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$271198.343698$ |
| 9.9.523587978117420993.1 |
$x^{9} - 3 x^{8} - 60 x^{7} + 144 x^{6} + 1008 x^{5} - 1104 x^{4} - 5760 x^{3} - 2112 x^{2} + 1920 x - 256$ |
$9$ |
[9,0] |
$3^{12}\cdot 7^{4}\cdot 17^{7}$ |
$3$ |
$93.0629102476$ |
$145.16443748707678$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$3070603.04888$ |
| 9.1.713288035860480000.1 |
$x^{9} - 3 x^{8} + 12 x^{7} - 84 x^{6} - 78 x^{5} + 138 x^{4} + 3972 x^{3} - 6012 x^{2} + 14265 x - 49803$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$96.3154824525$ |
$150.88450578609888$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[2]$ |
$2$ |
$4$ |
$551679.115962$ |
| 9.1.713288035860480000.2 |
$x^{9} - 3 x^{8} + 12 x^{7} - 36 x^{6} + 90 x^{5} + 450 x^{4} + 804 x^{3} + 3828 x^{2} + 11319 x - 4357$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$96.3154824525$ |
$150.88450578609888$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$1070705.80398$ |
| 9.9.893217975164080128.1 |
$x^{9} - 3 x^{8} - 39 x^{7} + 63 x^{6} + 597 x^{5} - 99 x^{4} - 3570 x^{3} - 3330 x^{2} + 2604 x + 2900$ |
$9$ |
[9,0] |
$2^{12}\cdot 3^{12}\cdot 17^{7}$ |
$3$ |
$98.7531206053$ |
$155.18731137725854$ |
|
|
|
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$6126483.81989$ |
| 9.9.1905899642487308288.1 |
$x^{9} - 3 x^{8} - 56 x^{7} + 168 x^{6} + 896 x^{5} - 2640 x^{4} - 3512 x^{3} + 10344 x^{2} - 4434 x - 698$ |
$9$ |
[9,0] |
$2^{31}\cdot 31^{6}$ |
$2$ |
$107.429171242$ |
$144.78793109115003$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3]$ |
$2$ |
$8$ |
$3529430.00404$ |
| 9.9.4423128914083118417.1 |
$x^{9} - 4 x^{8} - 27 x^{7} + 61 x^{6} + 168 x^{5} - 397 x^{4} - 177 x^{3} + 919 x^{2} - 713 x + 170$ |
$9$ |
[9,0] |
$17^{7}\cdot 47^{6}$ |
$2$ |
$117.963522641$ |
$155.37269953866775$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$9857850.5089$ |
| 9.1.178...000.1 |
$x^{9} - 12 x^{7} - 120 x^{6} + 114 x^{5} + 1800 x^{4} + 2652 x^{3} - 3000 x^{2} - 38769 x - 127400$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$137.728168412$ |
$225.62496183240916$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$5592002.60721$ |
| 9.9.178...000.1 |
$x^{9} - 3 x^{8} - 48 x^{7} + 144 x^{6} + 744 x^{5} - 2232 x^{4} - 4152 x^{3} + 12696 x^{2} + 6366 x - 20938$ |
$9$ |
[9,0] |
$2^{31}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$137.728168412$ |
$225.62496183240916$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$8$ |
$33755161.1223$ |
| 9.1.178...000.2 |
$x^{9} - 3 x^{8} - 12 x^{7} - 204 x^{6} - 1206 x^{5} - 4302 x^{4} - 11268 x^{3} - 27396 x^{2} - 41769 x - 40293$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$137.728168412$ |
$225.62496183240916$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$5229590.64065$ |
| 9.1.178...000.3 |
$x^{9} - 3 x^{8} - 12 x^{7} + 84 x^{6} + 450 x^{5} - 486 x^{4} + 4668 x^{3} + 5052 x^{2} + 3081 x + 32965$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$137.728168412$ |
$225.62496183240916$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$5045199.63706$ |
| 9.1.178...000.4 |
$x^{9} - 3 x^{8} + 96 x^{6} + 216 x^{5} - 3192 x^{4} + 21720 x^{3} - 20376 x^{2} - 175266 x + 378966$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$137.728168412$ |
$225.62496183240916$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$6301052.63556$ |
| 9.1.577...000.1 |
$x^{9} - 3 x^{8} + 48 x^{6} - 108 x^{5} + 36 x^{4} + 432 x^{3} - 144 x^{2} - 324 x + 1164$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}\cdot 5^{4}$ |
$3$ |
$156.945907429$ |
$231.30861026510016$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$16753500.506$ |
| 9.1.577...000.2 |
$x^{9} + 72 x^{7} - 96 x^{6} + 1188 x^{5} - 5472 x^{4} - 9456 x^{3} + 31968 x^{2} + 18594 x + 2656$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}\cdot 5^{4}$ |
$3$ |
$156.945907429$ |
$231.30861026510016$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$9682736.1268$ |
| 9.1.144...000.1 |
$x^{9} - 3 x^{8} - 48 x^{7} + 96 x^{6} + 1392 x^{5} - 912 x^{4} - 4992 x^{3} - 5376 x^{2} + 61728 x - 61792$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}\cdot 5^{6}$ |
$3$ |
$224.427805576$ |
$345.8870484458918$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[2]$ |
$2$ |
$4$ |
$19688930.8464$ |
| 9.1.144...000.3 |
$x^{9} - 72 x^{7} - 192 x^{6} + 4752 x^{5} + 5040 x^{4} - 113928 x^{3} - 172368 x^{2} + 1513998 x + 469664$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}\cdot 5^{6}$ |
$3$ |
$224.427805576$ |
$345.8870484458918$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
$[3, 3]$ |
$2$ |
$4$ |
$6087421.88971$ |
| 9.1.144...000.4 |
$x^{9} - 3 x^{8} + 12 x^{7} + 348 x^{6} + 1146 x^{5} - 12702 x^{4} + 136548 x^{3} - 158988 x^{2} + 117849 x + 3432229$ |
$9$ |
[1,4] |
$2^{31}\cdot 3^{16}\cdot 5^{6}$ |
$3$ |
$224.427805576$ |
$345.8870484458918$ |
|
|
? |
$C_3^2:C_8$ (as 9T15) |
trivial |
$2$ |
$4$ |
$41618808.3245$ |
