| 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 |
| 9.1.32206049.1 |
$x^{9} - 2 x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - 6 x^{4} + 5 x^{3} - 4 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 2647$ |
$2$ |
$6.82677001293$ |
$246.74075463935827$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.720252095298$ |
| 9.1.35028793.1 |
$x^{9} - 2 x^{8} + 4 x^{7} - 7 x^{6} + 10 x^{5} - 11 x^{4} + 11 x^{3} - 8 x^{2} + 4 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 2879$ |
$2$ |
$6.89079712201$ |
$257.3266406729004$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.760652964324$ |
| 9.1.38817673.1 |
$x^{9} - x^{7} - 2 x^{4} - 2 x^{3} + x^{2} + 3 x + 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 1303$ |
$2$ |
$6.96988318969$ |
$200.98009851724126$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.822727339615$ |
| 9.1.43302353.1 |
$x^{9} - 2 x^{7} + 2 x^{5} - x^{4} + 2 x^{3} - 2 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 3559$ |
$2$ |
$7.05506919073$ |
$286.1066234815265$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.876375147614$ |
| 9.1.44656709.1 |
$x^{9} - 3 x^{8} + 6 x^{7} - 10 x^{6} + 13 x^{5} - 13 x^{4} + 10 x^{3} - 7 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 1499$ |
$2$ |
$7.07925266065$ |
$215.56669501571898$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.904627574852$ |
| 9.1.44908397.1 |
$x^{9} + x^{7} - x^{6} + 3 x^{5} + 2 x^{3} + x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 3691$ |
$2$ |
$7.08367482946$ |
$291.3640334701591$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.909270314$ |
| 9.1.47159153.1 |
$x^{9} - x^{8} - 2 x^{7} + x^{6} + 2 x^{5} + x^{3} - 2 x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 1583$ |
$2$ |
$7.12227017395$ |
$221.5242650365869$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.927340454576$ |
| 9.1.49483189.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{4} + 2 x^{3} - x^{2} + x - 1$ |
$9$ |
[1,4] |
$7^{2}\cdot 23^{3}\cdot 83$ |
$3$ |
$7.16044053251$ |
$115.59844289608749$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.967836435735$ |
| 9.1.50797225.1 |
$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 4 x^{5} + x^{4} + 3 x^{3} - 2 x^{2} + 1$ |
$9$ |
[1,4] |
$5^{2}\cdot 23^{3}\cdot 167$ |
$3$ |
$7.18132270776$ |
$138.58210562695314$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$0.99135399817$ |
| 9.1.51478577.1 |
$x^{9} - x^{8} + 3 x^{7} - 5 x^{6} + 6 x^{5} - 7 x^{4} + 6 x^{3} - 5 x^{2} + 2 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4231$ |
$2$ |
$7.1919621414$ |
$311.95031655697994$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.00101578952$ |
| 9.1.53814641.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 6 x^{6} + 4 x^{5} - 2 x^{4} + x^{2} + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4423$ |
$2$ |
$7.22751395028$ |
$318.9498393164668$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.00414538811$ |
| 9.1.54982673.1 |
$x^{9} - 2 x^{8} + 3 x^{7} - 4 x^{6} + 4 x^{5} - 3 x^{4} + 3 x^{3} - 2 x^{2} - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4519$ |
$2$ |
$7.24477820597$ |
$322.39261778148705$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.04181323068$ |
| 9.1.56491381.1 |
$x^{9} - 4 x^{8} + 9 x^{7} - 15 x^{6} + 20 x^{5} - 20 x^{4} + 16 x^{3} - 10 x^{2} + 5 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4643$ |
$2$ |
$7.26660167523$ |
$326.78586260730435$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.05040427633$ |
| 9.1.58778777.1 |
$x^{9} - 2 x^{8} + 3 x^{7} - 3 x^{6} + x^{5} + x^{4} - 2 x^{3} + x^{2} - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4831$ |
$2$ |
$7.29872040509$ |
$333.3361666546251$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.09704059882$ |
| 9.1.58956389.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 1979$ |
$2$ |
$7.30116762752$ |
$247.6873028639135$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.08378947669$ |
| 9.1.59552209.1 |
$x^{9} - 2 x^{8} + 4 x^{7} - 6 x^{6} + 8 x^{5} - 9 x^{4} + 8 x^{3} - 5 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 1999$ |
$2$ |
$7.30932952839$ |
$248.93573467865156$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.08316800712$ |
| 9.1.59849473.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 6 x^{6} + 8 x^{5} - 10 x^{4} + 11 x^{3} - 9 x^{2} + 5 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 4919$ |
$2$ |
$7.31337452293$ |
$336.3584397632977$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.14447533875$ |
| 9.1.66078977.1 |
$x^{9} - x^{8} - x^{7} + x^{6} + 2 x^{4} - x^{3} - 2 x^{2} + x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 5431$ |
$2$ |
$7.39428053466$ |
$353.43033259752906$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.21658528983$ |
| 9.1.66711661.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 8 x^{6} + 11 x^{5} - 11 x^{4} + 10 x^{3} - 6 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 5483$ |
$2$ |
$7.4021136771$ |
$355.11829015132406$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.17347955045$ |
| 9.1.67149673.1 |
$x^{9} - 3 x^{8} + 4 x^{7} - 5 x^{5} + 5 x^{4} + x^{3} - 4 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 5519$ |
$2$ |
$7.40749803046$ |
$356.28219152800773$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.1924024692$ |
| 9.1.68755717.1 |
$x^{9} - x^{8} + 3 x^{7} - 2 x^{6} + 3 x^{5} + x^{4} + x^{2} + x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 5651$ |
$2$ |
$7.42697719851$ |
$360.5176833388343$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.19722306716$ |
| 9.1.72503153.1 |
$x^{9} - 3 x^{8} + 7 x^{7} - 12 x^{6} + 17 x^{5} - 19 x^{4} + 17 x^{3} - 12 x^{2} + 6 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 59\cdot 101$ |
$3$ |
$7.47090111582$ |
$370.2121013689315$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.28904079212$ |
| 9.1.73513792.1 |
$x^{9} - 3 x^{8} + 3 x^{7} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 5 x^{2} - 2 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 863$ |
$3$ |
$7.48240102059$ |
$154.66370308932883$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.2490309659$ |
| 9.1.74566873.1 |
$x^{9} - x^{8} - x^{7} + 2 x^{6} - 2 x^{5} + x^{3} - x^{2} + x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 2503$ |
$2$ |
$7.49423531658$ |
$278.5552009925501$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.24751877939$ |
| 9.1.74839217.1 |
$x^{9} - 3 x^{8} + 2 x^{7} + 2 x^{4} - 2 x^{2} - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 6151$ |
$2$ |
$7.49727167313$ |
$376.12896724394943$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.26299231697$ |
| 9.1.75401021.1 |
$x^{9} - x^{8} + 3 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 5 x^{3} - 5 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 2531$ |
$2$ |
$7.50350430936$ |
$280.108907391393$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.27276589382$ |
| 9.1.75909913.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - x^{6} + x^{5} - 3 x^{4} + 6 x^{3} - 3 x^{2} - x + 1$ |
$9$ |
[1,4] |
$17\cdot 23^{3}\cdot 367$ |
$3$ |
$7.50911441287$ |
$378.80997874924043$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.27659179008$ |
| 9.1.76639933.1 |
$x^{9} - x^{8} + 4 x^{7} - 2 x^{6} + 4 x^{5} + 2 x^{4} - x^{3} + 5 x^{2} - 2 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 6299$ |
$2$ |
$7.51710416768$ |
$380.6271141156394$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.27907520419$ |
| 9.1.76931941.1 |
$x^{9} - 2 x^{8} + x^{7} - x^{6} + 3 x^{5} - 4 x^{4} + x^{3} + 3 x^{2} - 2 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 6323$ |
$2$ |
$7.52028113978$ |
$381.35154385422385$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.31828660102$ |
| 9.1.78284096.1 |
$x^{9} - x^{8} - x^{7} + 2 x^{6} - 3 x^{4} + x^{3} + 3 x^{2} - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 919$ |
$3$ |
$7.53485393578$ |
$159.6028940426036$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.30168122946$ |
| 9.1.79073333.1 |
$x^{9} - x^{8} - 2 x^{7} + x^{6} + x^{4} + 4 x^{3} - x^{2} - 3 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 67\cdot 97$ |
$3$ |
$7.54325681657$ |
$386.62255495508794$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.30723193327$ |
| 9.1.80387369.1 |
$x^{9} - x^{8} + 4 x^{7} - 5 x^{6} + 6 x^{5} - 6 x^{4} + 3 x^{3} - x^{2} - x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 6607$ |
$2$ |
$7.55708316564$ |
$389.8217541389911$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.38872615482$ |
| 9.1.81117389.1 |
$x^{9} - x^{8} + x^{7} + x^{6} - x^{5} + 2 x^{4} + x^{3} + x^{2} + x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 59\cdot 113$ |
$3$ |
$7.56467789356$ |
$391.587793476763$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.36429268784$ |
| 9.1.82042081.1 |
$x^{9} - 3 x^{8} + 7 x^{7} - 12 x^{6} + 15 x^{5} - 16 x^{4} + 12 x^{3} - 8 x^{2} + 4 x - 1$ |
$9$ |
[1,4] |
$11\cdot 23^{3}\cdot 613$ |
$3$ |
$7.57421114183$ |
$393.81340759298683$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.31089303171$ |
| 9.1.82334089.1 |
$x^{9} - 2 x^{8} + x^{7} - x^{6} + 3 x^{5} - x^{4} - x^{3} + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 67\cdot 101$ |
$3$ |
$7.57720180133$ |
$394.51362460629923$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.35402539747$ |
| 9.1.82431425.1 |
$x^{9} - 2 x^{8} + 2 x^{7} + x^{6} - 2 x^{5} + 3 x^{3} - 2 x^{2} - x + 1$ |
$9$ |
[1,4] |
$5^{2}\cdot 23^{3}\cdot 271$ |
$3$ |
$7.57819659285$ |
$230.84930231252434$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.40959411571$ |
| 9.1.83319616.1 |
$x^{9} - 4 x^{8} + 9 x^{7} - 15 x^{6} + 17 x^{5} - 14 x^{4} + 8 x^{3} - x^{2} - x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 23^{3}\cdot 107$ |
$3$ |
$7.58722614521$ |
$78.74853273288694$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.34933902572$ |
| 9.1.89611328.1 |
$x^{9} - 2 x^{8} + 2 x^{7} + x^{6} - x^{5} - x^{4} + x^{3} + 2 x^{2} - 3 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 31^{3}\cdot 47$ |
$3$ |
$7.64884533493$ |
$107.96295661012624$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.43102382388$ |
| 9.1.90161381.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 8 x^{6} + 10 x^{5} - 11 x^{4} + 10 x^{3} - 8 x^{2} + 4 x - 1$ |
$9$ |
[1,4] |
$59^{3}\cdot 439$ |
$2$ |
$7.65404784765$ |
$160.93787621315252$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.42329967324$ |
| 9.1.92943713.1 |
$x^{9} - 3 x^{8} + 6 x^{7} - 7 x^{6} + 5 x^{5} - 4 x^{3} + 6 x^{2} - 4 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 7639$ |
$2$ |
$7.67993916346$ |
$419.1622597515191$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.45753700948$ |
| 9.1.92992381.1 |
$x^{9} - 2 x^{8} + 3 x^{7} - 5 x^{6} + 8 x^{5} - 10 x^{4} + 8 x^{3} - 2 x^{2} - x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 7643$ |
$2$ |
$7.68038588583$ |
$419.27198809364785$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.54370715357$ |
| 9.1.93381725.1 |
$x^{9} + x^{7} - 2 x^{6} - x^{5} - x^{4} + 2 x^{2} + 1$ |
$9$ |
[1,4] |
$5^{2}\cdot 23^{3}\cdot 307$ |
$3$ |
$7.68395220233$ |
$187.89624796679684$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.44217944547$ |
| 9.1.94943917.1 |
$x^{9} - 2 x^{8} + x^{7} + x^{6} - 2 x^{5} + x^{4} + x^{3} - x^{2} + 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 3187$ |
$2$ |
$7.69812995541$ |
$314.3199007380856$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.48868541497$ |
| 9.1.94987769.1 |
$x^{9} - 3 x^{8} + 4 x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 3 x^{3} + x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 37\cdot 211$ |
$3$ |
$7.6985249361$ |
$423.7463864152708$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.58115047745$ |
| 9.1.94987769.2 |
$x^{9} - 3 x^{8} + 4 x^{7} - 4 x^{6} + x^{5} + 3 x^{4} - 5 x^{3} + 6 x^{2} - 3 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 37\cdot 211$ |
$3$ |
$7.6985249361$ |
$423.7463864152708$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.54049731523$ |
| 9.1.97208033.1 |
$x^{9} - x^{8} - x^{7} + 3 x^{6} - 5 x^{4} + 8 x^{3} - 7 x^{2} + 4 x - 1$ |
$9$ |
[1,4] |
$13\cdot 31^{3}\cdot 251$ |
$3$ |
$7.71831433654$ |
$318.04559421567217$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.45182171922$ |
| 9.1.103894013.1 |
$x^{9} - x^{8} + x^{7} - 2 x^{6} + 3 x^{5} - x^{4} - 2 x^{3} - 3 x^{2} - 3 x - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 8539$ |
$2$ |
$7.77557080021$ |
$443.1670114076633$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.60369546064$ |
| 9.1.105901568.1 |
$x^{9} - 4 x^{8} + 8 x^{7} - 9 x^{6} + 7 x^{5} - 7 x^{4} + 11 x^{3} - 12 x^{2} + 7 x - 1$ |
$9$ |
[1,4] |
$2^{9}\cdot 17\cdot 23^{3}$ |
$3$ |
$7.79212339147$ |
$94.06019373893551$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.59028179517$ |
| 9.1.107300773.1 |
$x^{9} - x^{8} - 3 x^{7} + 3 x^{6} + 2 x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 3 x + 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 8819$ |
$2$ |
$7.8034958838$ |
$450.37428878656027$ |
|
|
✓ |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.57460709771$ |
| 9.1.108274133.1 |
$x^{9} + x^{7} - x^{6} + 2 x^{5} + 2 x^{3} + 2 x + 1$ |
$9$ |
[1,4] |
$11\cdot 23^{3}\cdot 809$ |
$3$ |
$7.81132969017$ |
$452.41242246428203$ |
|
|
? |
$S_3\wr S_3$ (as 9T31) |
trivial |
$2$ |
$4$ |
$1.59957197922$ |
