| 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 |
| 3.1.243.1 |
$x^{3} - 3$ |
$3$ |
[1,1] |
$-\,3^{5}$ |
$1$ |
$6.24025146916$ |
$7.494148598900439$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.52468140471$ |
| 3.1.3159.2 |
$x^{3} - 9 x - 15$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 13$ |
$2$ |
$14.6729197395$ |
$27.020537039282146$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$7.6916561974$ |
| 3.1.6804.2 |
$x^{3} + 18 x - 12$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 7$ |
$3$ |
$18.949078793$ |
$39.6553069617074$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$23.8299379675$ |
| 3.3.8505.1 |
$x^{3} - 27 x - 51$ |
$3$ |
[3,0] |
$3^{5}\cdot 5\cdot 7$ |
$3$ |
$20.4122763479$ |
$44.3359810174992$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$17.1804852427$ |
| 3.1.8991.1 |
$x^{3} + 27 x - 9$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 37$ |
$2$ |
$20.7939023053$ |
$45.58512629387849$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$5.50528202577$ |
| 3.1.9720.2 |
$x^{3} - 18 x - 48$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 5$ |
$3$ |
$21.3413598269$ |
$47.39715739257004$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$36.8168981134$ |
| 3.3.11421.1 |
$x^{3} - 18 x - 21$ |
$3$ |
[3,0] |
$3^{5}\cdot 47$ |
$2$ |
$22.5199822485$ |
$51.377294318140834$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$33.3588143865$ |
| 3.3.13608.1 |
$x^{3} - 27 x - 30$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{5}\cdot 7$ |
$3$ |
$23.8743432474$ |
$56.08107292531482$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$55.6031987016$ |
| 3.1.14823.2 |
$x^{3} + 9 x - 21$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 61$ |
$2$ |
$24.5647323302$ |
$58.531171665758464$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$11.7469140114$ |
| 3.1.17739.3 |
$x^{3} + 9 x - 102$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 73$ |
$2$ |
$26.0801275603$ |
$64.03003369697147$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$25.2981678936$ |
| 3.1.18468.2 |
$x^{3} - 18 x - 60$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 19$ |
$3$ |
$26.4326043447$ |
$65.33247282096788$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$50.3788690006$ |
| 3.1.21384.1 |
$x^{3} - 27 x - 78$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 11$ |
$3$ |
$27.7563900551$ |
$70.30134538948258$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$43.6773326533$ |
| 3.3.22356.3 |
$x^{3} - 18 x - 6$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 23$ |
$3$ |
$28.170725619$ |
$57.05226386049417$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$37.3485233327$ |
| 3.1.23571.3 |
$x^{3} + 27 x - 24$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 97$ |
$2$ |
$28.6720889929$ |
$73.80880389609993$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$25.7895542707$ |
| 3.1.24300.2 |
$x^{3} - 30$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 5^{2}$ |
$3$ |
$28.9646815382$ |
$34.78475645409113$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.79687983605$ |
| 3.1.24300.4 |
$x^{3} - 90$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 5^{2}$ |
$3$ |
$28.9646815382$ |
$34.78475645409113$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.0723298019$ |
| 3.1.30132.2 |
$x^{3} + 45 x - 66$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 31$ |
$3$ |
$31.1178311258$ |
$83.4513069974208$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$2$ |
$1$ |
$11.3510299373$ |
| 3.1.32319.3 |
$x^{3} + 9 x - 33$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7\cdot 19$ |
$3$ |
$31.8531684417$ |
$86.42673781058376$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$15.1473189016$ |
| 3.1.33048.1 |
$x^{3} + 27 x - 90$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 17$ |
$3$ |
$32.0908874474$ |
$87.39603994602153$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$62.1480292561$ |
| 3.1.35235.2 |
$x^{3} - 18 x - 183$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 29$ |
$3$ |
$32.7837094397$ |
$90.2414991411834$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$47.0000111752$ |
| 3.1.38151.3 |
$x^{3} - 9 x - 39$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 157$ |
$2$ |
$33.6642266419$ |
$93.9014128004314$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$18.087602272$ |
| 3.3.39852.1 |
$x^{3} - 54 x - 132$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 41$ |
$3$ |
$34.1572873984$ |
$95.97192906508565$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$86.6985411852$ |
| 3.1.44712.1 |
$x^{3} - 9 x - 42$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 23$ |
$3$ |
$35.4928901982$ |
$101.65557748063733$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$88.6313146963$ |
| 3.3.45684.1 |
$x^{3} - 54 x - 90$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 47$ |
$3$ |
$35.7482435116$ |
$81.55637104789656$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$25.9928120227$ |
| 3.3.45684.2 |
$x^{3} - 36 x - 12$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 47$ |
$3$ |
$35.7482435116$ |
$81.55637104789656$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$12.3281184559$ |
| 3.1.46899.2 |
$x^{3} - 36 x - 93$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 193$ |
$2$ |
$36.0623918059$ |
$104.11203965883807$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$29.9331897748$ |
| 3.1.47628.1 |
$x^{3} - 252$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 7^{2}$ |
$3$ |
$36.2482837079$ |
$43.531903466499294$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$7.03614617382$ |
| 3.1.47628.4 |
$x^{3} - 84$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 7^{2}$ |
$3$ |
$36.2482837079$ |
$43.531903466499294$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.1202872191$ |
| 3.1.49815.2 |
$x^{3} + 27 x - 252$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 41$ |
$3$ |
$36.7948224442$ |
$107.29987866065967$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$175.274734795$ |
| 3.1.52731.2 |
$x^{3} - 54 x - 159$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7\cdot 31$ |
$3$ |
$37.4991999829$ |
$110.39570244923988$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$39.6462233373$ |
| 3.1.53460.2 |
$x^{3} - 27 x - 186$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 5\cdot 11$ |
$4$ |
$37.6712170693$ |
$111.15618700247103$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$93.2509274509$ |
| 3.3.55161.1 |
$x^{3} - 63 x - 66$ |
$3$ |
[3,0] |
$3^{5}\cdot 227$ |
$2$ |
$38.0665960551$ |
$112.9107335530379$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$167.227382367$ |
| 3.3.58077.1 |
$x^{3} - 36 x - 69$ |
$3$ |
[3,0] |
$3^{5}\cdot 239$ |
$2$ |
$38.7258885729$ |
$115.85672578730134$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$85.2305463193$ |
| 3.1.58563.2 |
$x^{3} + 18 x - 231$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 241$ |
$2$ |
$38.8336106537$ |
$116.3404720490627$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$66.2799023893$ |
| 3.1.61479.1 |
$x^{3} - 9 x - 96$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 11\cdot 23$ |
$3$ |
$39.4677405788$ |
$119.20173067228326$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$41.6258996491$ |
| 3.1.61479.2 |
$x^{3} + 63 x - 141$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 11\cdot 23$ |
$3$ |
$39.4677405788$ |
$119.20173067228326$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.9980450965$ |
| 3.1.61479.3 |
$x^{3} - 27 x - 153$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 11\cdot 23$ |
$3$ |
$39.4677405788$ |
$119.20173067228326$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.78603079106$ |
| 3.3.63180.1 |
$x^{3} - 27 x - 24$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 5\cdot 13$ |
$4$ |
$39.8284318279$ |
$120.83951521677156$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$152.261918882$ |
| 3.1.64395.1 |
$x^{3} + 18 x - 39$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 53$ |
$3$ |
$40.0821229468$ |
$121.99590056201222$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$65.6217725946$ |
| 3.1.65124.1 |
$x^{3} - 63 x - 312$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 67$ |
$3$ |
$40.2328090367$ |
$122.68450001366749$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$36.55244808$ |
| 3.1.65124.2 |
$x^{3} + 9 x - 48$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 67$ |
$3$ |
$40.2328090367$ |
$122.68450001366749$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$19.0147125838$ |
| 3.1.65124.3 |
$x^{3} + 54 x - 252$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 67$ |
$3$ |
$40.2328090367$ |
$122.68450001366749$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$30.1853938223$ |
| 3.3.66825.1 |
$x^{3} - 45 x - 60$ |
$3$ |
[3,0] |
$3^{5}\cdot 5^{2}\cdot 11$ |
$3$ |
$40.5800884349$ |
$72.6772767594366$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$233.789168285$ |
| 3.1.67311.3 |
$x^{3} + 27 x - 84$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 277$ |
$2$ |
$40.6782268786$ |
$124.72749060493918$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$172.323945831$ |
| 3.1.68040.3 |
$x^{3} + 18 x - 96$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 5\cdot 7$ |
$4$ |
$40.8245526957$ |
$125.40109131212692$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$117.486350254$ |
| 3.3.69012.1 |
$x^{3} - 36 x - 66$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 71$ |
$3$ |
$41.0180368786$ |
$100.2393261419734$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$73.3836218053$ |
| 3.3.69741.1 |
$x^{3} - 54 x - 9$ |
$3$ |
[3,0] |
$3^{5}\cdot 7\cdot 41$ |
$3$ |
$41.1619609942$ |
$126.95892857467412$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$97.6052684346$ |
| 3.1.70227.1 |
$x^{3} - 153$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 17^{2}$ |
$2$ |
$41.2573540607$ |
$49.54748116432225$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$8.64189031103$ |
| 3.1.70227.2 |
$x^{3} - 51$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 17^{2}$ |
$2$ |
$41.2573540607$ |
$49.54748116432225$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$19.5948330739$ |
| 3.1.70956.4 |
$x^{3} + 36 x - 60$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 73$ |
$3$ |
$41.3996219247$ |
$101.64134284813179$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$19.6734484296$ |
