| 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 |
| 3.3.169.1 |
$x^{3} - x^{2} - 4 x - 1$ |
$3$ |
[3,0] |
$13^{2}$ |
$1$ |
$5.52877481368$ |
$5.528774813678872$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$1.36504986759$ |
| 3.1.4563.1 |
$x^{3} - 13$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 13^{2}$ |
$2$ |
$16.586324441$ |
$19.919129971779828$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.6420579792$ |
| 3.3.8281.1 |
$x^{3} - x^{2} - 30 x + 64$ |
$3$ |
[3,0] |
$7^{2}\cdot 13^{2}$ |
$2$ |
$20.2314772451$ |
$20.23147724512629$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$15.6222994475$ |
| 3.3.8281.2 |
$x^{3} - x^{2} - 30 x - 27$ |
$3$ |
[3,0] |
$7^{2}\cdot 13^{2}$ |
$2$ |
$20.2314772451$ |
$20.23147724512629$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$7.94957796855$ |
| 3.1.8619.1 |
$x^{3} - x^{2} + 9 x + 12$ |
$3$ |
[1,1] |
$-\,3\cdot 13^{2}\cdot 17$ |
$3$ |
$20.5030731066$ |
$39.483349629417994$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$2.65920416875$ |
| 3.1.11492.1 |
$x^{3} - x^{2} - 4 x - 40$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 17$ |
$3$ |
$22.5665519256$ |
$45.59144507410518$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$8.45168933011$ |
| 3.1.12675.1 |
$x^{3} - x^{2} + 22 x + 12$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$23.3157463848$ |
$28.000741470983698$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.4511172909$ |
| 3.1.13351.1 |
$x^{3} + 13 x - 13$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 79$ |
$2$ |
$23.7230904825$ |
$49.14082543353559$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.7609143894$ |
| 3.1.14703.3 |
$x^{3} - x^{2} - 4 x - 92$ |
$3$ |
[1,1] |
$-\,3\cdot 13^{2}\cdot 29$ |
$3$ |
$24.498264489$ |
$51.56897838635333$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$28.3557998473$ |
| 3.1.14872.1 |
$x^{3} - x^{2} + 22 x - 66$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 11\cdot 13^{2}$ |
$3$ |
$24.5917702217$ |
$51.86450503718846$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$4.89164726552$ |
| 3.3.19604.1 |
$x^{3} - x^{2} - 17 x - 1$ |
$3$ |
[3,0] |
$2^{2}\cdot 13^{2}\cdot 29$ |
$3$ |
$26.9638290223$ |
$47.26226862497353$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$13.4761273974$ |
| 3.1.20280.1 |
$x^{3} - x^{2} + 9 x + 51$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 5\cdot 13^{2}$ |
$4$ |
$27.2702624035$ |
$60.5646936163668$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$24.3758575064$ |
| 3.1.23660.1 |
$x^{3} - x^{2} + 35 x - 53$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7\cdot 13^{2}$ |
$4$ |
$28.7081306105$ |
$51.92178177076271$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.2416680138$ |
| 3.1.26871.1 |
$x^{3} + 39 x - 13$ |
$3$ |
[1,1] |
$-\,3\cdot 13^{2}\cdot 53$ |
$3$ |
$29.9521459291$ |
$69.7151977657584$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.86927299534$ |
| 3.1.29068.2 |
$x^{3} - x^{2} - 17 x + 77$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 43$ |
$3$ |
$30.7471630229$ |
$57.550591695302664$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.8762403139$ |
| 3.1.35659.2 |
$x^{3} - x^{2} + 35 x + 64$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 211$ |
$2$ |
$32.9146862737$ |
$80.31009306692427$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.9587334614$ |
| 3.1.35828.1 |
$x^{3} - x^{2} - 4 x + 220$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 53$ |
$3$ |
$32.9666022687$ |
$80.50017639333723$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$38.8838223005$ |
| 3.1.39715.1 |
$x^{3} - x^{2} + 9 x - 40$ |
$3$ |
[1,1] |
$-\,5\cdot 13^{2}\cdot 47$ |
$3$ |
$34.1181014022$ |
$84.75451298300825$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$19.1529531475$ |
| 3.1.41912.1 |
$x^{3} - x^{2} + 22 x - 14$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13^{2}\cdot 31$ |
$3$ |
$34.7359724622$ |
$87.06723283309124$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$9.98566593579$ |
| 3.1.43771.1 |
$x^{3} - 26 x - 65$ |
$3$ |
[1,1] |
$-\,7\cdot 13^{2}\cdot 37$ |
$3$ |
$35.2421305975$ |
$88.9772099672483$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$7.92948134015$ |
| 3.1.44447.1 |
$x^{3} - x^{2} + 22 x + 64$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 263$ |
$2$ |
$35.4226312138$ |
$89.66166013027681$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$9.61253307701$ |
| 3.3.44616.1 |
$x^{3} - x^{2} - 56 x + 12$ |
$3$ |
[3,0] |
$2^{3}\cdot 3\cdot 11\cdot 13^{2}$ |
$4$ |
$35.4674700354$ |
$89.83195783382237$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$41.3273038491$ |
| 3.3.46644.1 |
$x^{3} - x^{2} - 69 x - 183$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 13^{2}\cdot 23$ |
$4$ |
$35.9969133156$ |
$72.90211208684438$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$21.2997378031$ |
| 3.1.47827.2 |
$x^{3} - x^{2} - 30 x + 116$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 283$ |
$2$ |
$36.2986979273$ |
$93.00838841805972$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$6.18190557627$ |
| 3.1.54756.1 |
$x^{3} - 39 x - 104$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 13^{2}$ |
$3$ |
$37.9732036385$ |
$47.84323859612865$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$11.7301072347$ |
| 3.1.55432.1 |
$x^{3} - 26 x - 104$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13^{2}\cdot 41$ |
$3$ |
$38.1288332614$ |
$100.13037055979224$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$12.8575094098$ |
| 3.3.64220.1 |
$x^{3} - x^{2} - 56 x + 90$ |
$3$ |
[3,0] |
$2^{2}\cdot 5\cdot 13^{2}\cdot 19$ |
$4$ |
$40.045780916$ |
$107.77566217537493$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$48.0417795491$ |
| 3.3.65741.1 |
$x^{3} - 26 x - 13$ |
$3$ |
[3,0] |
$13^{2}\cdot 389$ |
$2$ |
$40.3594682213$ |
$109.04448411452947$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$21.9487032955$ |
| 3.1.66079.1 |
$x^{3} - x^{2} - 4 x + 51$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 17\cdot 23$ |
$3$ |
$40.4285179166$ |
$109.32444473988701$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.52058642487$ |
| 3.1.70135.1 |
$x^{3} - x^{2} + 74 x + 51$ |
$3$ |
[1,1] |
$-\,5\cdot 13^{2}\cdot 83$ |
$3$ |
$41.2393299614$ |
$112.6297058517578$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.9909547031$ |
| 3.1.70811.1 |
$x^{3} - 13 x - 104$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 419$ |
$2$ |
$41.3714023761$ |
$113.17119794371254$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.825624507$ |
| 3.1.72332.3 |
$x^{3} - x^{2} - 17 x - 53$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 107$ |
$3$ |
$41.6655217463$ |
$90.78361119887941$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.7053210629$ |
| 3.1.74867.1 |
$x^{3} + 26 x - 13$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 443$ |
$2$ |
$42.1466903943$ |
$116.36724825561461$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$4.67256751695$ |
| 3.1.76388.1 |
$x^{3} - x^{2} + 9 x + 103$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 113$ |
$3$ |
$42.4301968348$ |
$117.54336487036251$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$7.26753662843$ |
| 3.1.81796.2 |
$x^{3} - x^{2} + 48 x + 90$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 11^{2}\cdot 13^{2}$ |
$3$ |
$43.4087575325$ |
$54.69160736497349$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$47.983113794$ |
| 3.1.86359.1 |
$x^{3} - x^{2} - 30 x - 391$ |
$3$ |
[1,1] |
$-\,7\cdot 13^{2}\cdot 73$ |
$3$ |
$44.2013840397$ |
$124.97966366785035$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.7154839551$ |
| 3.1.88556.1 |
$x^{3} - x^{2} - 17 x - 339$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 131$ |
$3$ |
$44.5730819492$ |
$100.45029422055221$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$23.8327184713$ |
| 3.1.89908.1 |
$x^{3} - x^{2} - 56 x + 350$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 13^{2}\cdot 19$ |
$4$ |
$44.7987722878$ |
$127.52188322118192$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$42.1280597099$ |
| 3.3.89908.1 |
$x^{3} - x^{2} - 43 x - 79$ |
$3$ |
[3,0] |
$2^{2}\cdot 7\cdot 13^{2}\cdot 19$ |
$4$ |
$44.7987722878$ |
$101.21418578713504$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$22.1245211384$ |
| 3.1.90584.1 |
$x^{3} + 26 x - 104$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13^{2}\cdot 67$ |
$3$ |
$44.9107696846$ |
$128.0003910308021$ |
|
|
|
$S_3$ (as 3T2) |
$[18]$ |
$2$ |
$1$ |
$3.96707922147$ |
| 3.1.93964.3 |
$x^{3} - x^{2} - 69 x - 261$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 139$ |
$3$ |
$45.4625542252$ |
$103.47202902825593$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$28.3822115736$ |
| 3.3.95992.2 |
$x^{3} - 91 x - 234$ |
$3$ |
[3,0] |
$2^{3}\cdot 13^{2}\cdot 71$ |
$3$ |
$45.7872977621$ |
$131.7659111232115$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$2$ |
$43.9083835272$ |
| 3.1.96499.1 |
$x^{3} - x^{2} + 35 x - 300$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 571$ |
$2$ |
$45.8677676952$ |
$132.1134262175922$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$33.3618316235$ |
| 3.1.97175.2 |
$x^{3} - x^{2} + 22 x - 183$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 13^{2}\cdot 23$ |
$3$ |
$45.9746236847$ |
$77.53054242742431$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$7.26749231215$ |
| 3.1.99372.1 |
$x^{3} - x^{2} + 61 x - 27$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 13^{2}$ |
$4$ |
$46.3185203008$ |
$55.6256227382759$ |
|
|
|
$S_3$ (as 3T2) |
$[3, 3]$ |
$2$ |
$1$ |
$8.50045374333$ |
| 3.1.105287.1 |
$x^{3} - 13 x - 65$ |
$3$ |
[1,1] |
$-\,7\cdot 13^{2}\cdot 89$ |
$3$ |
$47.2198841339$ |
$137.9980421449899$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.92073777311$ |
| 3.3.109681.1 |
$x^{3} - x^{2} - 56 x - 131$ |
$3$ |
[3,0] |
$11\cdot 13^{2}\cdot 59$ |
$3$ |
$47.8678366666$ |
$140.8481833759315$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$10.0757283984$ |
| 3.1.110019.1 |
$x^{3} - x^{2} + 9 x - 66$ |
$3$ |
[1,1] |
$-\,3\cdot 7\cdot 13^{2}\cdot 31$ |
$4$ |
$47.9169571081$ |
$141.06503982979189$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$12.609635958$ |
| 3.3.110357.1 |
$x^{3} - 65 x - 156$ |
$3$ |
[3,0] |
$13^{2}\cdot 653$ |
$2$ |
$47.9659770472$ |
$141.28156342588198$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$41.4242694222$ |
| 3.1.114075.1 |
$x^{3} - 65$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$48.4987068773$ |
$58.24388936725177$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3, 6]$ |
$2$ |
$1$ |
$3.87637797602$ |
