| 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 |
| 3.1.676.1 |
$x^{3} - x^{2} - 4 x + 12$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}$ |
$2$ |
$8.77638295533$ |
$11.057549627357744$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.18608135926$ |
| 3.1.9295.1 |
$x^{3} - x^{2} - 30 x + 77$ |
$3$ |
[1,1] |
$-\,5\cdot 11\cdot 13^{2}$ |
$3$ |
$21.0256677827$ |
$41.00249140869786$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.20999355896$ |
| 3.3.13689.2 |
$x^{3} - 39 x - 91$ |
$3$ |
[3,0] |
$3^{4}\cdot 13^{2}$ |
$2$ |
$23.9216192981$ |
$23.921619298064325$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$5.61392117258$ |
| 3.1.14703.2 |
$x^{3} - x^{2} + 22 x + 51$ |
$3$ |
[1,1] |
$-\,3\cdot 13^{2}\cdot 29$ |
$3$ |
$24.498264489$ |
$51.56897838635333$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.44083969241$ |
| 3.1.16055.1 |
$x^{3} - 13 x - 52$ |
$3$ |
[1,1] |
$-\,5\cdot 13^{2}\cdot 19$ |
$3$ |
$25.2272611678$ |
$53.887831087687466$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$20.8030606582$ |
| 3.1.18252.1 |
$x^{3} - 52$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 13^{2}$ |
$3$ |
$26.329148866$ |
$31.619647871494593$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.44093891352$ |
| 3.3.18252.1 |
$x^{3} - 39 x - 78$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 13^{2}$ |
$3$ |
$26.329148866$ |
$39.838259943559656$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$20.5394886609$ |
| 3.1.21463.1 |
$x^{3} - x^{2} - 4 x - 27$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 127$ |
$2$ |
$27.7905286646$ |
$62.30612786417537$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.43855164609$ |
| 3.1.22139.1 |
$x^{3} - x^{2} - 4 x + 116$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 131$ |
$2$ |
$28.0792821033$ |
$63.27972007830352$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.48995029976$ |
| 3.1.23660.2 |
$x^{3} - x^{2} + 9 x + 25$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7\cdot 13^{2}$ |
$4$ |
$28.7081306105$ |
$51.92178177076271$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$8.83826052532$ |
| 3.1.24843.1 |
$x^{3} - 91$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$29.1788393635$ |
$35.04194650073235$ |
|
|
|
$S_3$ (as 3T2) |
$[3, 3]$ |
$2$ |
$1$ |
$5.49260395186$ |
| 3.3.27885.1 |
$x^{3} - x^{2} - 30 x + 12$ |
$3$ |
[3,0] |
$3\cdot 5\cdot 11\cdot 13^{2}$ |
$4$ |
$30.324260325$ |
$71.01839835677107$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$26.8344674616$ |
| 3.1.28392.1 |
$x^{3} - x^{2} + 48 x + 12$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 7\cdot 13^{2}$ |
$4$ |
$30.5069409985$ |
$71.66111189468201$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$28.1442700166$ |
| 3.1.29068.1 |
$x^{3} - x^{2} - 43 x + 129$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 43$ |
$3$ |
$30.7471630229$ |
$57.550591695302664$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.6233495492$ |
| 3.1.30251.1 |
$x^{3} - x^{2} + 9 x - 170$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 179$ |
$2$ |
$31.1587417613$ |
$73.96996565043275$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.4337024042$ |
| 3.1.34476.1 |
$x^{3} - x^{2} - 17 x - 105$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 13^{2}\cdot 17$ |
$4$ |
$32.546599818$ |
$62.675910736966344$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.1041488329$ |
| 3.1.35659.1 |
$x^{3} - x^{2} - 17 x - 40$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 211$ |
$2$ |
$32.9146862737$ |
$80.31009306692427$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$10.4170893049$ |
| 3.1.35828.3 |
$x^{3} + 26 x - 52$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 53$ |
$3$ |
$32.9666022687$ |
$80.50017639333723$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.6571676053$ |
| 3.3.35828.1 |
$x^{3} - x^{2} - 43 x + 25$ |
$3$ |
[3,0] |
$2^{2}\cdot 13^{2}\cdot 53$ |
$3$ |
$32.9666022687$ |
$63.89303234520457$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$17.6107909115$ |
| 3.1.41067.1 |
$x^{3} - 117$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 13^{2}$ |
$2$ |
$34.5009451537$ |
$41.433460023567555$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.8645817881$ |
| 3.1.42419.1 |
$x^{3} - x^{2} - 30 x - 92$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 251$ |
$2$ |
$34.8754758567$ |
$87.59226613139332$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.22915016065$ |
| 3.1.47827.1 |
$x^{3} - x^{2} + 9 x + 38$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 283$ |
$2$ |
$36.2986979273$ |
$93.00838841805972$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.1626499842$ |
| 3.1.50700.1 |
$x^{3} - 260$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 13^{2}$ |
$4$ |
$37.0114403386$ |
$44.448406466929114$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$23.3867938816$ |
| 3.1.52052.1 |
$x^{3} - x^{2} - 43 x + 155$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 11\cdot 13^{2}$ |
$4$ |
$37.3375491271$ |
$97.02960419188524$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.7543454493$ |
| 3.1.58643.1 |
$x^{3} - x^{2} + 22 x - 92$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 347$ |
$2$ |
$38.8512854956$ |
$102.98966344399975$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.1206455676$ |
| 3.1.59995.1 |
$x^{3} - x^{2} + 9 x - 144$ |
$3$ |
[1,1] |
$-\,5\cdot 13^{2}\cdot 71$ |
$3$ |
$39.1475889182$ |
$104.17009927916598$ |
|
|
|
$S_3$ (as 3T2) |
$[15]$ |
$2$ |
$1$ |
$4.30150111531$ |
| 3.3.61009.2 |
$x^{3} - x^{2} - 82 x + 311$ |
$3$ |
[3,0] |
$13^{2}\cdot 19^{2}$ |
$2$ |
$39.366907718$ |
$39.36690771803849$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$7.55764880123$ |
| 3.1.63544.1 |
$x^{3} - x^{2} - 56 x + 272$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13^{2}\cdot 47$ |
$3$ |
$39.9047734776$ |
$107.20692120184714$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$22.1288135483$ |
| 3.3.64389.1 |
$x^{3} - x^{2} - 69 x - 144$ |
$3$ |
[3,0] |
$3\cdot 13^{2}\cdot 127$ |
$3$ |
$40.0808780251$ |
$107.91737908363469$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$33.2194056748$ |
| 3.3.66417.1 |
$x^{3} - x^{2} - 30 x + 51$ |
$3$ |
[3,0] |
$3\cdot 13^{2}\cdot 131$ |
$3$ |
$40.497332548$ |
$109.60369026435812$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$24.297205261$ |
| 3.1.67431.1 |
$x^{3} + 39 x - 117$ |
$3$ |
[1,1] |
$-\,3\cdot 7\cdot 13^{2}\cdot 19$ |
$4$ |
$40.7023858289$ |
$110.4371904079761$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.4071505146$ |
| 3.1.68276.1 |
$x^{3} - x^{2} + 61 x - 261$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 101$ |
$3$ |
$40.8716988671$ |
$111.12699842931698$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$66.0079853379$ |
| 3.1.70811.2 |
$x^{3} - x^{2} - 17 x + 64$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 419$ |
$2$ |
$41.3714023761$ |
$113.17119794371254$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$4.21603262355$ |
| 3.1.70980.1 |
$x^{3} - x^{2} + 9 x - 105$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5\cdot 7\cdot 13^{2}$ |
$5$ |
$41.4042890373$ |
$113.3061666236897$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$51.1956451834$ |
| 3.1.72332.1 |
$x^{3} - 52 x - 390$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 107$ |
$3$ |
$41.6655217463$ |
$90.78361119887941$ |
|
|
|
$S_3$ (as 3T2) |
$[15]$ |
$2$ |
$1$ |
$6.03770570783$ |
| 3.3.73177.1 |
$x^{3} - x^{2} - 56 x - 27$ |
$3$ |
[3,0] |
$13^{2}\cdot 433$ |
$2$ |
$41.8271429212$ |
$115.0463513423183$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$26.4823545828$ |
| 3.1.77571.1 |
$x^{3} + 39 x - 52$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 13^{2}\cdot 17$ |
$3$ |
$42.6481106919$ |
$82.12867684405477$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.8275619165$ |
| 3.1.78923.1 |
$x^{3} + 65 x - 78$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 467$ |
$2$ |
$42.8944590334$ |
$119.4778343005627$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$18.7338448368$ |
| 3.1.79599.1 |
$x^{3} - x^{2} - 4 x - 53$ |
$3$ |
[1,1] |
$-\,3\cdot 13^{2}\cdot 157$ |
$3$ |
$43.0165791486$ |
$119.9884256622871$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$5.25295815604$ |
| 3.3.79768.1 |
$x^{3} - x^{2} - 43 x - 1$ |
$3$ |
[3,0] |
$2^{3}\cdot 13^{2}\cdot 59$ |
$3$ |
$43.0470010676$ |
$120.11573437253992$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$32.5511823084$ |
| 3.1.88387.1 |
$x^{3} + 52 x - 247$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 523$ |
$2$ |
$44.5447095151$ |
$126.43861966113609$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$11.444154004$ |
| 3.3.90584.1 |
$x^{3} - x^{2} - 30 x + 38$ |
$3$ |
[3,0] |
$2^{3}\cdot 13^{2}\cdot 67$ |
$3$ |
$44.9107696846$ |
$128.0003910308021$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$45.2892054805$ |
| 3.1.93795.1 |
$x^{3} - x^{2} + 35 x - 170$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 13^{2}\cdot 37$ |
$4$ |
$45.4352821405$ |
$130.24929854669185$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$39.232827243$ |
| 3.1.93964.2 |
$x^{3} - 26 x - 78$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13^{2}\cdot 139$ |
$3$ |
$45.4625542252$ |
$103.47202902825593$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.81928976949$ |
| 3.3.95992.1 |
$x^{3} - x^{2} - 56 x - 92$ |
$3$ |
[3,0] |
$2^{3}\cdot 13^{2}\cdot 71$ |
$3$ |
$45.7872977621$ |
$131.7659111232115$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$37.1486799056$ |
| 3.1.97175.1 |
$x^{3} - x^{2} + 22 x - 53$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 13^{2}\cdot 23$ |
$3$ |
$45.9746236847$ |
$77.53054242742431$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.06727042445$ |
| 3.1.98696.1 |
$x^{3} - x^{2} + 48 x + 324$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13^{2}\cdot 73$ |
$3$ |
$46.2132505735$ |
$133.60888050266715$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$52.8561238401$ |
| 3.1.101231.1 |
$x^{3} - 13 x - 429$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 599$ |
$2$ |
$46.6055719789$ |
$135.31386925692996$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$8.13972776953$ |
| 3.1.103935.1 |
$x^{3} - x^{2} - 30 x + 207$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 13^{2}\cdot 41$ |
$4$ |
$47.0168944848$ |
$137.10915661737351$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$16.8849789095$ |
| 3.1.112723.1 |
$x^{3} - x^{2} + 22 x + 116$ |
$3$ |
[1,1] |
$-\,13^{2}\cdot 23\cdot 29$ |
$3$ |
$48.3063450864$ |
$142.788035483463$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$13.0993813047$ |
