| 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 |
| 3.3.49.1 |
$x^{3} - x^{2} - 2 x + 1$ |
$3$ |
[3,0] |
$7^{2}$ |
$1$ |
$3.65930571002$ |
$3.6593057100229713$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$0.525454682123$ |
| 3.3.81.1 |
$x^{3} - 3 x - 1$ |
$3$ |
[3,0] |
$3^{4}$ |
$1$ |
$4.32674871092$ |
$4.326748710922225$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$0.849287450646$ |
| 3.3.148.1 |
$x^{3} - x^{2} - 3 x + 1$ |
$3$ |
[3,0] |
$2^{2}\cdot 37$ |
$2$ |
$5.28957247269$ |
$9.65578363946814$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$1.66233652077$ |
| 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 |
$2$ |
$2$ |
$1.36504986759$ |
| 3.3.229.1 |
$x^{3} - 4 x - 1$ |
$3$ |
[3,0] |
$229$ |
$1$ |
$6.11803317264$ |
$15.132745950421556$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$2.35545459084$ |
| 3.3.257.1 |
$x^{3} - x^{2} - 4 x + 3$ |
$3$ |
[3,0] |
$257$ |
$1$ |
$6.35786117973$ |
$16.0312195418814$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$1.97459387078$ |
| 3.3.316.1 |
$x^{3} - x^{2} - 4 x + 2$ |
$3$ |
[3,0] |
$2^{2}\cdot 79$ |
$2$ |
$6.81128460769$ |
$17.776388834631177$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.91345849211$ |
| 3.3.321.1 |
$x^{3} - x^{2} - 4 x + 1$ |
$3$ |
[3,0] |
$3\cdot 107$ |
$2$ |
$6.84702127757$ |
$17.916472867168917$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$2.56925968013$ |
| 3.3.361.1 |
$x^{3} - x^{2} - 6 x + 7$ |
$3$ |
[3,0] |
$19^{2}$ |
$1$ |
$7.1203673589$ |
$7.120367358901993$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$1.95215669651$ |
| 3.3.404.1 |
$x^{3} - x^{2} - 5 x - 1$ |
$3$ |
[3,0] |
$2^{2}\cdot 101$ |
$2$ |
$7.39254179171$ |
$15.953183133116863$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.75987912189$ |
| 3.3.469.1 |
$x^{3} - x^{2} - 5 x + 4$ |
$3$ |
[3,0] |
$7\cdot 67$ |
$2$ |
$7.76946201167$ |
$21.656407827707714$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.85282661562$ |
| 3.3.473.1 |
$x^{3} - 5 x - 1$ |
$3$ |
[3,0] |
$11\cdot 43$ |
$2$ |
$7.79148753564$ |
$21.748563170931547$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$2.84322939957$ |
| 3.3.564.1 |
$x^{3} - x^{2} - 5 x + 3$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 47$ |
$3$ |
$8.26214922567$ |
$18.849343120394256$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.40274790998$ |
| 3.3.568.1 |
$x^{3} - x^{2} - 6 x - 2$ |
$3$ |
[3,0] |
$2^{3}\cdot 71$ |
$2$ |
$8.28163549885$ |
$23.83275057562597$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.08739090714$ |
| 3.3.621.1 |
$x^{3} - 6 x - 3$ |
$3$ |
[3,0] |
$3^{3}\cdot 23$ |
$2$ |
$8.53160093955$ |
$17.278473921432806$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.39970280308$ |
| 3.3.697.1 |
$x^{3} - 7 x - 5$ |
$3$ |
[3,0] |
$17\cdot 41$ |
$2$ |
$8.86633751079$ |
$26.40075756488817$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$2.71184965988$ |
| 3.3.733.1 |
$x^{3} - x^{2} - 7 x + 8$ |
$3$ |
[3,0] |
$733$ |
$1$ |
$9.01643088997$ |
$27.073972741361768$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.30908411022$ |
| 3.3.756.1 |
$x^{3} - 6 x - 2$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 7$ |
$3$ |
$9.10976691563$ |
$15.13133155729692$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.69171840461$ |
| 3.3.761.1 |
$x^{3} - x^{2} - 6 x - 1$ |
$3$ |
[3,0] |
$761$ |
$1$ |
$9.12980606272$ |
$27.586228448267445$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.52628052045$ |
| 3.3.785.1 |
$x^{3} - x^{2} - 6 x + 5$ |
$3$ |
[3,0] |
$5\cdot 157$ |
$2$ |
$9.22479135747$ |
$28.0178514522438$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$4.09826602583$ |
| 3.3.788.1 |
$x^{3} - x^{2} - 7 x - 3$ |
$3$ |
[3,0] |
$2^{2}\cdot 197$ |
$2$ |
$9.2365277459$ |
$22.280235493786417$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.98654600643$ |
| 3.3.837.1 |
$x^{3} - 6 x - 1$ |
$3$ |
[3,0] |
$3^{3}\cdot 31$ |
$2$ |
$9.42414195717$ |
$20.05960194310363$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.80136952587$ |
| 3.3.892.1 |
$x^{3} - x^{2} - 8 x + 10$ |
$3$ |
[3,0] |
$2^{2}\cdot 223$ |
$2$ |
$9.62620157035$ |
$29.866369046136157$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.32319936299$ |
| 3.3.940.1 |
$x^{3} - 7 x - 4$ |
$3$ |
[3,0] |
$2^{2}\cdot 5\cdot 47$ |
$3$ |
$9.79586108716$ |
$30.659419433511783$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.90818681934$ |
| 3.3.961.1 |
$x^{3} - x^{2} - 10 x + 8$ |
$3$ |
[3,0] |
$31^{2}$ |
$1$ |
$9.86827240322$ |
$9.868272403218974$ |
|
✓ |
|
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$12.1957819126$ |
| 3.3.985.1 |
$x^{3} - x^{2} - 6 x + 1$ |
$3$ |
[3,0] |
$5\cdot 197$ |
$2$ |
$9.9497478956$ |
$31.38470965295043$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.72417366067$ |
| 3.3.993.1 |
$x^{3} - x^{2} - 6 x + 3$ |
$3$ |
[3,0] |
$3\cdot 331$ |
$2$ |
$9.9766120095$ |
$31.51190251317746$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$5.5546439553$ |
| 3.3.1016.1 |
$x^{3} - x^{2} - 6 x + 2$ |
$3$ |
[3,0] |
$2^{3}\cdot 127$ |
$2$ |
$10.0530513906$ |
$31.874754901018456$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$10.1289270726$ |
| 3.3.1076.1 |
$x^{3} - 8 x - 6$ |
$3$ |
[3,0] |
$2^{2}\cdot 269$ |
$2$ |
$10.2471735217$ |
$26.035313035249676$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.93232675724$ |
| 3.3.1101.1 |
$x^{3} - x^{2} - 9 x + 12$ |
$3$ |
[3,0] |
$3\cdot 367$ |
$2$ |
$10.3259283287$ |
$33.18132004607411$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$9.18395840633$ |
| 3.3.1129.1 |
$x^{3} - 7 x - 3$ |
$3$ |
[3,0] |
$1129$ |
$1$ |
$10.4127309576$ |
$33.60059523282288$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.72755301312$ |
| 3.3.1229.1 |
$x^{3} - x^{2} - 7 x + 6$ |
$3$ |
[3,0] |
$1229$ |
$1$ |
$10.7115082748$ |
$35.05709628591621$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.2319189887$ |
| 3.3.1257.1 |
$x^{3} - x^{2} - 8 x + 9$ |
$3$ |
[3,0] |
$3\cdot 419$ |
$2$ |
$10.7922440886$ |
$35.45419580247167$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.19689047505$ |
| 3.3.1300.1 |
$x^{3} - 10 x - 10$ |
$3$ |
[3,0] |
$2^{2}\cdot 5^{2}\cdot 13$ |
$3$ |
$10.9139288306$ |
$16.735486539211966$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.55000546582$ |
| 3.3.1304.1 |
$x^{3} - 11 x - 2$ |
$3$ |
[3,0] |
$2^{3}\cdot 163$ |
$2$ |
$10.9251111426$ |
$36.11094017053558$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$11.9265379008$ |
| 3.3.1345.1 |
$x^{3} - 7 x - 1$ |
$3$ |
[3,0] |
$5\cdot 269$ |
$2$ |
$11.0384330549$ |
$36.6742416417845$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$4.92253081641$ |
| 3.3.1369.1 |
$x^{3} - x^{2} - 12 x - 11$ |
$3$ |
[3,0] |
$37^{2}$ |
$1$ |
$11.1037024686$ |
$11.103702468586786$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$3.12623019091$ |
| 3.3.1373.1 |
$x^{3} - 8 x - 5$ |
$3$ |
[3,0] |
$1373$ |
$1$ |
$11.1145063698$ |
$37.05401462729781$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$9.42256505342$ |
| 3.3.1384.1 |
$x^{3} - x^{2} - 10 x + 14$ |
$3$ |
[3,0] |
$2^{3}\cdot 173$ |
$2$ |
$11.1441093111$ |
$37.20215047547655$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$10.3825345235$ |
| 3.3.1396.1 |
$x^{3} - x^{2} - 7 x + 5$ |
$3$ |
[3,0] |
$2^{2}\cdot 349$ |
$2$ |
$11.1762250774$ |
$29.65509893469623$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.14646414913$ |
| 3.3.1425.1 |
$x^{3} - x^{2} - 8 x - 3$ |
$3$ |
[3,0] |
$3\cdot 5^{2}\cdot 19$ |
$3$ |
$11.2530855734$ |
$22.07584980930199$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.6762639812$ |
| 3.3.1436.1 |
$x^{3} - 11 x - 12$ |
$3$ |
[3,0] |
$2^{2}\cdot 359$ |
$2$ |
$11.2819666943$ |
$37.89459064299283$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$12.7000456752$ |
| 3.3.1489.1 |
$x^{3} - x^{2} - 10 x - 7$ |
$3$ |
[3,0] |
$1489$ |
$1$ |
$11.4190918416$ |
$38.58756276314948$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$3.36064354605$ |
| 3.3.1492.1 |
$x^{3} - x^{2} - 9 x - 5$ |
$3$ |
[3,0] |
$2^{2}\cdot 373$ |
$2$ |
$11.4267556639$ |
$30.657806562465872$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$7.64636835507$ |
| 3.3.1509.1 |
$x^{3} - x^{2} - 7 x + 4$ |
$3$ |
[3,0] |
$3\cdot 503$ |
$2$ |
$11.4699910738$ |
$38.84584919911006$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$11.2956582948$ |
| 3.3.1524.1 |
$x^{3} - x^{2} - 7 x + 1$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 127$ |
$3$ |
$11.507871108$ |
$30.984832418780215$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$10.4495665174$ |
| 3.3.1556.1 |
$x^{3} - x^{2} - 9 x + 11$ |
$3$ |
[3,0] |
$2^{2}\cdot 389$ |
$2$ |
$11.5878588784$ |
$31.30844258052788$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.37584491331$ |
| 3.3.1573.1 |
$x^{3} - x^{2} - 7 x + 2$ |
$3$ |
[3,0] |
$11^{2}\cdot 13$ |
$2$ |
$11.6299069738$ |
$17.833371889561775$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$8.44494130232$ |
| 3.3.1593.1 |
$x^{3} - 9 x - 7$ |
$3$ |
[3,0] |
$3^{3}\cdot 59$ |
$2$ |
$11.6789892476$ |
$27.67371536012528$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$6.33079430444$ |
| 3.3.1620.1 |
$x^{3} - 12 x - 14$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 5$ |
$3$ |
$11.7446029235$ |
$15.357953166968596$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$10.1679428335$ |
