| 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 |
| 3.1.23.1 |
$x^{3} - x^{2} + 1$ |
$3$ |
[1,1] |
$-\,23$ |
$1$ |
$2.84386697985$ |
$4.795831523312719$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$0.281199574323$ |
| 3.1.31.1 |
$x^{3} + x - 1$ |
$3$ |
[1,1] |
$-\,31$ |
$1$ |
$3.14138065239$ |
$5.5677643628300215$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$0.38224508584$ |
| 3.1.44.1 |
$x^{3} - x^{2} + x + 1$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 11$ |
$2$ |
$3.53034833533$ |
$5.264813681193971$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$0.609377863436$ |
| 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 |
$2$ |
$2$ |
$0.525454682123$ |
| 3.1.59.1 |
$x^{3} + 2 x - 1$ |
$3$ |
[1,1] |
$-\,59$ |
$1$ |
$3.89299641587$ |
$7.681145747868608$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$0.790985720639$ |
| 3.1.76.1 |
$x^{3} - 2 x - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19$ |
$2$ |
$4.23582358425$ |
$6.919320768399539$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.01859181978$ |
| 3.3.81.1 |
$x^{3} - 3 x - 1$ |
$3$ |
[3,0] |
$3^{4}$ |
$1$ |
$4.32674871092$ |
$4.326748710922225$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$0.849287450646$ |
| 3.1.83.1 |
$x^{3} - x^{2} + x - 2$ |
$3$ |
[1,1] |
$-\,83$ |
$1$ |
$4.36207067145$ |
$9.1104335791443$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.04069259944$ |
| 3.1.87.1 |
$x^{3} - x^{2} + 2 x + 1$ |
$3$ |
[1,1] |
$-\,3\cdot 29$ |
$2$ |
$4.43104762169$ |
$9.327379053088816$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$0.934844845546$ |
| 3.1.104.1 |
$x^{3} - x - 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 13$ |
$2$ |
$4.70266937544$ |
$10.198039027185569$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.57608295323$ |
| 3.1.107.1 |
$x^{3} - x^{2} + 3 x - 2$ |
$3$ |
[1,1] |
$-\,107$ |
$1$ |
$4.74745939852$ |
$10.344080432788601$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.25605672147$ |
| 3.1.108.1 |
$x^{3} - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}$ |
$2$ |
$4.7622031559$ |
$5.71910575798162$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.34737734833$ |
| 3.1.116.1 |
$x^{3} - x^{2} - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 29$ |
$2$ |
$4.87699896107$ |
$10.770329614269007$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.71752979598$ |
| 3.1.135.1 |
$x^{3} + 3 x - 1$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5$ |
$2$ |
$5.12992784003$ |
$8.05613000539548$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.13262826357$ |
| 3.1.139.1 |
$x^{3} - x^{2} + x + 2$ |
$3$ |
[1,1] |
$-\,139$ |
$1$ |
$5.18010146738$ |
$11.789826122551595$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.66355473537$ |
| 3.1.140.1 |
$x^{3} + 2 x - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7$ |
$3$ |
$5.19249410185$ |
$9.391191271220128$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.47367088284$ |
| 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 |
$2$ |
$2$ |
$1.66233652077$ |
| 3.1.152.1 |
$x^{3} - x^{2} - 2 x - 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19$ |
$2$ |
$5.33680329744$ |
$12.328828005937952$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.13064558596$ |
| 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 |
$2$ |
$2$ |
$1.36504986759$ |
| 3.1.172.1 |
$x^{3} - x^{2} - x + 3$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 43$ |
$2$ |
$5.56129776652$ |
$10.409284811693793$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.88195290962$ |
| 3.1.175.1 |
$x^{3} - x^{2} + 2 x - 3$ |
$3$ |
[1,1] |
$-\,5^{2}\cdot 7$ |
$2$ |
$5.59344471041$ |
$7.736223764452809$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.28850651272$ |
| 3.1.199.1 |
$x^{3} - x^{2} + 4 x - 1$ |
$3$ |
[1,1] |
$-\,199$ |
$1$ |
$5.83827246081$ |
$14.106735979665885$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.33665777698$ |
| 3.1.200.1 |
$x^{3} - x^{2} + 2 x + 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}$ |
$2$ |
$5.84803547643$ |
$8.270371084000274$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.60439940759$ |
| 3.1.204.1 |
$x^{3} - x^{2} + x - 3$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 17$ |
$3$ |
$5.88676531688$ |
$11.336311000024526$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.35464367875$ |
| 3.1.211.1 |
$x^{3} - 2 x - 3$ |
$3$ |
[1,1] |
$-\,211$ |
$1$ |
$5.95334181314$ |
$14.52583904633395$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.2376328728$ |
| 3.1.212.1 |
$x^{3} - x^{2} + 4 x - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 53$ |
$2$ |
$5.96273195774$ |
$14.560219778561036$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.71275620908$ |
| 3.1.216.1 |
$x^{3} + 3 x - 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}$ |
$2$ |
$6.0$ |
$10.190287977389717$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.02357707871$ |
| 3.3.229.1 |
$x^{3} - 4 x - 1$ |
$3$ |
[3,0] |
$229$ |
$1$ |
$6.11803317264$ |
$15.132745950421556$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$2.35545459084$ |
| 3.1.231.1 |
$x^{3} - x^{2} + 3$ |
$3$ |
[1,1] |
$-\,3\cdot 7\cdot 11$ |
$3$ |
$6.13579243966$ |
$15.198684153570664$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.74549013515$ |
| 3.1.239.1 |
$x^{3} - x - 3$ |
$3$ |
[1,1] |
$-\,239$ |
$1$ |
$6.2058217949$ |
$15.459624833740307$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.09654202363$ |
| 3.1.243.1 |
$x^{3} - 3$ |
$3$ |
[1,1] |
$-\,3^{5}$ |
$1$ |
$6.24025146916$ |
$7.494148598900439$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.52468140471$ |
| 3.1.244.1 |
$x^{3} + x - 6$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 61$ |
$2$ |
$6.24879976953$ |
$15.620499351813308$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.30267551049$ |
| 3.1.247.1 |
$x^{3} + x - 3$ |
$3$ |
[1,1] |
$-\,13\cdot 19$ |
$2$ |
$6.27430535741$ |
$15.716233645501712$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.54453228949$ |
| 3.1.255.1 |
$x^{3} - x^{2} - 3$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 17$ |
$3$ |
$6.34132570538$ |
$15.968719422671311$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.99294483445$ |
| 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 |
$2$ |
$2$ |
$1.97459387078$ |
| 3.1.268.1 |
$x^{3} - x^{2} - 3 x + 5$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 67$ |
$2$ |
$6.44730572727$ |
$12.993437600801144$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.52123333635$ |
| 3.1.283.1 |
$x^{3} + 4 x - 1$ |
$3$ |
[1,1] |
$-\,283$ |
$1$ |
$6.56541442735$ |
$16.822603841260722$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$1.40134232731$ |
| 3.1.300.1 |
$x^{3} - x^{2} - 3 x - 3$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}$ |
$3$ |
$6.69432950082$ |
$8.039467687661697$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.14854957566$ |
| 3.1.307.1 |
$x^{3} - x^{2} + 3 x + 2$ |
$3$ |
[1,1] |
$-\,307$ |
$1$ |
$6.74599671171$ |
$17.52141546793523$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.9581482587$ |
| 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 |
$2$ |
$2$ |
$2.56925968013$ |
| 3.1.324.1 |
$x^{3} - 3 x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}$ |
$2$ |
$6.86828545532$ |
$8.65349742184445$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.04764172645$ |
| 3.1.327.1 |
$x^{3} - x^{2} - 2 x - 3$ |
$3$ |
[1,1] |
$-\,3\cdot 109$ |
$2$ |
$6.88941877452$ |
$18.083141320025124$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.1985916392$ |
| 3.1.331.1 |
$x^{3} - x^{2} + 3 x - 4$ |
$3$ |
[1,1] |
$-\,331$ |
$1$ |
$6.91739641661$ |
$18.193405398660254$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$1.50285283332$ |
| 3.1.335.1 |
$x^{3} - x^{2} + 4 x + 1$ |
$3$ |
[1,1] |
$-\,5\cdot 67$ |
$2$ |
$6.94514955803$ |
$18.303005217723125$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.45573302761$ |
| 3.1.339.1 |
$x^{3} - x^{2} - x + 4$ |
$3$ |
[1,1] |
$-\,3\cdot 113$ |
$2$ |
$6.97268264894$ |
$18.411952639521967$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.54626923722$ |
| 3.1.351.1 |
$x^{3} + 3 x - 3$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 13$ |
$2$ |
$7.05400406316$ |
$12.99011931146003$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.70227535834$ |
| 3.1.356.1 |
$x^{3} - x^{2} + x + 7$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 89$ |
$2$ |
$7.0873410615$ |
$18.867962264113206$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.75521003542$ |
| 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 |
$2$ |
$2$ |
$1.95215669651$ |
| 3.1.364.1 |
$x^{3} + 4 x - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 13$ |
$3$ |
$7.14003698192$ |
$15.142840918429636$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.93617392275$ |
