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 |
$2$ |
$1$ |
$0.609377863436$ |
3.1.59.1 |
$x^{3} + 2 x - 1$ |
$3$ |
[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 |
$2$ |
$1$ |
$1.01859181978$ |
3.1.83.1 |
$x^{3} - x^{2} + x - 2$ |
$3$ |
[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 |
$2$ |
$1$ |
$1.47367088284$ |
3.1.152.1 |
$x^{3} - x^{2} - 2 x - 2$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19$ |
$2$ |
$5.33680329744$ |
$12.328828005937952$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.13064558596$ |
3.1.172.1 |
$x^{3} - x^{2} - x + 3$ |
$3$ |
[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 |
$2$ |
$1$ |
$3.02357707871$ |
3.1.231.1 |
$x^{3} - x^{2} + 3$ |
$3$ |
[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 |
$2$ |
$1$ |
$1.99294483445$ |
3.1.268.1 |
$x^{3} - x^{2} - 3 x + 5$ |
$3$ |
[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 |
$2$ |
$1$ |
$2.9581482587$ |
3.1.324.1 |
$x^{3} - 3 x - 4$ |
$3$ |
[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 |
$2$ |
$1$ |
$3.75521003542$ |
3.1.364.1 |
$x^{3} + 4 x - 2$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 13$ |
$3$ |
$7.14003698192$ |
$15.142840918429636$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.93617392275$ |
3.1.367.1 |
$x^{3} - x^{2} + 2 x + 3$ |
$3$ |
[1,1] |
$-\,367$ |
$1$ |
$7.15959882483$ |
$19.157244060668017$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$1.85619737398$ |
3.1.379.1 |
$x^{3} - x^{2} + x - 4$ |
$3$ |
[1,1] |
$-\,379$ |
$1$ |
$7.2367972159$ |
$19.467922333931785$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.27262528009$ |
3.1.411.1 |
$x^{3} - x^{2} + 5 x - 2$ |
$3$ |
[1,1] |
$-\,3\cdot 137$ |
$2$ |
$7.43499374162$ |
$20.273134932713294$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.02853094339$ |
3.1.419.1 |
$x^{3} - 4 x - 5$ |
$3$ |
[1,1] |
$-\,419$ |
$1$ |
$7.48292411435$ |
$20.46948949045872$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$3.34476559827$ |
3.1.424.1 |
$x^{3} - x^{2} + 8$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 53$ |
$2$ |
$7.51257150844$ |
$20.591260281974$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.85854853369$ |
3.1.431.1 |
$x^{3} - x - 8$ |
$3$ |
[1,1] |
$-\,431$ |
$1$ |
$7.553688825$ |
$20.760539492026695$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$6.15468225563$ |
3.1.436.1 |
$x^{3} + x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 109$ |
$2$ |
$7.58278652688$ |
$20.8806130178211$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.9481057151$ |
3.1.439.1 |
$x^{3} - x^{2} - 2 x + 5$ |
$3$ |
[1,1] |
$-\,439$ |
$1$ |
$7.60013850163$ |
$20.952326839756964$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.43008661497$ |
3.1.440.1 |
$x^{3} + 2 x - 8$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5\cdot 11$ |
$3$ |
$7.60590492152$ |
$20.97617696340303$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.53433053794$ |