| 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 |
| 3.1.5415.1 |
$x^{3} - x^{2} - 6 x + 45$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 19^{2}$ |
$3$ |
$17.5603359542$ |
$27.57706419990631$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.07349607774$ |
| 3.1.14440.1 |
$x^{3} - x^{2} - 6 x + 26$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5\cdot 19^{2}$ |
$3$ |
$24.3513138304$ |
$45.0331572624958$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.0156599625$ |
| 3.3.15884.1 |
$x^{3} - 38 x - 76$ |
$3$ |
[3,0] |
$2^{2}\cdot 11\cdot 19^{2}$ |
$3$ |
$25.1373770524$ |
$47.23117379794351$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$17.2843457876$ |
| 3.3.17689.2 |
$x^{3} - x^{2} - 44 x + 64$ |
$3$ |
[3,0] |
$7^{2}\cdot 19^{2}$ |
$2$ |
$26.0556009339$ |
$26.05560093389125$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$32.4707206114$ |
| 3.1.20216.1 |
$x^{3} - 19 x - 114$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7\cdot 19^{2}$ |
$3$ |
$27.2415455073$ |
$53.28395024995941$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$13.3569436752$ |
| 3.1.28519.1 |
$x^{3} - x^{2} - 6 x - 31$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 79$ |
$2$ |
$30.5523601189$ |
$63.28720940862885$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.25763111933$ |
| 3.1.38988.1 |
$x^{3} - 76$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 19^{2}$ |
$3$ |
$33.9086359078$ |
$40.722133961240765$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$6.8189204833$ |
| 3.1.45847.1 |
$x^{3} + 19 x - 76$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 127$ |
$2$ |
$35.7907094896$ |
$80.24246493201747$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$43.2066670639$ |
| 3.1.47652.1 |
$x^{3} - x^{2} + 32 x - 164$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 11\cdot 19^{2}$ |
$4$ |
$36.2543712525$ |
$81.80679271915406$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$31.8659936081$ |
| 3.1.53428.1 |
$x^{3} - x^{2} + 13 x + 83$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 37$ |
$3$ |
$37.6636991771$ |
$86.62300754537509$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$28.4638576771$ |
| 3.3.53789.1 |
$x^{3} - x^{2} - 25 x - 12$ |
$3$ |
[3,0] |
$19^{2}\cdot 149$ |
$2$ |
$37.748336988$ |
$86.91516017089208$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$20.6813113072$ |
| 3.3.56677.1 |
$x^{3} - x^{2} - 25 x + 26$ |
$3$ |
[3,0] |
$19^{2}\cdot 157$ |
$2$ |
$38.4121796579$ |
$89.21794728717738$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$2$ |
$9.783672685$ |
| 3.1.59204.1 |
$x^{3} - 19 x - 190$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 41$ |
$3$ |
$38.9747809783$ |
$91.18519363042215$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$27.7293946108$ |
| 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) |
$[3]$ |
$2$ |
$2$ |
$7.55764880123$ |
| 3.1.72200.2 |
$x^{3} - x^{2} + 32 x - 88$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}\cdot 19^{2}$ |
$3$ |
$41.64016092$ |
$58.888080312522455$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$24.0507076661$ |
| 3.1.73644.2 |
$x^{3} - x^{2} + 13 x + 45$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 17\cdot 19^{2}$ |
$4$ |
$41.9159316119$ |
$80.71869881493625$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$30.6684830218$ |
| 3.1.79059.1 |
$x^{3} - x^{2} - 25 x + 178$ |
$3$ |
[1,1] |
$-\,3\cdot 19^{2}\cdot 73$ |
$3$ |
$42.9190834512$ |
$105.37181435437094$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$15.4450604618$ |
| 3.1.85196.1 |
$x^{3} - x^{2} - 25 x + 349$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 59$ |
$3$ |
$44.0020660187$ |
$86.81905817297995$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$24.3201240884$ |
| 3.3.85557.1 |
$x^{3} - x^{2} - 82 x + 292$ |
$3$ |
[3,0] |
$3\cdot 19^{2}\cdot 79$ |
$3$ |
$44.0641282533$ |
$109.61666216499624$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$44.1873591133$ |
| 3.1.87723.1 |
$x^{3} - 171$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 19^{2}$ |
$2$ |
$44.4328828723$ |
$53.36109106637179$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$9.81465581926$ |
| 3.1.93860.1 |
$x^{3} + 38 x - 76$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 13\cdot 19^{2}$ |
$4$ |
$45.4457752777$ |
$114.81247382007936$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$31.0044175188$ |
| 3.1.96748.1 |
$x^{3} - x^{2} - 25 x - 69$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 67$ |
$3$ |
$45.9071852533$ |
$92.51804897267431$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$10.1987283753$ |
| 3.1.99636.1 |
$x^{3} + 57 x - 76$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 23$ |
$4$ |
$46.3595019207$ |
$118.2924268323965$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$33.6793316773$ |
| 3.1.103607.1 |
$x^{3} - x^{2} - 44 x + 463$ |
$3$ |
[1,1] |
$-\,7\cdot 19^{2}\cdot 41$ |
$3$ |
$46.9673834364$ |
$120.62667279868398$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.14920749608$ |
| 3.1.106495.1 |
$x^{3} - x^{2} + 70 x + 197$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 59$ |
$3$ |
$47.3997887319$ |
$122.29632554204767$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$5.9270469119$ |
| 3.1.108300.2 |
$x^{3} - 190$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 19^{2}$ |
$4$ |
$47.6660852674$ |
$57.24396330617363$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$38.8204508012$ |
| 3.3.108661.1 |
$x^{3} - 76 x - 247$ |
$3$ |
[3,0] |
$7\cdot 19^{2}\cdot 43$ |
$3$ |
$47.7189888461$ |
$123.53375663777412$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$24.337087451$ |
| 3.3.111188.1 |
$x^{3} - x^{2} - 63 x + 45$ |
$3$ |
[3,0] |
$2^{2}\cdot 7\cdot 11\cdot 19^{2}$ |
$4$ |
$48.0860724167$ |
$99.1823575052225$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$38.5846138869$ |
| 3.1.112632.1 |
$x^{3} - x^{2} + 32 x - 392$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 13\cdot 19^{2}$ |
$4$ |
$48.2933425319$ |
$125.77076358845758$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$55.7620829684$ |
| 3.3.118769.1 |
$x^{3} - x^{2} - 82 x + 235$ |
$3$ |
[3,0] |
$7\cdot 19^{2}\cdot 47$ |
$3$ |
$49.154999945$ |
$129.151766175151$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$28.9343058404$ |
| 3.3.125628.1 |
$x^{3} - x^{2} - 63 x + 159$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 19^{2}\cdot 29$ |
$4$ |
$50.083593498$ |
$132.82873070743958$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$87.0525115295$ |
| 3.1.128155.1 |
$x^{3} - x^{2} - 6 x + 140$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 71$ |
$3$ |
$50.4171762654$ |
$134.1580005837502$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$19.8220664753$ |
| 3.1.128516.2 |
$x^{3} - 19 x - 76$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 89$ |
$3$ |
$50.4644719557$ |
$134.34682263438623$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$18.1603859656$ |
| 3.1.131404.1 |
$x^{3} - 38 x - 114$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 13\cdot 19^{2}$ |
$4$ |
$50.8396862674$ |
$107.82259019663186$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$22.2598730294$ |
| 3.1.135736.1 |
$x^{3} - x^{2} + 13 x - 145$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19^{2}\cdot 47$ |
$3$ |
$51.3923348499$ |
$138.0690456926156$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$61.5458324298$ |
| 3.1.138263.1 |
$x^{3} - x^{2} + 32 x - 31$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 383$ |
$2$ |
$51.7092999942$ |
$139.3483361857959$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$3.49469396441$ |
| 3.1.140068.1 |
$x^{3} - x^{2} + 32 x + 634$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 97$ |
$3$ |
$51.933346553$ |
$140.25497122875245$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$19.9201684799$ |
| 3.1.142595.1 |
$x^{3} - x^{2} + 89 x + 140$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 79$ |
$3$ |
$52.2438009174$ |
$141.51450234395836$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$30.6425974539$ |
| 3.3.146205.1 |
$x^{3} - 57 x - 76$ |
$3$ |
[3,0] |
$3^{4}\cdot 5\cdot 19^{2}$ |
$3$ |
$52.6810078626$ |
$68.88887234517178$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$56.7909397054$ |
| 3.3.153425.1 |
$x^{3} - 95 x - 190$ |
$3$ |
[3,0] |
$5^{2}\cdot 17\cdot 19^{2}$ |
$3$ |
$53.5342896029$ |
$85.84339087052626$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$127.727511285$ |
| 3.1.154508.3 |
$x^{3} - x^{2} - 25 x - 373$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 107$ |
$3$ |
$53.6599574105$ |
$116.91788573201529$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.87801587867$ |
| 3.3.160284.1 |
$x^{3} - 114 x - 76$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 19^{2}\cdot 37$ |
$4$ |
$54.3204539544$ |
$150.03545017301187$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$79.2659507724$ |
| 3.1.161367.1 |
$x^{3} - x^{2} - 44 x + 273$ |
$3$ |
[1,1] |
$-\,3\cdot 19^{2}\cdot 149$ |
$3$ |
$54.4425228007$ |
$150.54147336397196$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$23.1451003687$ |
| 3.1.162811.1 |
$x^{3} - 38 x - 551$ |
$3$ |
[1,1] |
$-\,11\cdot 19^{2}\cdot 41$ |
$3$ |
$54.6044346025$ |
$151.2135368540077$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$36.8039805548$ |
| 3.1.165699.2 |
$x^{3} - 114 x - 475$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 17\cdot 19^{2}$ |
$3$ |
$54.925408526$ |
$105.77141763549201$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$21.5961748723$ |
| 3.1.170031.1 |
$x^{3} + 57 x - 171$ |
$3$ |
[1,1] |
$-\,3\cdot 19^{2}\cdot 157$ |
$3$ |
$55.3999496061$ |
$154.5300176483931$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$6.55824608948$ |
| 3.1.176168.1 |
$x^{3} - x^{2} - 6 x + 406$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19^{2}\cdot 61$ |
$3$ |
$56.0586121019$ |
$157.2940561081374$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$45.9153363208$ |
| 3.1.185915.1 |
$x^{3} - x^{2} - 25 x - 88$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 103$ |
$3$ |
$57.0739780194$ |
$161.5868501232208$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$27.4051923451$ |
| 3.1.186276.2 |
$x^{3} - x^{2} - 44 x - 126$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 43$ |
$4$ |
$57.1108952212$ |
$161.74365447852955$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$106.803807539$ |
| 3.3.192413.1 |
$x^{3} - 95 x - 114$ |
$3$ |
[3,0] |
$13\cdot 19^{2}\cdot 41$ |
$3$ |
$57.7313177077$ |
$164.3864455987997$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$2$ |
$24.0336160609$ |
