| 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 |
| 3.3.361.1 |
$x^{3} - x^{2} - 6 x + 7$ |
$3$ |
[3,0] |
$19^{2}$ |
$1$ |
$7.1203673589$ |
$7.120367358901993$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$1.95215669651$ |
| 3.1.1083.1 |
$x^{3} - x^{2} - 6 x - 12$ |
$3$ |
[1,1] |
$-\,3\cdot 19^{2}$ |
$2$ |
$10.2693467638$ |
$12.332838034173273$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.62907295987$ |
| 3.1.18772.1 |
$x^{3} - x^{2} + 32 x - 50$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 13\cdot 19^{2}$ |
$3$ |
$26.5768506077$ |
$51.34569922532248$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$18.7008480285$ |
| 3.1.25631.1 |
$x^{3} - x^{2} - 6 x + 64$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 71$ |
$2$ |
$29.4841435422$ |
$59.99728180614438$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$20.0171994152$ |
| 3.3.29241.1 |
$x^{3} - 57 x - 152$ |
$3$ |
[3,0] |
$3^{4}\cdot 19^{2}$ |
$2$ |
$30.8080402914$ |
$30.80804029142189$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$39.6683040644$ |
| 3.3.29241.2 |
$x^{3} - 57 x - 19$ |
$3$ |
[3,0] |
$3^{4}\cdot 19^{2}$ |
$2$ |
$30.8080402914$ |
$30.80804029142189$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$9.7184036612$ |
| 3.1.37183.1 |
$x^{3} + 19 x - 19$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 103$ |
$2$ |
$33.3770648238$ |
$72.26383622911841$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$3.08488194502$ |
| 3.1.48735.1 |
$x^{3} - 57 x - 209$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5\cdot 19^{2}$ |
$3$ |
$36.5269707457$ |
$57.36260512948892$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$9.18502253243$ |
| 3.1.49096.1 |
$x^{3} - x^{2} - 6 x - 126$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 17\cdot 19^{2}$ |
$3$ |
$36.6169390173$ |
$83.03703908676842$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$9.16733010523$ |
| 3.1.55955.1 |
$x^{3} + 38 x - 209$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 31$ |
$3$ |
$38.2483730636$ |
$88.64785871912602$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.296256321$ |
| 3.1.64619.1 |
$x^{3} - x^{2} + 13 x - 50$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 179$ |
$2$ |
$40.1285447967$ |
$95.26402262818495$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$20.5823445997$ |
| 3.3.67868.1 |
$x^{3} - x^{2} - 63 x - 145$ |
$3$ |
[3,0] |
$2^{2}\cdot 19^{2}\cdot 47$ |
$3$ |
$40.790123202$ |
$97.62955848120377$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$43.2486985765$ |
| 3.1.72200.1 |
$x^{3} - x^{2} + 32 x + 292$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5^{2}\cdot 19^{2}$ |
$3$ |
$41.64016092$ |
$58.888080312522455$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$55.5828205662$ |
| 3.1.73644.1 |
$x^{3} - x^{2} - 25 x - 107$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 17\cdot 19^{2}$ |
$4$ |
$41.9159316119$ |
$80.71869881493625$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$23.331270961$ |
| 3.1.85196.2 |
$x^{3} - x^{2} - 25 x + 83$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 59$ |
$3$ |
$44.0020660187$ |
$86.81905817297995$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.64633568821$ |
| 3.3.88084.1 |
$x^{3} - 76 x - 228$ |
$3$ |
[3,0] |
$2^{2}\cdot 19^{2}\cdot 61$ |
$3$ |
$44.4937499112$ |
$88.27830420301467$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$48.1841624456$ |
| 3.1.96748.2 |
$x^{3} - x^{2} + 13 x - 183$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 67$ |
$3$ |
$45.9071852533$ |
$92.51804897267431$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.2116507327$ |
| 3.1.101080.1 |
$x^{3} - 38 x - 152$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5\cdot 7\cdot 19^{2}$ |
$4$ |
$46.5823875677$ |
$119.14653486862615$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$50.0144879022$ |
| 3.3.122740.1 |
$x^{3} - x^{2} - 101 x - 335$ |
$3$ |
[3,0] |
$2^{2}\cdot 5\cdot 17\cdot 19^{2}$ |
$4$ |
$49.6968321672$ |
$104.20739207926015$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$23.9086098844$ |
| 3.1.124184.1 |
$x^{3} - x^{2} + 70 x - 278$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19^{2}\cdot 43$ |
$3$ |
$49.8909623888$ |
$132.06314086847485$ |
|
|
|
$S_3$ (as 3T2) |
$[21]$ |
$2$ |
$1$ |
$6.04240144334$ |
| 3.1.128516.3 |
$x^{3} - x^{2} - 44 x - 164$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 89$ |
$3$ |
$50.4644719557$ |
$134.34682263438623$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.1149061907$ |
| 3.1.131404.2 |
$x^{3} - x^{2} + 51 x - 31$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7\cdot 13\cdot 19^{2}$ |
$4$ |
$50.8396862674$ |
$107.82259019663186$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$39.9524602952$ |
| 3.1.154508.2 |
$x^{3} - x^{2} - 25 x + 691$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 19^{2}\cdot 107$ |
$3$ |
$53.6599574105$ |
$116.91788573201529$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$41.9728542098$ |
| 3.1.162811.2 |
$x^{3} + 19 x - 152$ |
$3$ |
[1,1] |
$-\,11\cdot 19^{2}\cdot 41$ |
$3$ |
$54.6044346025$ |
$151.2135368540077$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$8.69114802386$ |
| 3.1.165699.1 |
$x^{3} - 57 x - 228$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 17\cdot 19^{2}$ |
$3$ |
$54.925408526$ |
$105.77141763549201$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$20.2868409842$ |
| 3.3.166421.1 |
$x^{3} - x^{2} - 101 x + 26$ |
$3$ |
[3,0] |
$19^{2}\cdot 461$ |
$2$ |
$55.0050684034$ |
$152.88077067164306$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$67.3922805163$ |
| 3.1.174363.1 |
$x^{3} - x^{2} + 13 x + 558$ |
$3$ |
[1,1] |
$-\,3\cdot 7\cdot 19^{2}\cdot 23$ |
$4$ |
$55.8664974625$ |
$156.4861716904126$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$17.1013497242$ |
| 3.1.175807.1 |
$x^{3} - x^{2} - 6 x + 83$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 487$ |
$2$ |
$56.0202945151$ |
$157.1328115182318$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$16.2027014703$ |
| 3.1.185915.3 |
$x^{3} - x^{2} - 6 x - 164$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 103$ |
$3$ |
$57.0739780194$ |
$161.5868501232208$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$28.0919910157$ |
| 3.1.186276.1 |
$x^{3} - x^{2} - 44 x + 216$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 43$ |
$4$ |
$57.1108952212$ |
$161.74365447852955$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$63.8954732419$ |
| 3.1.188803.1 |
$x^{3} - x^{2} - 44 x + 368$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 523$ |
$2$ |
$57.3679895333$ |
$162.8370571563794$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$15.7761723644$ |
| 3.1.193135.1 |
$x^{3} - x^{2} - 6 x + 425$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 107$ |
$3$ |
$57.8034368554$ |
$164.69457416459892$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.5172798387$ |
| 3.3.193857.1 |
$x^{3} - x^{2} - 82 x - 107$ |
$3$ |
[3,0] |
$3\cdot 19^{2}\cdot 179$ |
$3$ |
$57.8753764901$ |
$165.00212732540754$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$27.4094433624$ |
| 3.1.197467.3 |
$x^{3} - 95 x - 494$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 547$ |
$2$ |
$58.2324205396$ |
$166.53137342605197$ |
|
|
|
$S_3$ (as 3T2) |
$[12]$ |
$2$ |
$1$ |
$10.0478908753$ |
| 3.1.201799.1 |
$x^{3} - x^{2} + 70 x + 539$ |
$3$ |
[1,1] |
$-\,13\cdot 19^{2}\cdot 43$ |
$3$ |
$58.6551752343$ |
$168.3481330786765$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.5520578252$ |
| 3.1.203604.1 |
$x^{3} - x^{2} + 13 x - 525$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 47$ |
$4$ |
$58.8295376608$ |
$169.09935560996192$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$101.67434301$ |
| 3.1.209380.1 |
$x^{3} - x^{2} + 89 x - 449$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 19^{2}\cdot 29$ |
$4$ |
$59.3806661259$ |
$171.48115397592773$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$16.9492112099$ |
| 3.3.209741.1 |
$x^{3} - 38 x - 19$ |
$3$ |
[3,0] |
$7\cdot 19^{2}\cdot 83$ |
$3$ |
$59.4147733512$ |
$171.62891889259674$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$50.3042004318$ |
| 3.1.210824.1 |
$x^{3} + 38 x - 152$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19^{2}\cdot 73$ |
$3$ |
$59.5168607914$ |
$172.0714522929899$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$17.5233352867$ |
| 3.1.219127.1 |
$x^{3} - x^{2} + 32 x - 69$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 607$ |
$2$ |
$60.288150972$ |
$175.4271250824974$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.69200533793$ |
| 3.1.220571.1 |
$x^{3} - x^{2} + 51 x + 216$ |
$3$ |
[1,1] |
$-\,13\cdot 19^{2}\cdot 47$ |
$3$ |
$60.4202898078$ |
$176.00418955244518$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$21.7839168974$ |
| 3.3.228152.1 |
$x^{3} - x^{2} - 63 x + 83$ |
$3$ |
[3,0] |
$2^{3}\cdot 19^{2}\cdot 79$ |
$3$ |
$61.1047202377$ |
$179.0032597408581$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$88.8942109889$ |
| 3.1.229235.1 |
$x^{3} + 38 x - 19$ |
$3$ |
[1,1] |
$-\,5\cdot 19^{2}\cdot 127$ |
$3$ |
$61.2012523417$ |
$179.4276062701341$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[12]$ |
$2$ |
$1$ |
$5.04330049227$ |
| 3.1.233928.2 |
$x^{3} - 57 x - 494$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$61.6160805828$ |
$87.1382968205312$ |
|
|
|
$S_3$ (as 3T2) |
$[3, 3]$ |
$2$ |
$1$ |
$20.1756419615$ |
| 3.1.239704.1 |
$x^{3} - x^{2} - 82 x + 330$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 19^{2}\cdot 83$ |
$3$ |
$62.1190912525$ |
$183.47903204528865$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[18]$ |
$2$ |
$1$ |
$13.5883903582$ |
| 3.1.246563.1 |
$x^{3} - x^{2} + 32 x - 772$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 683$ |
$2$ |
$62.7060294171$ |
$186.08559373434764$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$26.4487792873$ |
| 3.1.252339.1 |
$x^{3} - x^{2} - 82 x - 620$ |
$3$ |
[1,1] |
$-\,3\cdot 19^{2}\cdot 233$ |
$3$ |
$63.191906644$ |
$188.25260236362246$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$73.1209793481$ |
| 3.3.252700.1 |
$x^{3} - x^{2} - 63 x + 7$ |
$3$ |
[3,0] |
$2^{2}\cdot 5^{2}\cdot 7\cdot 19^{2}$ |
$4$ |
$63.2220267185$ |
$110.16951034714337$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$66.0284793818$ |
| 3.1.258115.1 |
$x^{3} - 38 x - 133$ |
$3$ |
[1,1] |
$-\,5\cdot 11\cdot 13\cdot 19^{2}$ |
$4$ |
$63.6704248701$ |
$190.39494845685277$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$20.0422018359$ |
| 3.1.268223.3 |
$x^{3} - x^{2} - 6 x - 297$ |
$3$ |
[1,1] |
$-\,19^{2}\cdot 743$ |
$2$ |
$64.4909347675$ |
$194.0871610256786$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$40.5478250643$ |
