| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 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 |
trivial |
$2$ |
$2$ |
$1.66233652077$ |
$3$ |
$37$ |
| 3.1.888.1 |
$x^{3} - x^{2} + 9 x + 3$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 37$ |
$3$ |
$9.61179106741$ |
$29.79932885150268$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.6414091891$ |
$1$ |
$37$ |
| 3.1.999.1 |
$x^{3} + 3 x - 12$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 37$ |
$2$ |
$9.99666555494$ |
$21.915042936585067$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.5105786612$ |
$1$ |
$37$ |
| 3.1.1036.1 |
$x^{3} + 4 x - 12$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 7\cdot 37$ |
$3$ |
$10.1185881266$ |
$25.546802223478856$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.23153744514$ |
$1$ |
$37$ |
| 3.1.1147.1 |
$x^{3} - x^{2} - 3 x + 8$ |
$3$ |
(1, 1) |
$-\,31\cdot 37$ |
$2$ |
$10.4677772542$ |
$33.8673884437522$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.6038483382$ |
$1$ |
$37$ |
| 3.1.1295.1 |
$x^{3} - x^{2} + 7$ |
$3$ |
(1, 1) |
$-\,5\cdot 7\cdot 37$ |
$3$ |
$10.899918637$ |
$35.98610843089316$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.52724980954$ |
$1$ |
$37$ |
| 3.1.1480.1 |
$x^{3} + 7 x - 2$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 37$ |
$3$ |
$11.3960384306$ |
$38.47076812334269$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.8563236363$ |
$1$ |
$37$ |
| 3.1.2183.1 |
$x^{3} - x - 9$ |
$3$ |
(1, 1) |
$-\,37\cdot 59$ |
$2$ |
$12.9723277254$ |
$46.72258554489466$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$4.02947715838$ |
$1$ |
$59$ |
| 3.1.2220.1 |
$x^{3} - x^{2} - 11 x + 21$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 5\cdot 37$ |
$4$ |
$13.0452075002$ |
$37.39668923024215$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.0511308265$ |
$1$ |
$37$ |
| 3.1.2479.1 |
$x^{3} - 11 x - 17$ |
$3$ |
(1, 1) |
$-\,37\cdot 67$ |
$2$ |
$13.5339793318$ |
$49.78955713801841$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.26288098313$ |
$1$ |
$67$ |
| 3.1.2516.1 |
$x^{3} - 7 x - 12$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17\cdot 37$ |
$3$ |
$13.6009803215$ |
$50.15974481593781$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.2643139551$ |
$1$ |
$37$ |
| 3.1.2627.1 |
$x^{3} - x^{2} + 9 x - 2$ |
$3$ |
(1, 1) |
$-\,37\cdot 71$ |
$2$ |
$13.7981233883$ |
$51.254268114957995$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.22254484118$ |
$1$ |
$71$ |
| 3.1.2923.1 |
$x^{3} - x^{2} + 14 x - 12$ |
$3$ |
(1, 1) |
$-\,37\cdot 79$ |
$2$ |
$14.2980322329$ |
$54.064775963653084$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.587160601$ |
$1$ |
$79$ |
| 3.1.3256.1 |
$x^{3} - x^{2} + 14 x + 22$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 37$ |
$3$ |
$14.8215901108$ |
$57.06137047074842$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.5966582352$ |
$1$ |
$37$ |
| 3.1.3404.1 |
$x^{3} - x^{2} + 15 x - 11$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 23\cdot 37$ |
$3$ |
$15.0428404926$ |
$46.30751156044853$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.45992946076$ |
$1$ |
$37$ |
| 3.1.3700.1 |
$x^{3} + 10 x - 20$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5^{2}\cdot 37$ |
$3$ |
$15.4668037377$ |
$35.57221107185714$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.6504937158$ |
$1$ |
$37$ |
| 3.1.4255.1 |
$x^{3} - x^{2} + 4 x + 11$ |
$3$ |
(1, 1) |
$-\,5\cdot 23\cdot 37$ |
$3$ |
$16.204408697$ |
$65.23036102920173$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.15848492721$ |
$1$ |
$37$ |
| 3.1.4292.1 |
$x^{3} - 10 x - 28$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 29\cdot 37$ |
$3$ |
$16.2512425085$ |
$65.5133574166368$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.6111281312$ |
$1$ |
$37$ |
| 3.1.4699.1 |
$x^{3} - x^{2} - 11 x - 16$ |
$3$ |
(1, 1) |
$-\,37\cdot 127$ |
$2$ |
$16.7494987598$ |
$68.54925236645546$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.9351804259$ |
$1$ |
$127$ |
| 3.1.4995.1 |
$x^{3} - 12 x - 21$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 5\cdot 37$ |
$3$ |
$17.0940576459$ |
$49.003525736030824$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.1259584938$ |
$1$ |
$37$ |
| 3.1.5032.1 |
$x^{3} - x^{2} + 16 x + 8$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 37$ |
$3$ |
$17.1361614063$ |
$70.9365914038728$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.6980027009$ |
$1$ |
$37$ |
| 3.1.5291.1 |
$x^{3} - x - 28$ |
$3$ |
(1, 1) |
$-\,11\cdot 13\cdot 37$ |
$3$ |
$17.4252594774$ |
$72.73926037567333$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.2338904361$ |
$1$ |
$37$ |
| 3.1.5439.1 |
$x^{3} - x^{2} - 2 x + 15$ |
$3$ |
(1, 1) |
$-\,3\cdot 7^{2}\cdot 37$ |
$3$ |
$17.5862409683$ |
$38.553177936638974$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.61551337389$ |
$1$ |
$37$ |
| 3.3.5624.1 |
$x^{3} - x^{2} - 19 x - 9$ |
$3$ |
(3, 0) |
$2^{3}\cdot 19\cdot 37$ |
$3$ |
$17.7834125657$ |
$74.9933330370107$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$29.6426090841$ |
$3$ |
$37$ |
| 3.1.5772.1 |
$x^{3} - x^{2} - 3 x + 45$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 13\cdot 37$ |
$4$ |
$17.9380586981$ |
$60.30034950144654$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.0070337806$ |
$1$ |
$37$ |
| 3.1.6068.1 |
$x^{3} - x^{2} - 3 x - 29$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 37\cdot 41$ |
$3$ |
$18.2395949946$ |
$77.89736837660179$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.1752552719$ |
$1$ |
$41$ |
| 3.1.6179.1 |
$x^{3} - x^{2} + 18 x + 4$ |
$3$ |
(1, 1) |
$-\,37\cdot 167$ |
$2$ |
$18.3501406934$ |
$78.60661549767933$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.09492760582$ |
$1$ |
$167$ |
| 3.1.6216.1 |
$x^{3} - x^{2} + 16 x - 24$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 7\cdot 37$ |
$4$ |
$18.3866948551$ |
$78.8416133777081$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.6681548353$ |
$1$ |
$37$ |
| 3.3.6401.1 |
$x^{3} - x^{2} - 22 x + 45$ |
$3$ |
(3, 0) |
$37\cdot 173$ |
$2$ |
$18.5673222818$ |
$80.00624975587844$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$16.5600241192$ |
$3$ |
$173$ |
| 3.3.6549.1 |
$x^{3} - x^{2} - 15 x - 12$ |
$3$ |
(3, 0) |
$3\cdot 37\cdot 59$ |
$3$ |
$18.7093340878$ |
$80.92589202474076$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$27.1673738401$ |
$3$ |
$59$ |
| 3.1.6623.1 |
$x^{3} + 11 x - 28$ |
$3$ |
(1, 1) |
$-\,37\cdot 179$ |
$2$ |
$18.7795386258$ |
$81.38181615078395$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$34.3450400862$ |
$1$ |
$179$ |
| 3.1.6956.1 |
$x^{3} - x^{2} - 9 x + 37$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 37\cdot 47$ |
$3$ |
$19.0891470922$ |
$66.1967175283969$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.96641539563$ |
$1$ |
$47$ |
| 3.1.7215.1 |
$x^{3} + 3 x - 49$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 13\cdot 37$ |
$4$ |
$19.3231879655$ |
$84.94115610232768$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.5596093309$ |
$1$ |
$37$ |
| 3.1.7511.1 |
$x^{3} + 11 x - 9$ |
$3$ |
(1, 1) |
$-\,7\cdot 29\cdot 37$ |
$3$ |
$19.5839032076$ |
$86.66602563865497$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.5135318726$ |
$1$ |
$37$ |
| 3.1.7807.1 |
$x^{3} + x - 17$ |
$3$ |
(1, 1) |
$-\,37\cdot 211$ |
$2$ |
$19.8378556801$ |
$88.35722947218298$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.43220382845$ |
$1$ |
$211$ |
| 3.3.7881.1 |
$x^{3} - x^{2} - 24 x + 51$ |
$3$ |
(3, 0) |
$3\cdot 37\cdot 71$ |
$3$ |
$19.9003375278$ |
$88.77499647986475$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$14.7835844331$ |
$2$ |
$71$ |
| 3.1.8103.1 |
$x^{3} - 9 x - 53$ |
$3$ |
(1, 1) |
$-\,3\cdot 37\cdot 73$ |
$3$ |
$20.0854675777$ |
$90.0166651237425$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.4759709888$ |
$1$ |
$73$ |
| 3.1.8140.1 |
$x^{3} - x^{2} - 11 x - 19$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 11\cdot 37$ |
$4$ |
$20.1159926514$ |
$71.60920801874668$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.2821061884$ |
$1$ |
$37$ |
| 3.1.8695.1 |
$x^{3} - x^{2} + 4 x - 19$ |
$3$ |
(1, 1) |
$-\,5\cdot 37\cdot 47$ |
$3$ |
$20.5631603493$ |
$93.24698386543128$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.2175218312$ |
$1$ |
$47$ |
| 3.3.8769.1 |
$x^{3} - x^{2} - 22 x - 29$ |
$3$ |
(3, 0) |
$3\cdot 37\cdot 79$ |
$3$ |
$20.6213308441$ |
$93.64293886887575$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$17.0338433739$ |
$3$ |
$79$ |
| 3.1.8991.1 |
$x^{3} + 27 x - 9$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 37$ |
$2$ |
$20.7939023053$ |
$45.58512629387849$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.50528202577$ |
$1$ |
$37$ |
| 3.1.8991.2 |
$x^{3} - 9 x - 21$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 37$ |
$2$ |
$20.7939023053$ |
$45.58512629387849$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.63108913817$ |
$1$ |
$37$ |
| 3.1.8991.3 |
$x^{3} + 9 x - 15$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 37$ |
$2$ |
$20.7939023053$ |
$45.58512629387849$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.195773681$ |
$1$ |
$37$ |
| 3.1.9028.1 |
$x^{3} - x^{2} - 23 x - 49$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 37\cdot 61$ |
$3$ |
$20.8223871386$ |
$95.01578816175763$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$18.033648605$ |
$1$ |
$61$ |
| 3.1.9139.1 |
$x^{3} - x^{2} - x - 18$ |
$3$ |
(1, 1) |
$-\,13\cdot 19\cdot 37$ |
$3$ |
$20.9073774159$ |
$95.59811713627$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.0725491741$ |
$1$ |
$37$ |
| 3.1.9287.1 |
$x^{3} - x^{2} + 16 x + 45$ |
$3$ |
(1, 1) |
$-\,37\cdot 251$ |
$2$ |
$21.0196339429$ |
$96.36908217888141$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$3.47253249308$ |
$1$ |
$251$ |
| 3.3.9805.1 |
$x^{3} - x^{2} - 15 x - 8$ |
$3$ |
(3, 0) |
$5\cdot 37\cdot 53$ |
$3$ |
$21.4033884057$ |
$99.02019995940222$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$25.2561875047$ |
$3$ |
$53$ |
| 3.1.10175.1 |
$x^{3} - x^{2} + 22 x - 8$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 11\cdot 37$ |
$3$ |
$21.6692961963$ |
$58.98983854433811$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$44.0849991045$ |
$1$ |
$37$ |
| 3.1.10212.1 |
$x^{3} - x^{2} + 4 x + 18$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 23\cdot 37$ |
$4$ |
$21.6955302367$ |
$101.05444077327824$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$41.5330076348$ |
$1$ |
$37$ |
| 3.1.10360.1 |
$x^{3} - x^{2} + 9 x + 35$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 7\cdot 37$ |
$4$ |
$21.799837274$ |
$101.78408519999579$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$41.9774408413$ |
$1$ |
$37$ |
