| 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 $p$ |
| 3.1.867.1 |
$x^{3} - x^{2} + 6 x - 12$ |
$3$ |
(1, 1) |
$-\,3\cdot 17^{2}$ |
$2$ |
$9.53541719596$ |
$11.451434893652847$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.87929864473$ |
$1$ |
$17$ |
| 3.1.2023.1 |
$x^{3} - x^{2} + 6 x + 5$ |
$3$ |
(1, 1) |
$-\,7\cdot 17^{2}$ |
$2$ |
$12.647323508$ |
$17.492355738674252$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.67671865574$ |
$1$ |
$17$ |
| 3.1.3179.1 |
$x^{3} - x^{2} - 11 x + 22$ |
$3$ |
(1, 1) |
$-\,11\cdot 17^{2}$ |
$2$ |
$14.7038199461$ |
$21.92782837978011$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.65493163366$ |
$1$ |
$17$ |
| 3.1.5780.1 |
$x^{3} - x^{2} - 11 x - 29$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 17^{2}$ |
$3$ |
$17.9463422636$ |
$29.567477755530653$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.8024574373$ |
$1$ |
$17$ |
| 3.3.5780.1 |
$x^{3} - x^{2} - 11 x + 5$ |
$3$ |
(3, 0) |
$2^{2}\cdot 5\cdot 17^{2}$ |
$3$ |
$17.9463422636$ |
$23.46772264658785$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$22.0733702187$ |
$2$ |
$17$ |
| 3.1.6936.1 |
$x^{3} - x^{2} - 11 x + 39$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 17^{2}$ |
$3$ |
$19.0708343919$ |
$32.38954907047272$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$35.2199773688$ |
$1$ |
$17$ |
| 3.3.8092.1 |
$x^{3} - x^{2} - 28 x - 46$ |
$3$ |
(3, 0) |
$2^{2}\cdot 7\cdot 17^{2}$ |
$3$ |
$20.0763746411$ |
$34.984711477348505$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$32.5595102689$ |
$2$ |
$17$ |
| 3.1.11271.1 |
$x^{3} - x^{2} + 6 x - 63$ |
$3$ |
(1, 1) |
$-\,3\cdot 13\cdot 17^{2}$ |
$3$ |
$22.4209572148$ |
$41.28873568670286$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.2581146595$ |
$1$ |
$17$ |
| 3.1.11560.1 |
$x^{3} - 17 x - 34$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 17^{2}$ |
$3$ |
$22.6109743866$ |
$41.81472804703625$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$37.6840155834$ |
$1$ |
$17$ |
| 3.3.11849.1 |
$x^{3} - 17 x - 17$ |
$3$ |
(3, 0) |
$17^{2}\cdot 41$ |
$2$ |
$22.797850418$ |
$42.33418557960918$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$15.1953364722$ |
$3$ |
$41$ |
| 3.1.12716.1 |
$x^{3} - x^{2} + 23 x + 5$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 17^{2}$ |
$3$ |
$23.3408592503$ |
$34.80825783744108$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.13961568278$ |
$1$ |
$17$ |
| 3.1.12716.2 |
$x^{3} - x^{2} - 11 x - 63$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 17^{2}$ |
$3$ |
$23.3408592503$ |
$34.80825783744108$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$11.4587543188$ |
$1$ |
$17$ |
| 3.1.16184.1 |
$x^{3} - x^{2} + 6 x + 22$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 17^{2}$ |
$3$ |
$25.2946470159$ |
$49.47585344697593$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$27.056715318$ |
$1$ |
$17$ |
| 3.1.20519.1 |
$x^{3} - x^{2} + 6 x - 29$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 71$ |
$2$ |
$27.3769710777$ |
$55.7093966932374$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.81438362719$ |
$1$ |
$71$ |
| 3.1.22831.1 |
$x^{3} - x^{2} + 6 x + 56$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 79$ |
$2$ |
$28.3688443632$ |
$58.76419978400123$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$78.4537691921$ |
$1$ |
$79$ |
| 3.1.25432.1 |
$x^{3} - x^{2} + 6 x + 90$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 17^{2}$ |
$3$ |
$29.4076398921$ |
$62.02126457614936$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$55.7289377998$ |
$1$ |
$17$ |
| 3.1.26299.1 |
$x^{3} - 17 x - 68$ |
$3$ |
(1, 1) |
$-\,7\cdot 13\cdot 17^{2}$ |
$3$ |
$29.7380904711$ |
$63.06958554444678$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$38.0334898923$ |
$1$ |
$17$ |
| 3.1.27455.1 |
$x^{3} + 17 x - 17$ |
$3$ |
(1, 1) |
$-\,5\cdot 17^{2}\cdot 19$ |
$3$ |
$30.1675806662$ |
$64.44082377587246$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$2.9882752809$ |
$1$ |
$19$ |
| 3.1.31212.1 |
$x^{3} - 68$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$31.4852538689$ |
$37.81180491429508$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.90204729005$ |
$1$ |
$17$ |
| 3.1.31212.2 |
$x^{3} - 34$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$31.4852538689$ |
$37.81180491429508$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.8179665377$ |
$1$ |
$17$ |
| 3.3.31212.1 |
$x^{3} - 51 x - 136$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$31.4852538689$ |
$47.63988894603878$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$81.3594512431$ |
$3$ |
$17$ |
| 3.3.33524.1 |
$x^{3} - x^{2} - 45 x - 97$ |
$3$ |
(3, 0) |
$2^{2}\cdot 17^{2}\cdot 29$ |
$3$ |
$32.2442250742$ |
$56.517760359550685$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$35.4612571634$ |
$3$ |
$29$ |
| 3.3.37281.1 |
$x^{3} - 51 x - 85$ |
$3$ |
(3, 0) |
$3\cdot 17^{2}\cdot 43$ |
$3$ |
$33.4063621093$ |
$75.09208033017536$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$55.5378788527$ |
$3$ |
$43$ |
| 3.1.37859.1 |
$x^{3} - 34 x - 85$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 131$ |
$2$ |
$33.5781202035$ |
$75.67195056555559$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$40.3164493577$ |
$1$ |
$131$ |
| 3.1.41327.1 |
$x^{3} - x^{2} + 6 x - 80$ |
$3$ |
(1, 1) |
$-\,11\cdot 13\cdot 17^{2}$ |
$3$ |
$34.5736018812$ |
$79.06190958287164$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$91.5948548367$ |
$1$ |
$17$ |
| 3.1.42772.1 |
$x^{3} - x^{2} - 11 x + 243$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17^{2}\cdot 37$ |
$3$ |
$34.9719503156$ |
$80.43223534190828$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$81.0274273653$ |
$1$ |
$37$ |
| 3.3.45084.1 |
$x^{3} - 51 x - 68$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 13\cdot 17^{2}$ |
$4$ |
$35.5910510688$ |
$82.57747137340571$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$114.67852884$ |
$3$ |
$17$ |
| 3.1.45951.1 |
$x^{3} - x^{2} + 6 x + 39$ |
$3$ |
(1, 1) |
$-\,3\cdot 17^{2}\cdot 53$ |
$3$ |
$35.8177517738$ |
$83.3677044157341$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$8.73085005111$ |
$1$ |
$53$ |
| 3.1.47107.1 |
$x^{3} - x^{2} + 23 x - 12$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 163$ |
$2$ |
$36.1156261722$ |
$84.40984117811128$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$53.9331636788$ |
$1$ |
$163$ |
| 3.1.47396.1 |
$x^{3} - x^{2} + 40 x + 124$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17^{2}\cdot 41$ |
$3$ |
$36.1893317362$ |
$84.66837115921837$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$5.48533031534$ |
$1$ |
$41$ |
| 3.1.48263.1 |
$x^{3} - x^{2} + 40 x + 175$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 167$ |
$2$ |
$36.4086663743$ |
$85.43926752892214$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.845619556$ |
$1$ |
$167$ |
| 3.3.49997.1 |
$x^{3} - x^{2} - 62 x - 148$ |
$3$ |
(3, 0) |
$17^{2}\cdot 173$ |
$2$ |
$36.8395781654$ |
$86.96056093497712$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$77.9711767937$ |
$2$ |
$173$ |
| 3.1.50575.1 |
$x^{3} - x^{2} - 28 x - 63$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 7\cdot 17^{2}$ |
$3$ |
$36.9809982782$ |
$51.14795846301313$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$9.3481874159$ |
$1$ |
$17$ |
| 3.1.50575.2 |
$x^{3} - x^{2} - 28 x + 192$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 7\cdot 17^{2}$ |
$3$ |
$36.9809982782$ |
$51.14795846301313$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$51.9886992411$ |
$1$ |
$17$ |
| 3.3.51153.1 |
$x^{3} - x^{2} - 28 x - 29$ |
$3$ |
(3, 0) |
$3\cdot 17^{2}\cdot 59$ |
$3$ |
$37.1213449677$ |
$87.96014044037578$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$23.0309181605$ |
$3$ |
$59$ |
| 3.3.52309.1 |
$x^{3} - x^{2} - 45 x + 124$ |
$3$ |
(3, 0) |
$17^{2}\cdot 181$ |
$2$ |
$37.3988980392$ |
$88.94848764568957$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$36.4110151651$ |
$2$ |
$181$ |
| 3.1.53176.1 |
$x^{3} - x^{2} + 6 x - 46$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17^{2}\cdot 23$ |
$3$ |
$37.6043906145$ |
$89.68260040598155$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$108.612437604$ |
$1$ |
$23$ |
| 3.3.53176.1 |
$x^{3} - x^{2} - 62 x - 114$ |
$3$ |
(3, 0) |
$2^{3}\cdot 17^{2}\cdot 23$ |
$3$ |
$37.6043906145$ |
$89.68260040598155$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$169.290994371$ |
$3$ |
$23$ |
| 3.1.60979.1 |
$x^{3} - x^{2} - 45 x - 250$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 211$ |
$2$ |
$39.3604540207$ |
$96.03742533872455$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$25.2238220469$ |
$1$ |
$211$ |
| 3.1.60979.2 |
$x^{3} - 68 x - 221$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 211$ |
$2$ |
$39.3604540207$ |
$96.03742533872455$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$20.08854256$ |
$1$ |
$211$ |
| 3.1.60979.3 |
$x^{3} - x^{2} - 11 x - 46$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 211$ |
$2$ |
$39.3604540207$ |
$96.03742533872455$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$1$ |
$3.99375716322$ |
$1$ |
$211$ |
| 3.1.62135.1 |
$x^{3} - x^{2} + 40 x - 233$ |
$3$ |
(1, 1) |
$-\,5\cdot 17^{2}\cdot 43$ |
$3$ |
$39.6076219047$ |
$96.94345885027958$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.5422416903$ |
$1$ |
$43$ |
| 3.1.62424.1 |
$x^{3} + 51 x - 34$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$39.6689341107$ |
$67.37297705743613$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$17.0396885017$ |
$1$ |
$17$ |
| 3.1.62424.2 |
$x^{3} - 51 x - 170$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$39.6689341107$ |
$67.37297705743613$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$39.6819952484$ |
$1$ |
$17$ |
| 3.3.62424.1 |
$x^{3} - 51 x - 102$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3^{3}\cdot 17^{2}$ |
$3$ |
$39.6689341107$ |
$67.37297705743613$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$109.162993556$ |
$2$ |
$17$ |
| 3.1.65603.1 |
$x^{3} + 68 x - 119$ |
$3$ |
(1, 1) |
$-\,17^{2}\cdot 227$ |
$2$ |
$40.3312082906$ |
$99.61212606078705$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.0185763035$ |
$1$ |
$227$ |
| 3.1.65892.1 |
$x^{3} - x^{2} - 28 x + 124$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 17^{2}\cdot 19$ |
$4$ |
$40.3903450444$ |
$99.83129491993641$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$121.314536597$ |
$1$ |
$19$ |
| 3.1.67048.1 |
$x^{3} - x^{2} - 11 x - 97$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17^{2}\cdot 29$ |
$3$ |
$40.6251779085$ |
$100.70320051297317$ |
|
|
|
$S_3$ (as 3T2) |
$[13]$ |
$[13]$ |
$2$ |
$1$ |
$7.5352861555$ |
$1$ |
$29$ |
| 3.3.67337.1 |
$x^{3} - x^{2} - 28 x + 39$ |
$3$ |
(3, 0) |
$17^{2}\cdot 233$ |
$2$ |
$40.683463753$ |
$100.91999990387075$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$41.3304758783$ |
$2$ |
$233$ |
| 3.1.67915.1 |
$x^{3} - x^{2} - 11 x + 56$ |
$3$ |
(1, 1) |
$-\,5\cdot 17^{2}\cdot 47$ |
$3$ |
$40.7995370318$ |
$101.35220744847963$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$81.6480700893$ |
$1$ |
$47$ |
