| 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 $p$ |
| 3.1.59.1 |
$x^{3} + 2 x - 1$ |
$3$ |
(1, 1) |
$-\,59$ |
$1$ |
$3.89299641587$ |
$7.681145747868608$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$0.790985720639$ |
$1$ |
$59$ |
| 3.1.472.1 |
$x^{3} - 5 x - 6$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 59$ |
$2$ |
$7.78599283175$ |
$21.72556098240043$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.38047034098$ |
$1$ |
$59$ |
| 3.3.1593.1 |
$x^{3} - 9 x - 7$ |
$3$ |
(3, 0) |
$3^{3}\cdot 59$ |
$2$ |
$11.6789892476$ |
$27.67371536012528$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$6.33079430444$ |
$2$ |
$59$ |
| 3.1.2183.1 |
$x^{3} - x - 9$ |
$3$ |
(1, 1) |
$-\,37\cdot 59$ |
$2$ |
$12.9723277254$ |
$46.72258554489466$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$4.02947715838$ |
$1$ |
$59$ |
| 3.1.2891.1 |
$x^{3} - x^{2} + 5 x + 8$ |
$3$ |
(1, 1) |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.34123738956$ |
$1$ |
$59$ |
| 3.1.2891.2 |
$x^{3} - x^{2} - 9 x + 36$ |
$3$ |
(1, 1) |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.74005132064$ |
$1$ |
$59$ |
| 3.1.2891.3 |
$x^{3} - x^{2} - 2 x - 20$ |
$3$ |
(1, 1) |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.63060662824$ |
$1$ |
$59$ |
| 3.1.3127.1 |
$x^{3} - x^{2} - 16 x + 33$ |
$3$ |
(1, 1) |
$-\,53\cdot 59$ |
$2$ |
$14.6232069782$ |
$55.91958512006326$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.52941340259$ |
$1$ |
$59$ |
| 3.1.3304.1 |
$x^{3} - x^{2} - 7 x - 21$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 59$ |
$3$ |
$14.8940684767$ |
$57.48043145279966$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$3.50648561424$ |
$1$ |
$59$ |
| 3.1.3540.1 |
$x^{3} - x^{2} + 4 x - 24$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 5\cdot 59$ |
$4$ |
$15.2405656957$ |
$59.49789912257407$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.7860368873$ |
$1$ |
$59$ |
| 3.3.3540.1 |
$x^{3} - x^{2} - 15 x - 15$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 5\cdot 59$ |
$4$ |
$15.2405656957$ |
$47.22351382853594$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$20.309560157$ |
$3$ |
$59$ |
| 3.1.3599.1 |
$x^{3} - x^{2} - 6 x - 11$ |
$3$ |
(1, 1) |
$-\,59\cdot 61$ |
$2$ |
$15.3247694249$ |
$59.99166608788257$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.89349056616$ |
$1$ |
$61$ |
| 3.1.3835.1 |
$x^{3} - 17 x - 36$ |
$3$ |
(1, 1) |
$-\,5\cdot 13\cdot 59$ |
$3$ |
$15.6526709674$ |
$61.927376821564145$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.5558656986$ |
$1$ |
$59$ |
| 3.1.4012.1 |
$x^{3} - x^{2} + 3 x - 13$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17\cdot 59$ |
$3$ |
$15.8898686826$ |
$50.27326949870195$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.2942096554$ |
$1$ |
$59$ |
| 3.1.4307.1 |
$x^{3} - 4 x - 13$ |
$3$ |
(1, 1) |
$-\,59\cdot 73$ |
$2$ |
$16.2701525122$ |
$65.62773803811922$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.2743270005$ |
$1$ |
$73$ |
| 3.3.5369.1 |
$x^{3} - 17 x - 23$ |
$3$ |
(3, 0) |
$7\cdot 13\cdot 59$ |
$3$ |
$17.5104699253$ |
$73.27346040688948$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$11.0396330048$ |
$3$ |
$59$ |
| 3.1.5959.1 |
$x^{3} - x^{2} + 8 x - 15$ |
$3$ |
(1, 1) |
$-\,59\cdot 101$ |
$2$ |
$18.1297213226$ |
$77.19455939378112$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.6532751324$ |
$1$ |
$101$ |
| 3.1.6372.1 |
$x^{3} - 15 x - 38$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 59$ |
$3$ |
$18.5392398176$ |
$55.34743072025056$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.6387262159$ |
$1$ |
$59$ |
| 3.1.6431.1 |
$x^{3} - 7 x - 17$ |
$3$ |
(1, 1) |
$-\,59\cdot 109$ |
$2$ |
$18.5962839919$ |
$80.19351594736322$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.06074526235$ |
$1$ |
$109$ |
| 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 |
$2$ |
$2$ |
$27.1673738401$ |
$3$ |
$59$ |
| 3.1.7788.1 |
$x^{3} - x^{2} + 3 x + 33$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 11\cdot 59$ |
$4$ |
$19.821749389$ |
$70.04379036210588$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.5882758609$ |
$1$ |
$59$ |
| 3.1.8024.1 |
$x^{3} + 11 x - 10$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 59$ |
$3$ |
$20.0199800333$ |
$89.57678270623477$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$27.727263517$ |
$1$ |
$59$ |
| 3.1.8260.1 |
$x^{3} - x^{2} - 15 x + 47$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 7\cdot 59$ |
$4$ |
$20.2143609279$ |
$90.8845421400141$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$36.0197581914$ |
$1$ |
$59$ |
| 3.3.8909.1 |
$x^{3} - x^{2} - 25 x + 54$ |
$3$ |
(3, 0) |
$59\cdot 151$ |
$2$ |
$20.7304940804$ |
$94.38749917229505$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$26.2377984835$ |
$3$ |
$151$ |
| 3.1.9204.1 |
$x^{3} - x^{2} - 16 x - 26$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 13\cdot 59$ |
$4$ |
$20.9568274047$ |
$95.93747964169165$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$41.9975315893$ |
$1$ |
$59$ |
| 3.3.9204.1 |
$x^{3} - x^{2} - 29 x - 39$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 13\cdot 59$ |
$4$ |
$20.9568274047$ |
$76.14562805319953$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$29.7951079558$ |
$3$ |
$59$ |
| 3.1.9676.1 |
$x^{3} - x^{2} + 11 x - 39$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 59$ |
$3$ |
$21.3091087875$ |
$78.0736705899716$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.8255434722$ |
$1$ |
$59$ |
| 3.3.9676.1 |
$x^{3} - 22 x - 12$ |
$3$ |
(3, 0) |
$2^{2}\cdot 41\cdot 59$ |
$3$ |
$21.3091087875$ |
$98.3666610188635$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$61.8715966852$ |
$3$ |
$59$ |
| 3.1.10148.1 |
$x^{3} - x^{2} + 17 x + 23$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 59$ |
$3$ |
$21.6501122727$ |
$100.73728207570423$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.0120443872$ |
$1$ |
$59$ |
| 3.3.10561.1 |
$x^{3} - 19 x - 25$ |
$3$ |
(3, 0) |
$59\cdot 179$ |
$2$ |
$21.939918714$ |
$102.76672613253767$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$16.3038875847$ |
$3$ |
$179$ |
| 3.1.10915.1 |
$x^{3} - x^{2} - 21 x + 50$ |
$3$ |
(1, 1) |
$-\,5\cdot 37\cdot 59$ |
$3$ |
$22.1823683828$ |
$104.47487736293353$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$28.011871761$ |
$1$ |
$59$ |
| 3.3.11092.1 |
$x^{3} - 16 x - 14$ |
$3$ |
(3, 0) |
$2^{2}\cdot 47\cdot 59$ |
$3$ |
$22.3016307199$ |
$83.59139993275006$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$21.5458426211$ |
$3$ |
$59$ |
| 3.1.11151.1 |
$x^{3} - 3 x - 61$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 59$ |
$3$ |
$22.341102715$ |
$73.21776869607976$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.17625979292$ |
$1$ |
$59$ |
| 3.3.11505.1 |
$x^{3} - x^{2} - 26 x - 39$ |
$3$ |
(3, 0) |
$3\cdot 5\cdot 13\cdot 59$ |
$4$ |
$22.5750579769$ |
$107.26136303441235$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$24.3224874011$ |
$2$ |
$59$ |
| 3.1.11623.1 |
$x^{3} - x^{2} - 2 x + 63$ |
$3$ |
(1, 1) |
$-\,59\cdot 197$ |
$2$ |
$22.6519752934$ |
$107.81001808737442$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.4456025$ |
$1$ |
$197$ |
| 3.1.11800.1 |
$x^{3} - x^{2} + 22 x + 42$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 59$ |
$3$ |
$22.7663811496$ |
$63.525925685164204$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.7034308534$ |
$1$ |
$59$ |
| 3.1.11800.2 |
$x^{3} - x^{2} + 17 x + 27$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 59$ |
$3$ |
$22.7663811496$ |
$63.525925685164204$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.0338665276$ |
$1$ |
$59$ |
| 3.1.11800.3 |
$x^{3} + 10 x - 40$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 59$ |
$3$ |
$22.7663811496$ |
$63.525925685164204$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$10.9988112057$ |
$1$ |
$59$ |
| 3.3.12685.1 |
$x^{3} - x^{2} - 26 x - 20$ |
$3$ |
(3, 0) |
$5\cdot 43\cdot 59$ |
$3$ |
$23.3218764617$ |
$112.62770529492288$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$27.4229521425$ |
$3$ |
$59$ |
| 3.1.12744.1 |
$x^{3} + 18 x - 32$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 59$ |
$3$ |
$23.3579784952$ |
$78.27308716708362$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$32.7468489432$ |
$1$ |
$59$ |
| 3.3.12744.1 |
$x^{3} - 21 x - 30$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3^{3}\cdot 59$ |
$3$ |
$23.3579784952$ |
$78.27308716708362$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$60.3891398307$ |
$3$ |
$59$ |
| 3.1.12980.1 |
$x^{3} - x^{2} + 22$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 11\cdot 59$ |
$4$ |
$23.5012825617$ |
$113.92980294900892$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$4.55575640566$ |
$1$ |
$59$ |
| 3.1.13039.1 |
$x^{3} - x^{2} - 16 x + 39$ |
$3$ |
(1, 1) |
$-\,13\cdot 17\cdot 59$ |
$3$ |
$23.5368367498$ |
$114.18844074598795$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.5542490322$ |
$1$ |
$59$ |
| 3.1.13452.1 |
$x^{3} + 30 x - 22$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 59$ |
$4$ |
$23.7827618037$ |
$92.0555755051964$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$28.6012497505$ |
$1$ |
$59$ |
| 3.3.13688.1 |
$x^{3} - 26 x - 24$ |
$3$ |
(3, 0) |
$2^{3}\cdot 29\cdot 59$ |
$3$ |
$23.9210367816$ |
$116.99572641767733$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$54.0214861339$ |
$3$ |
$59$ |
| 3.1.13747.1 |
$x^{3} + 10 x - 19$ |
$3$ |
(1, 1) |
$-\,59\cdot 233$ |
$2$ |
$23.9553568241$ |
$117.24760125478048$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.7704745952$ |
$1$ |
$233$ |
| 3.1.13983.1 |
$x^{3} - x^{2} - 6 x + 48$ |
$3$ |
(1, 1) |
$-\,3\cdot 59\cdot 79$ |
$3$ |
$24.0916633528$ |
$118.24973572909158$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$87.0898151629$ |
$1$ |
$79$ |
| 3.1.14632.1 |
$x^{3} - x^{2} - 6 x - 22$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 31\cdot 59$ |
$3$ |
$24.4587672413$ |
$120.96280420029953$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.7250445962$ |
$1$ |
$59$ |
| 3.1.15163.1 |
$x^{3} - x^{2} + 3 x - 72$ |
$3$ |
(1, 1) |
$-\,59\cdot 257$ |
$2$ |
$24.7511307853$ |
$123.13813381727043$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$5.73678038263$ |
$1$ |
$257$ |
| 3.3.15517.1 |
$x^{3} - 25 x - 4$ |
$3$ |
(3, 0) |
$59\cdot 263$ |
$2$ |
$24.9422667776$ |
$124.5672509129105$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$28.6696170963$ |
$3$ |
$263$ |
