| 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 |
| 3.1.972.1 |
$x^{3} - 12$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}$ |
$2$ |
$9.90578174668$ |
$11.896219369500566$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$5.10583548555$ |
| 3.3.1944.1 |
$x^{3} - 9 x - 6$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{5}$ |
$2$ |
$12.4805029383$ |
$21.196653174008656$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$15.6005131144$ |
| 3.1.3159.3 |
$x^{3} + 9 x - 3$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 13$ |
$2$ |
$14.6729197395$ |
$27.020537039282146$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.43039304741$ |
| 3.1.6075.2 |
$x^{3} - 15$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5^{2}$ |
$2$ |
$18.2466059867$ |
$21.91302343598798$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$9.69295167783$ |
| 3.1.6804.3 |
$x^{3} + 9 x - 30$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 7$ |
$3$ |
$18.949078793$ |
$39.6553069617074$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$34.6557490982$ |
| 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 |
$2$ |
$1$ |
$9.63108913817$ |
| 3.1.9720.1 |
$x^{3} + 27 x - 18$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 5$ |
$3$ |
$21.3413598269$ |
$47.39715739257004$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$38.3744175529$ |
| 3.1.11907.1 |
$x^{3} - 63$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7^{2}$ |
$2$ |
$22.8349878331$ |
$27.423380759717027$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$3.86596074415$ |
| 3.1.14823.1 |
$x^{3} - 9 x - 48$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 61$ |
$2$ |
$24.5647323302$ |
$58.531171665758464$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$68.4534913133$ |
| 3.1.17739.2 |
$x^{3} - 36 x - 87$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 73$ |
$2$ |
$26.0801275603$ |
$64.03003369697147$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$21.5455539012$ |
| 3.1.18468.3 |
$x^{3} + 9 x - 24$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 19$ |
$3$ |
$26.4326043447$ |
$65.33247282096788$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$21.7413955723$ |
| 3.1.20655.1 |
$x^{3} + 27 x - 63$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 17$ |
$3$ |
$27.4373228213$ |
$69.0926361771218$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$3.66749987517$ |
| 3.1.20655.2 |
$x^{3} - 27 x - 99$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 17$ |
$3$ |
$27.4373228213$ |
$69.0926361771218$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.98871636925$ |
| 3.1.20655.3 |
$x^{3} + 27 x - 12$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 17$ |
$3$ |
$27.4373228213$ |
$69.0926361771218$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$29.4759684632$ |
| 3.1.21384.3 |
$x^{3} + 18 x - 48$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 11$ |
$3$ |
$27.7563900551$ |
$70.30134538948258$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$35.94492462$ |
| 3.3.22356.1 |
$x^{3} - 36 x - 60$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{5}\cdot 23$ |
$3$ |
$28.170725619$ |
$57.05226386049417$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$49.5559975328$ |
| 3.3.23085.1 |
$x^{3} - 18 x - 3$ |
$3$ |
[3,0] |
$3^{5}\cdot 5\cdot 19$ |
$3$ |
$28.4736598741$ |
$73.04392518292082$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$55.0398325956$ |
| 3.1.23571.1 |
$x^{3} - 9 x - 60$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 97$ |
$2$ |
$28.6720889929$ |
$73.80880389609993$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$48.3704191613$ |
| 3.1.24300.3 |
$x^{3} - 150$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 5^{2}$ |
$3$ |
$28.9646815382$ |
$34.78475645409113$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.70072657259$ |
| 3.1.26487.1 |
$x^{3} - 45 x - 132$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 109$ |
$2$ |
$29.8087838016$ |
$78.24120839584313$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$32.3487579516$ |
| 3.1.26487.2 |
$x^{3} - 9 x - 33$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 109$ |
$2$ |
$29.8087838016$ |
$78.24120839584313$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.81740336264$ |
| 3.1.26487.3 |
$x^{3} + 27 x - 147$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 109$ |
$2$ |
$29.8087838016$ |
$78.24120839584313$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$8.07869399809$ |
| 3.1.29403.1 |
$x^{3} - 99$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 11^{2}$ |
$2$ |
$30.8648294343$ |
$37.066714282861305$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$50.3160022497$ |
| 3.1.30132.1 |
$x^{3} + 18 x - 60$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 31$ |
$3$ |
$31.1178311258$ |
$83.4513069974208$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$56.8360002495$ |
| 3.3.31833.1 |
$x^{3} - 45 x - 111$ |
$3$ |
[3,0] |
$3^{5}\cdot 131$ |
$2$ |
$31.6926963573$ |
$85.77445122024731$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$21.0962388836$ |
| 3.1.32319.1 |
$x^{3} + 9 x - 138$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7\cdot 19$ |
$3$ |
$31.8531684417$ |
$86.42673781058376$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$105.244889483$ |
| 3.1.33048.3 |
$x^{3} - 27 x - 150$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 17$ |
$3$ |
$32.0908874474$ |
$87.39603994602153$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$62.5279615398$ |
| 3.3.34749.1 |
$x^{3} - 36 x - 75$ |
$3$ |
[3,0] |
$3^{5}\cdot 11\cdot 13$ |
$3$ |
$32.6322813712$ |
$89.61698299319946$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$78.7305762266$ |
| 3.1.35235.3 |
$x^{3} + 18 x - 21$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 29$ |
$3$ |
$32.7837094397$ |
$90.2414991411834$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$48.729363107$ |
| 3.3.37665.1 |
$x^{3} - 27 x - 39$ |
$3$ |
[3,0] |
$3^{5}\cdot 5\cdot 31$ |
$3$ |
$33.520667428$ |
$93.30139762871839$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$37.3762527156$ |
| 3.1.38151.1 |
$x^{3} + 27 x - 99$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 157$ |
$2$ |
$33.6642266419$ |
$93.9014128004314$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$7.48719817387$ |
| 3.3.40581.1 |
$x^{3} - 54 x - 99$ |
$3$ |
[3,0] |
$3^{5}\cdot 167$ |
$2$ |
$34.3643063155$ |
$96.84574310800159$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$2$ |
$26.0900678051$ |
| 3.1.41067.2 |
$x^{3} - 39$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 13^{2}$ |
$2$ |
$34.5009451537$ |
$41.433460023567555$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$7.36962811616$ |
| 3.1.41796.1 |
$x^{3} - 18 x - 84$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 43$ |
$3$ |
$34.7038965579$ |
$98.2848374585472$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$23.0410330151$ |
| 3.1.41796.2 |
$x^{3} + 9 x - 78$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 43$ |
$3$ |
$34.7038965579$ |
$98.2848374585472$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$21.8973427486$ |
| 3.1.41796.3 |
$x^{3} - 27 x - 204$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 43$ |
$3$ |
$34.7038965579$ |
$98.2848374585472$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$8.75163668193$ |
| 3.3.43497.1 |
$x^{3} - 45 x - 84$ |
$3$ |
[3,0] |
$3^{5}\cdot 179$ |
$2$ |
$35.1684397729$ |
$100.26487479077532$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$171.686275506$ |
| 3.1.44712.3 |
$x^{3} + 45 x - 114$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{5}\cdot 23$ |
$3$ |
$35.4928901982$ |
$101.65557748063733$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$2$ |
$1$ |
$16.3241095641$ |
| 3.3.46413.1 |
$x^{3} - 54 x - 147$ |
$3$ |
[3,0] |
$3^{5}\cdot 191$ |
$2$ |
$35.937391178$ |
$103.57119423603586$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$74.1121099422$ |
| 3.1.46899.1 |
$x^{3} - 18 x - 51$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 193$ |
$2$ |
$36.0623918059$ |
$104.11203965883807$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$32.9909731168$ |
| 3.1.47628.2 |
$x^{3} - 42$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 7^{2}$ |
$3$ |
$36.2482837079$ |
$43.531903466499294$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.0589054143$ |
| 3.1.49815.1 |
$x^{3} - 27 x - 69$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 41$ |
$3$ |
$36.7948224442$ |
$107.29987866065967$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$19.5114314915$ |
| 3.1.52731.1 |
$x^{3} + 18 x - 33$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7\cdot 31$ |
$3$ |
$37.4991999829$ |
$110.39570244923988$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$29.2426541741$ |
| 3.1.53460.1 |
$x^{3} - 27 x - 144$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{5}\cdot 5\cdot 11$ |
$4$ |
$37.6712170693$ |
$111.15618700247103$ |
|
|
|
$S_3$ (as 3T2) |
$[8]$ |
$2$ |
$1$ |
$12.0952136825$ |
| 3.3.58077.3 |
$x^{3} - 54 x - 63$ |
$3$ |
[3,0] |
$3^{5}\cdot 239$ |
$2$ |
$38.7258885729$ |
$115.85672578730134$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$80.2669304819$ |
| 3.1.58563.3 |
$x^{3} + 9 x - 186$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 241$ |
$2$ |
$38.8336106537$ |
$116.3404720490627$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$59.7721940593$ |
| 3.3.60264.1 |
$x^{3} - 54 x - 120$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{5}\cdot 31$ |
$3$ |
$39.2060104625$ |
$118.01797015351328$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$150.015833783$ |
| 3.1.64395.2 |
$x^{3} - 18 x - 57$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 5\cdot 53$ |
$3$ |
$40.0821229468$ |
$121.99590056201222$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$72.5343997356$ |
| 3.3.66825.2 |
$x^{3} - 45 x - 105$ |
$3$ |
[3,0] |
$3^{5}\cdot 5^{2}\cdot 11$ |
$3$ |
$40.5800884349$ |
$72.6772767594366$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$44.3697036553$ |
| 3.1.67311.1 |
$x^{3} + 63 x - 159$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 277$ |
$2$ |
$40.6782268786$ |
$124.72749060493918$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$29.347747476$ |
