| 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 $p$ |
| 3.1.652.1 |
$x^{3} - x^{2} + 7 x + 5$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 163$ |
$2$ |
$8.67126646029$ |
$20.266579935098292$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.32049906833$ |
$1$ |
$163$ |
| 3.1.815.1 |
$x^{3} - 7 x - 9$ |
$3$ |
(1, 1) |
$-\,5\cdot 163$ |
$2$ |
$9.34083863428$ |
$28.548204847240395$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.06359522663$ |
$1$ |
$163$ |
| 3.3.1304.1 |
$x^{3} - 11 x - 2$ |
$3$ |
(3, 0) |
$2^{3}\cdot 163$ |
$2$ |
$10.9251111426$ |
$36.11094017053558$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$11.9265379008$ |
$3$ |
$163$ |
| 3.1.3912.1 |
$x^{3} - x^{2} - 24$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 163$ |
$3$ |
$15.7567368509$ |
$62.545983084447556$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.1992962751$ |
$1$ |
$163$ |
| 3.1.4075.1 |
$x^{3} - x^{2} - 13 x - 18$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 163$ |
$2$ |
$15.9726093864$ |
$37.331359425307674$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.4332459161$ |
$1$ |
$163$ |
| 3.1.4564.1 |
$x^{3} + x - 26$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 7\cdot 163$ |
$3$ |
$16.587536006$ |
$67.55738301621814$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$10.5244669198$ |
$1$ |
$163$ |
| 3.1.4727.1 |
$x^{3} - x^{2} + 8 x - 13$ |
$3$ |
(1, 1) |
$-\,29\cdot 163$ |
$2$ |
$16.7827013929$ |
$68.75318174455637$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.8469733327$ |
$1$ |
$163$ |
| 3.1.5379.1 |
$x^{3} - x^{2} + 11 x - 8$ |
$3$ |
(1, 1) |
$-\,3\cdot 11\cdot 163$ |
$3$ |
$17.5213345244$ |
$73.34166619323561$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.7727392877$ |
$1$ |
$163$ |
| 3.1.7172.1 |
$x^{3} - x^{2} + 17 x - 25$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 163$ |
$3$ |
$19.2847239677$ |
$84.68766143896052$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.493737034$ |
$1$ |
$163$ |
| 3.1.10595.1 |
$x^{3} - x^{2} - 20 x - 80$ |
$3$ |
(1, 1) |
$-\,5\cdot 13\cdot 163$ |
$3$ |
$21.9634378932$ |
$102.93201639917486$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.9204603191$ |
$1$ |
$163$ |
| 3.1.11084.1 |
$x^{3} + 14 x - 2$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17\cdot 163$ |
$3$ |
$22.296267817$ |
$83.56124974243376$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.53523495451$ |
$1$ |
$163$ |
| 3.1.11899.1 |
$x^{3} - x^{2} + 3 x + 20$ |
$3$ |
(1, 1) |
$-\,73\cdot 163$ |
$2$ |
$22.8298726115$ |
$109.0825375575761$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$29.2384202354$ |
$1$ |
$163$ |
| 3.1.12551.1 |
$x^{3} - x^{2} + 6 x + 19$ |
$3$ |
(1, 1) |
$-\,7\cdot 11\cdot 163$ |
$3$ |
$23.2394641438$ |
$112.03124564156198$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.1968305693$ |
$1$ |
$163$ |
| 3.1.13203.1 |
$x^{3} - 30 x - 67$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 163$ |
$2$ |
$23.6351052764$ |
$55.24022961951863$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.6729762536$ |
$1$ |
$163$ |
| 3.1.14507.1 |
$x^{3} - x^{2} - 7 x - 22$ |
$3$ |
(1, 1) |
$-\,89\cdot 163$ |
$2$ |
$24.3889181962$ |
$120.44500819876264$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.8378219074$ |
$1$ |
$163$ |
| 3.1.15159.1 |
$x^{3} - x^{2} + 4 x - 96$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 163$ |
$3$ |
$24.7489541442$ |
$123.12189082368741$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$83.3116489358$ |
$1$ |
$163$ |
| 3.1.15811.1 |
$x^{3} - 2 x - 121$ |
$3$ |
(1, 1) |
$-\,97\cdot 163$ |
$2$ |
$25.0988089571$ |
$125.7417989373462$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$37.4887182057$ |
$1$ |
$163$ |
| 3.1.16300.1 |
$x^{3} - x^{2} - 13 x + 57$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5^{2}\cdot 163$ |
$3$ |
$25.3549369426$ |
$59.25983922313636$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.96657430526$ |
$1$ |
$163$ |
| 3.1.16300.2 |
$x^{3} - 20 x - 60$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5^{2}\cdot 163$ |
$3$ |
$25.3549369426$ |
$59.25983922313636$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.0780781823$ |
$1$ |
$163$ |
| 3.3.16300.1 |
$x^{3} - x^{2} - 28 x + 62$ |
$3$ |
(3, 0) |
$2^{2}\cdot 5^{2}\cdot 163$ |
$3$ |
$25.3549369426$ |
$74.66271885061535$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$43.186307024$ |
$3$ |
$163$ |
| 3.3.16952.1 |
$x^{3} - 17 x - 10$ |
$3$ |
(3, 0) |
$2^{3}\cdot 13\cdot 163$ |
$3$ |
$25.6885927967$ |
$130.19984639007836$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$62.8299039558$ |
$3$ |
$163$ |
| 3.1.17604.1 |
$x^{3} + 9 x - 50$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 163$ |
$3$ |
$26.0137993809$ |
$91.99521986801201$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$27.2185725462$ |
$1$ |
$163$ |
| 3.1.17767.1 |
$x^{3} - x^{2} - 14 x - 75$ |
$3$ |
(1, 1) |
$-\,109\cdot 163$ |
$2$ |
$26.0938423449$ |
$133.29291053915807$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.4896335432$ |
$1$ |
$163$ |
| 3.1.19723.1 |
$x^{3} - x^{2} - 18 x + 68$ |
$3$ |
(1, 1) |
$-\,11^{2}\cdot 163$ |
$2$ |
$27.0182775192$ |
$63.147417226603835$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$17.0456122167$ |
$1$ |
$163$ |
| 3.3.20212.1 |
$x^{3} - x^{2} - 33 x + 61$ |
$3$ |
(3, 0) |
$2^{2}\cdot 31\cdot 163$ |
$3$ |
$27.2397486901$ |
$112.83954151908624$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$22.8801143478$ |
$2$ |
$163$ |
| 3.3.22005.1 |
$x^{3} - 18 x - 7$ |
$3$ |
(3, 0) |
$3^{3}\cdot 5\cdot 163$ |
$3$ |
$28.0225159028$ |
$102.85378261495704$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$60.9911936566$ |
$2$ |
$163$ |
| 3.1.22168.1 |
$x^{3} + 10 x - 56$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 163$ |
$3$ |
$28.0915371568$ |
$148.889220563478$ |
|
|
|
$S_3$ (as 3T2) |
$[17]$ |
$[17]$ |
$2$ |
$1$ |
$3.60429825157$ |
$1$ |
$163$ |
| 3.3.22168.1 |
$x^{3} - x^{2} - 38 x - 74$ |
$3$ |
(3, 0) |
$2^{3}\cdot 17\cdot 163$ |
$3$ |
$28.0915371568$ |
$148.889220563478$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$48.9496346774$ |
$2$ |
$163$ |
| 3.1.23635.1 |
$x^{3} - x^{2} - x + 30$ |
$3$ |
(1, 1) |
$-\,5\cdot 29\cdot 163$ |
$3$ |
$28.6980157021$ |
$153.73678805022564$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$35.9332117832$ |
$1$ |
$163$ |
| 3.1.24287.1 |
$x^{3} - 13 x - 35$ |
$3$ |
(1, 1) |
$-\,149\cdot 163$ |
$2$ |
$28.9595154473$ |
$155.8428695834365$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.95261109873$ |
$1$ |
$163$ |
| 3.3.25428.1 |
$x^{3} - 42 x - 50$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 13\cdot 163$ |
$4$ |
$29.4060980455$ |
$126.56475112906996$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$68.1174229044$ |
$3$ |
$163$ |
| 3.1.26243.1 |
$x^{3} - x^{2} - 21 x + 108$ |
$3$ |
(1, 1) |
$-\,7\cdot 23\cdot 163$ |
$3$ |
$29.7169677859$ |
$161.99691355084516$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$14.3300106221$ |
$1$ |
$163$ |
| 3.1.26732.1 |
$x^{3} - x^{2} + 27 x + 25$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 163$ |
$3$ |
$29.9004105043$ |
$129.7694291922981$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$7.57816561833$ |
$1$ |
$163$ |
| 3.1.26895.1 |
$x^{3} - 27 x - 109$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 11\cdot 163$ |
$4$ |
$29.9610605904$ |
$163.99695119117305$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.3638024591$ |
$1$ |
$163$ |
| 3.3.27221.1 |
$x^{3} - x^{2} - 29 x + 62$ |
$3$ |
(3, 0) |
$163\cdot 167$ |
$2$ |
$30.0816295377$ |
$164.98787834262248$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$49.2497627945$ |
$2$ |
$167$ |
| 3.1.28199.1 |
$x^{3} - x^{2} + 10 x + 93$ |
$3$ |
(1, 1) |
$-\,163\cdot 173$ |
$2$ |
$30.4376582021$ |
$167.92557875439942$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.4601819918$ |
$1$ |
$173$ |
| 3.1.30155.1 |
$x^{3} - x^{2} - 11 x - 164$ |
$3$ |
(1, 1) |
$-\,5\cdot 37\cdot 163$ |
$3$ |
$31.1257466098$ |
$173.65195075207188$ |
|
|
|
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$10.281513344$ |
$1$ |
$163$ |
| 3.1.30644.1 |
$x^{3} + 26 x - 44$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 47\cdot 163$ |
$3$ |
$31.2930925497$ |
$175.05427729707148$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.9022770404$ |
$1$ |
$163$ |
| 3.1.30807.1 |
$x^{3} - 45 x - 121$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 163$ |
$3$ |
$31.3484786698$ |
$121.69823678873404$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.4262784646$ |
$1$ |
$163$ |
| 3.3.31785.1 |
$x^{3} - x^{2} - 20 x + 15$ |
$3$ |
(3, 0) |
$3\cdot 5\cdot 13\cdot 163$ |
$4$ |
$31.6767588639$ |
$178.28348212888372$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$46.0939887396$ |
$2$ |
$163$ |
| 3.1.33252.1 |
$x^{3} - x^{2} - 39 x - 105$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 17\cdot 163$ |
$4$ |
$32.1567826786$ |
$182.3513092906108$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$81.7210306853$ |
$1$ |
$163$ |
| 3.1.35208.1 |
$x^{3} - 30 x - 96$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 163$ |
$3$ |
$32.7753334277$ |
$130.1008876108374$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$19.6320322496$ |
$1$ |
$163$ |
| 3.1.35208.2 |
$x^{3} + 21 x - 62$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 163$ |
$3$ |
$32.7753334277$ |
$130.1008876108374$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$23.4394686972$ |
$1$ |
$163$ |
| 3.1.35208.3 |
$x^{3} + 15 x - 106$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 163$ |
$3$ |
$32.7753334277$ |
$130.1008876108374$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$8.7168647549$ |
$1$ |
$163$ |
| 3.1.37164.1 |
$x^{3} - x^{2} + 11 x + 31$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 163$ |
$4$ |
$33.371378782$ |
$153.0093230791723$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$33.6606974189$ |
$1$ |
$163$ |
| 3.1.39935.1 |
$x^{3} + 35 x - 175$ |
$3$ |
(1, 1) |
$-\,5\cdot 7^{2}\cdot 163$ |
$3$ |
$34.1809841508$ |
$104.46660900841225$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.10027538624$ |
$1$ |
$163$ |
| 3.1.39935.2 |
$x^{3} - 7 x - 154$ |
$3$ |
(1, 1) |
$-\,5\cdot 7^{2}\cdot 163$ |
$3$ |
$34.1809841508$ |
$104.46660900841225$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$16.5054208887$ |
$1$ |
$163$ |
| 3.1.39935.3 |
$x^{3} - x^{2} - 30 x + 85$ |
$3$ |
(1, 1) |
$-\,5\cdot 7^{2}\cdot 163$ |
$3$ |
$34.1809841508$ |
$104.46660900841225$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.50418731542$ |
$1$ |
$163$ |
| 3.3.40424.1 |
$x^{3} - 29 x - 46$ |
$3$ |
(3, 0) |
$2^{3}\cdot 31\cdot 163$ |
$3$ |
$34.3199327685$ |
$201.05720578979506$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$88.7718258584$ |
$3$ |
$163$ |
| 3.1.41891.1 |
$x^{3} - x^{2} + 15 x + 28$ |
$3$ |
(1, 1) |
$-\,163\cdot 257$ |
$2$ |
$34.7301700088$ |
$204.67290978534507$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$4.59399665675$ |
$1$ |
$257$ |
