| 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 $p$ |
| 3.1.1351.1 |
$x^{3} - x^{2} - 7$ |
$3$ |
(1, 1) |
$-\,7\cdot 193$ |
$2$ |
$11.0548227346$ |
$36.75595189897821$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.5340812844$ |
$1$ |
$193$ |
| 3.1.2316.1 |
$x^{3} - x^{2} + x + 9$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 193$ |
$3$ |
$13.2305993516$ |
$38.1967089652795$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.8139641808$ |
$1$ |
$193$ |
| 3.1.2895.1 |
$x^{3} + 3 x - 31$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 193$ |
$3$ |
$14.2522311065$ |
$53.80520420925842$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.23722212582$ |
$1$ |
$193$ |
| 3.3.3281.1 |
$x^{3} - x^{2} - 14 x - 13$ |
$3$ |
(3, 0) |
$17\cdot 193$ |
$2$ |
$14.8594274805$ |
$57.28001396647874$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$7.45000920901$ |
$3$ |
$193$ |
| 3.1.4632.1 |
$x^{3} - x^{2} + 17 x - 5$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 193$ |
$3$ |
$16.6695106258$ |
$68.05879810869422$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.4997634548$ |
$1$ |
$193$ |
| 3.3.4825.1 |
$x^{3} - x^{2} - 18 x - 8$ |
$3$ |
(3, 0) |
$5^{2}\cdot 193$ |
$2$ |
$16.8978884656$ |
$40.621752652279945$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$36.3964999556$ |
$2$ |
$193$ |
| 3.1.5211.1 |
$x^{3} - 6 x - 15$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 193$ |
$2$ |
$17.3369896955$ |
$50.05184815392902$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.937704382$ |
$1$ |
$193$ |
| 3.1.8492.1 |
$x^{3} - 4 x - 18$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 193$ |
$3$ |
$20.4018709036$ |
$73.14112918087628$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$15.2345932099$ |
$1$ |
$193$ |
| 3.1.9071.1 |
$x^{3} - x^{2} + 8 x - 19$ |
$3$ |
(1, 1) |
$-\,47\cdot 193$ |
$2$ |
$20.8553935214$ |
$95.24179754708538$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$2.75272362745$ |
$1$ |
$193$ |
| 3.1.9843.1 |
$x^{3} - x^{2} + 11 x + 10$ |
$3$ |
(1, 1) |
$-\,3\cdot 17\cdot 193$ |
$3$ |
$21.4310028987$ |
$99.21189444819608$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$15.2145212229$ |
$1$ |
$193$ |
| 3.1.10615.1 |
$x^{3} - x^{2} - 10 x + 27$ |
$3$ |
(1, 1) |
$-\,5\cdot 11\cdot 193$ |
$3$ |
$21.9772492082$ |
$103.02912209661888$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.6374486927$ |
$1$ |
$193$ |
| 3.1.10808.1 |
$x^{3} + 2 x - 40$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 193$ |
$3$ |
$22.1096454692$ |
$103.96153134693621$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.8600363572$ |
$1$ |
$193$ |
| 3.3.14089.1 |
$x^{3} - x^{2} - 22 x + 41$ |
$3$ |
(3, 0) |
$73\cdot 193$ |
$2$ |
$24.1523868605$ |
$118.69709347747316$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$7.0215106937$ |
$2$ |
$193$ |
| 3.1.14668.1 |
$x^{3} - x^{2} + 29 x - 47$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 19\cdot 193$ |
$3$ |
$24.478809944$ |
$96.12627622002738$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$23.1721229145$ |
$1$ |
$193$ |
| 3.3.14668.1 |
$x^{3} - x^{2} - 28 x + 44$ |
$3$ |
(3, 0) |
$2^{2}\cdot 19\cdot 193$ |
$3$ |
$24.478809944$ |
$121.11151885762146$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$44.4546201216$ |
$2$ |
$193$ |
| 3.1.16019.1 |
$x^{3} - x^{2} - 21 x - 38$ |
$3$ |
(1, 1) |
$-\,83\cdot 193$ |
$2$ |
$25.2083914273$ |
$126.56618821786489$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.6839080299$ |
$1$ |
$193$ |
| 3.1.16984.1 |
$x^{3} - x^{2} - 32 x - 76$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 193$ |
$3$ |
$25.7047466087$ |
$130.3226764611593$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$43.5339028812$ |
$1$ |
$193$ |
| 3.1.19300.1 |
$x^{3} - x^{2} - 8 x - 78$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5^{2}\cdot 193$ |
$3$ |
$26.8237259263$ |
$81.24350530455989$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.9660857236$ |
$1$ |
$193$ |
| 3.1.20651.1 |
$x^{3} - x^{2} + 20 x - 112$ |
$3$ |
(1, 1) |
$-\,107\cdot 193$ |
$2$ |
$27.4355515573$ |
$143.7045580348793$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.7682881823$ |
$1$ |
$193$ |
| 3.1.20844.1 |
$x^{3} + 12 x - 138$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 193$ |
$3$ |
$27.5207556805$ |
$79.45235641249951$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$10.5096872292$ |
$1$ |
$193$ |
| 3.1.20844.2 |
$x^{3} + 24 x - 70$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 193$ |
$3$ |
$27.5207556805$ |
$79.45235641249951$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.6391945297$ |
$1$ |
$193$ |
| 3.3.21809.1 |
$x^{3} - x^{2} - 40 x - 81$ |
$3$ |
(3, 0) |
$113\cdot 193$ |
$2$ |
$27.9390681805$ |
$147.6787053031005$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$16.1428392525$ |
$2$ |
$193$ |
| 3.1.22195.1 |
$x^{3} - x^{2} + 5 x - 30$ |
$3$ |
(1, 1) |
$-\,5\cdot 23\cdot 193$ |
$3$ |
$28.1029374301$ |
$148.9798644112687$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$10.2616866976$ |
$1$ |
$193$ |
| 3.1.22967.1 |
$x^{3} + 23 x - 40$ |
$3$ |
(1, 1) |
$-\,7\cdot 17\cdot 193$ |
$3$ |
$28.4250621855$ |
$151.5486720496092$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$69.0731242478$ |
$1$ |
$193$ |
| 3.3.23353.1 |
$x^{3} - x^{2} - 18 x + 13$ |
$3$ |
(3, 0) |
$11^{2}\cdot 193$ |
$2$ |
$28.5834223455$ |
$68.71324277225357$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$15.233994078$ |
$3$ |
$193$ |
| 3.1.25283.1 |
$x^{3} + 2 x - 153$ |
$3$ |
(1, 1) |
$-\,131\cdot 193$ |
$2$ |
$29.3500965938$ |
$159.00628918379297$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$64.3555243938$ |
$1$ |
$193$ |
| 3.1.25476.1 |
$x^{3} - x^{2} + 36 x - 54$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 11\cdot 193$ |
$4$ |
$29.4245895442$ |
$159.6120296218302$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$29.3549627517$ |
$1$ |
$193$ |
| 3.1.26248.1 |
$x^{3} - x^{2} + 17 x + 51$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 193$ |
$3$ |
$29.7188549609$ |
$162.01234520862909$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$49.5281287056$ |
$1$ |
$193$ |
| 3.1.27020.1 |
$x^{3} + 32 x - 142$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 7\cdot 193$ |
$4$ |
$30.0074055792$ |
$130.46659872963554$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$28.8409803226$ |
$1$ |
$193$ |
| 3.3.27213.1 |
$x^{3} - x^{2} - 33 x + 78$ |
$3$ |
(3, 0) |
$3\cdot 47\cdot 193$ |
$3$ |
$30.0786823448$ |
$164.96363235574077$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$69.8448138597$ |
$3$ |
$193$ |
| 3.1.28371.1 |
$x^{3} - x^{2} - 37 x + 106$ |
$3$ |
(1, 1) |
$-\,3\cdot 7^{2}\cdot 193$ |
$3$ |
$30.4994177081$ |
$88.05174662535941$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.93538558687$ |
$1$ |
$193$ |
| 3.1.28564.1 |
$x^{3} - x^{2} + 21 x - 61$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 37\cdot 193$ |
$3$ |
$30.5684211508$ |
$169.00887550658396$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$75.4303154331$ |
$1$ |
$193$ |
| 3.1.29915.1 |
$x^{3} - x^{2} + 29 x + 146$ |
$3$ |
(1, 1) |
$-\,5\cdot 31\cdot 193$ |
$3$ |
$31.0429512153$ |
$172.9595328393321$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$31.7950192072$ |
$1$ |
$193$ |
| 3.1.30687.1 |
$x^{3} - x^{2} - 2 x - 33$ |
$3$ |
(1, 1) |
$-\,3\cdot 53\cdot 193$ |
$3$ |
$31.3077226468$ |
$175.17705329180532$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$35.7153374263$ |
$1$ |
$193$ |
| 3.1.31652.1 |
$x^{3} - x^{2} + 48 x - 68$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 193$ |
$3$ |
$31.6325147353$ |
$177.9100896520487$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$36.784138016$ |
$1$ |
$193$ |
| 3.1.33196.1 |
$x^{3} - 32 x - 78$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 193$ |
$3$ |
$32.1387206905$ |
$144.61040621668658$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.6535713858$ |
$1$ |
$193$ |
| 3.1.35319.1 |
$x^{3} - 9 x - 109$ |
$3$ |
(1, 1) |
$-\,3\cdot 61\cdot 193$ |
$3$ |
$32.8097408111$ |
$187.9334988765973$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.2676202882$ |
$1$ |
$193$ |
| 3.3.36477.1 |
$x^{3} - 48 x - 65$ |
$3$ |
(3, 0) |
$3^{3}\cdot 7\cdot 193$ |
$3$ |
$33.1644682038$ |
$132.42474287446353$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$71.6118594825$ |
$3$ |
$193$ |
| 3.1.38407.1 |
$x^{3} - x^{2} - 2 x - 37$ |
$3$ |
(1, 1) |
$-\,193\cdot 199$ |
$2$ |
$33.7393564975$ |
$195.97703947146462$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.7025736369$ |
$1$ |
$199$ |
| 3.1.41495.1 |
$x^{3} - x^{2} + 64 x - 35$ |
$3$ |
(1, 1) |
$-\,5\cdot 43\cdot 193$ |
$3$ |
$34.6203873744$ |
$203.70321548763044$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.0750713048$ |
$1$ |
$193$ |
| 3.1.42267.1 |
$x^{3} - x^{2} - 15 x + 126$ |
$3$ |
(1, 1) |
$-\,3\cdot 73\cdot 193$ |
$3$ |
$34.8337695714$ |
$205.5893966137359$ |
|
|
|
$S_3$ (as 3T2) |
$[8]$ |
$[8]$ |
$2$ |
$1$ |
$7.91718526966$ |
$1$ |
$193$ |
| 3.1.44004.1 |
$x^{3} + 9 x - 242$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 193$ |
$4$ |
$35.3045531234$ |
$209.77130404323657$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$26.0665573203$ |
$1$ |
$193$ |
| 3.1.44004.2 |
$x^{3} - 18 x - 244$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 193$ |
$4$ |
$35.3045531234$ |
$209.77130404323657$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$28.6821975302$ |
$1$ |
$193$ |
| 3.1.44004.3 |
$x^{3} - x^{2} - 52 x + 184$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 193$ |
$4$ |
$35.3045531234$ |
$209.77130404323657$ |
|
|
|
$S_3$ (as 3T2) |
$[21]$ |
$[21]$ |
$2$ |
$1$ |
$4.39307647346$ |
$1$ |
$193$ |
| 3.1.44004.4 |
$x^{3} - x^{2} + x - 81$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 193$ |
$4$ |
$35.3045531234$ |
$209.77130404323657$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$42.1205586456$ |
$1$ |
$193$ |
| 3.1.45355.1 |
$x^{3} - 2 x - 41$ |
$3$ |
(1, 1) |
$-\,5\cdot 47\cdot 193$ |
$3$ |
$35.66222128$ |
$212.96713361455565$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$54.9173230974$ |
$1$ |
$193$ |
| 3.1.45548.1 |
$x^{3} - 28 x - 100$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 59\cdot 193$ |
$3$ |
$35.7127344088$ |
$169.39138700154103$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.8106049919$ |
$1$ |
$193$ |
| 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 |
trivial |
$2$ |
$1$ |
$32.9909731168$ |
$1$ |
$193$ |
| 3.1.46899.2 |
$x^{3} - 36 x - 93$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 193$ |
$2$ |
$36.0623918059$ |
$104.11203965883807$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$29.9331897748$ |
$1$ |
$193$ |
| 3.1.46899.3 |
$x^{3} - 9 x - 84$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 193$ |
$2$ |
$36.0623918059$ |
$104.11203965883807$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.0290940806$ |
$1$ |
$193$ |
