| 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 $p$ |
| 3.1.356.1 |
$x^{3} - x^{2} + x + 7$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 89$ |
$2$ |
$7.0873410615$ |
$18.867962264113206$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.75521003542$ |
$1$ |
$89$ |
| 3.1.1068.1 |
$x^{3} - x^{2} - x + 13$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 89$ |
$3$ |
$10.2217146006$ |
$25.93834691424768$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.16938023975$ |
$1$ |
$89$ |
| 3.1.1691.1 |
$x^{3} - x^{2} + x - 24$ |
$3$ |
(1, 1) |
$-\,19\cdot 89$ |
$2$ |
$11.9137331742$ |
$41.12177038990418$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.2275307861$ |
$1$ |
$89$ |
| 3.1.2047.1 |
$x^{3} + 7 x - 5$ |
$3$ |
(1, 1) |
$-\,23\cdot 89$ |
$2$ |
$12.6971411508$ |
$45.24378410345447$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.31855543785$ |
$1$ |
$89$ |
| 3.1.2403.1 |
$x^{3} - 6 x - 11$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 89$ |
$2$ |
$13.3942352868$ |
$33.98884972775975$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.2990036664$ |
$1$ |
$89$ |
| 3.1.2759.1 |
$x^{3} - x^{2} + 4 x - 11$ |
$3$ |
(1, 1) |
$-\,31\cdot 89$ |
$2$ |
$14.0254638611$ |
$52.52618394667559$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$2.44889225965$ |
$1$ |
$89$ |
| 3.1.3115.1 |
$x^{3} - x^{2} - 5 x - 10$ |
$3$ |
(1, 1) |
$-\,5\cdot 7\cdot 89$ |
$3$ |
$14.6044772657$ |
$55.812185049503306$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.3337029794$ |
$1$ |
$89$ |
| 3.1.3471.1 |
$x^{3} - x^{2} + 6 x - 24$ |
$3$ |
(1, 1) |
$-\,3\cdot 13\cdot 89$ |
$3$ |
$15.1408946583$ |
$58.915193286621744$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$33.3613959484$ |
$1$ |
$89$ |
| 3.1.3560.1 |
$x^{3} - x^{2} - 11 x + 31$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 89$ |
$3$ |
$15.269213443$ |
$59.665735560705194$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.4341727951$ |
$1$ |
$89$ |
| 3.1.3916.1 |
$x^{3} - x^{2} + 3 x + 11$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 89$ |
$3$ |
$15.7621054159$ |
$49.66815293217739$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$12.2557528981$ |
$1$ |
$89$ |
| 3.3.4628.1 |
$x^{3} - x^{2} - 13 x - 9$ |
$3$ |
(3, 0) |
$2^{2}\cdot 13\cdot 89$ |
$3$ |
$16.6647108816$ |
$53.99497485374668$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$16.7152101414$ |
$3$ |
$89$ |
| 3.3.5073.1 |
$x^{3} - x^{2} - 18 x + 33$ |
$3$ |
(3, 0) |
$3\cdot 19\cdot 89$ |
$3$ |
$17.1825765512$ |
$71.22499561249548$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$14.2864682842$ |
$2$ |
$89$ |
| 3.1.5963.1 |
$x^{3} - x^{2} + 11 x - 10$ |
$3$ |
(1, 1) |
$-\,67\cdot 89$ |
$2$ |
$18.1337769619$ |
$77.22046360907191$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$2.4713308177$ |
$1$ |
$89$ |
| 3.1.6675.1 |
$x^{3} - x^{2} + 7 x + 12$ |
$3$ |
(1, 1) |
$-\,3\cdot 5^{2}\cdot 89$ |
$3$ |
$18.8285592793$ |
$47.77884352737507$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.0659240733$ |
$1$ |
$89$ |
| 3.1.7031.1 |
$x^{3} - x^{2} + 18 x - 45$ |
$3$ |
(1, 1) |
$-\,79\cdot 89$ |
$2$ |
$19.1575087525$ |
$83.85105843100611$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.7096002661$ |
$1$ |
$89$ |
| 3.3.8277.1 |
$x^{3} - x^{2} - 22 x + 28$ |
$3$ |
(3, 0) |
$3\cdot 31\cdot 89$ |
$3$ |
$20.2282192271$ |
$90.97801932335085$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$35.3501486324$ |
$3$ |
$89$ |
| 3.1.9167.1 |
$x^{3} - x^{2} + 2 x - 19$ |
$3$ |
(1, 1) |
$-\,89\cdot 103$ |
$2$ |
$20.9287076026$ |
$95.74445153636842$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.24134216561$ |
$1$ |
$103$ |
| 3.1.9523.1 |
$x^{3} - x^{2} - 3 x + 20$ |
$3$ |
(1, 1) |
$-\,89\cdot 107$ |
$2$ |
$21.196196066$ |
$97.58585963140357$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.257594399$ |
$1$ |
$107$ |
| 3.1.9612.1 |
$x^{3} + 12 x - 10$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 89$ |
$3$ |
$21.2620231845$ |
$53.95393581303488$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.80843997917$ |
$1$ |
$89$ |
| 3.1.9612.2 |
$x^{3} + 24 x - 34$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 89$ |
$3$ |
$21.2620231845$ |
$53.95393581303488$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.60910937229$ |
$1$ |
$89$ |
| 3.3.9612.1 |
$x^{3} - 15 x - 12$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3^{3}\cdot 89$ |
$3$ |
$21.2620231845$ |
$67.9776994555195$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$41.0496580113$ |
$2$ |
$89$ |
| 3.1.10324.1 |
$x^{3} - 14 x - 44$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 29\cdot 89$ |
$3$ |
$21.7745571926$ |
$101.6070863670443$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$29.8651021081$ |
$1$ |
$89$ |
| 3.3.10324.1 |
$x^{3} - x^{2} - 29 x + 27$ |
$3$ |
(3, 0) |
$2^{2}\cdot 29\cdot 89$ |
$3$ |
$21.7745571926$ |
$80.6455978932349$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$41.2769285833$ |
$3$ |
$89$ |
| 3.1.11748.1 |
$x^{3} - x^{2} - 8 x + 66$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 11\cdot 89$ |
$4$ |
$22.7328897632$ |
$108.38819123871383$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$48.1693070998$ |
$1$ |
$89$ |
| 3.1.12015.1 |
$x^{3} + 3 x - 21$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 5\cdot 89$ |
$3$ |
$22.9038201645$ |
$76.00137846829602$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.4870473858$ |
$1$ |
$89$ |
| 3.1.12104.1 |
$x^{3} - x^{2} + 16 x + 76$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 89$ |
$3$ |
$22.9602337425$ |
$110.01818031580054$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$20.3973495286$ |
$1$ |
$89$ |
| 3.1.12727.1 |
$x^{3} - x^{2} + 6 x + 63$ |
$3$ |
(1, 1) |
$-\,11\cdot 13\cdot 89$ |
$3$ |
$23.3475876621$ |
$112.81400622263178$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.3151822065$ |
$1$ |
$89$ |
| 3.3.13172.1 |
$x^{3} - 26 x - 46$ |
$3$ |
(3, 0) |
$2^{2}\cdot 37\cdot 89$ |
$3$ |
$23.6165927552$ |
$91.09248066996328$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$29.4583124183$ |
$3$ |
$89$ |
| 3.1.13439.1 |
$x^{3} - 13 x - 113$ |
$3$ |
(1, 1) |
$-\,89\cdot 151$ |
$2$ |
$23.7750981216$ |
$115.92670097954138$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.67229137205$ |
$1$ |
$151$ |
| 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 |
$2$ |
$1$ |
$14.8378219074$ |
$1$ |
$163$ |
| 3.1.14863.1 |
$x^{3} + 13 x - 15$ |
$3$ |
(1, 1) |
$-\,89\cdot 167$ |
$2$ |
$24.5868085355$ |
$121.91390404707742$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$2.78433972654$ |
$1$ |
$167$ |
| 3.1.14952.1 |
$x^{3} - x^{2} + 2 x + 70$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 7\cdot 89$ |
$4$ |
$24.6357863712$ |
$122.27837094106218$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$58.3841721388$ |
$1$ |
$89$ |
| 3.1.15308.1 |
$x^{3} - x^{2} - 3 x + 25$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 89$ |
$3$ |
$24.8297769282$ |
$98.20099651172262$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$8.74877965544$ |
$1$ |
$89$ |
| 3.1.15575.1 |
$x^{3} - x^{2} - 8 x - 23$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 7\cdot 89$ |
$3$ |
$24.9733048382$ |
$72.98338902721571$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.08114019341$ |
$1$ |
$89$ |
| 3.1.15931.1 |
$x^{3} - x^{2} + 15 x - 16$ |
$3$ |
(1, 1) |
$-\,89\cdot 179$ |
$2$ |
$25.1621460724$ |
$126.21806526801146$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[8]$ |
$[8]$ |
$2$ |
$1$ |
$2.78054781595$ |
$1$ |
$179$ |
| 3.1.16287.1 |
$x^{3} - 15 x - 77$ |
$3$ |
(1, 1) |
$-\,3\cdot 61\cdot 89$ |
$3$ |
$25.3481945736$ |
$127.62053126358627$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$12.3131047684$ |
$1$ |
$89$ |
| 3.1.16376.1 |
$x^{3} - x^{2} + 6 x - 26$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 23\cdot 89$ |
$3$ |
$25.3942823016$ |
$127.96874618437113$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$39.2487360672$ |
$1$ |
$89$ |
| 3.3.16376.1 |
$x^{3} - x^{2} - 40 x - 72$ |
$3$ |
(3, 0) |
$2^{3}\cdot 23\cdot 89$ |
$3$ |
$25.3942823016$ |
$127.96874618437113$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$53.787870419$ |
$3$ |
$89$ |
| 3.1.16999.1 |
$x^{3} - x^{2} + 16 x - 13$ |
$3$ |
(1, 1) |
$-\,89\cdot 191$ |
$2$ |
$25.7123117238$ |
$130.3802132227126$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.3370539269$ |
$1$ |
$191$ |
| 3.1.17800.1 |
$x^{3} - x^{2} - 3 x - 153$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 89$ |
$3$ |
$26.1099877122$ |
$78.02252476156511$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.1991702637$ |
$1$ |
$89$ |
| 3.3.17800.1 |
$x^{3} - x^{2} - 18 x + 22$ |
$3$ |
(3, 0) |
$2^{3}\cdot 5^{2}\cdot 89$ |
$3$ |
$26.1099877122$ |
$78.02252476156511$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$45.0496156495$ |
$2$ |
$89$ |
| 3.3.17889.1 |
$x^{3} - x^{2} - 30 x + 69$ |
$3$ |
(3, 0) |
$3\cdot 67\cdot 89$ |
$3$ |
$26.1534320314$ |
$133.7497663549361$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$22.4985823721$ |
$3$ |
$89$ |
| 3.1.18156.1 |
$x^{3} - 24 x - 90$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 17\cdot 89$ |
$4$ |
$26.2829065774$ |
$106.9465440813571$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$40.6290819972$ |
$1$ |
$89$ |
| 3.1.18779.1 |
$x^{3} + 14 x - 17$ |
$3$ |
(1, 1) |
$-\,89\cdot 211$ |
$2$ |
$26.5801536626$ |
$137.03649149040558$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.5539522649$ |
$1$ |
$211$ |
| 3.1.18868.1 |
$x^{3} - x^{2} + 4 x + 78$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 53\cdot 89$ |
$3$ |
$26.6220782646$ |
$137.3608386695422$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$43.3264566525$ |
$1$ |
$89$ |
| 3.1.19224.1 |
$x^{3} + 27 x - 122$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 89$ |
$3$ |
$26.7884705735$ |
$96.13498450891784$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$58.0561057242$ |
$1$ |
$89$ |
| 3.1.19847.1 |
$x^{3} - x^{2} - 18 x - 56$ |
$3$ |
(1, 1) |
$-\,89\cdot 223$ |
$2$ |
$27.0747812577$ |
$140.87938103214395$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$60.2093602895$ |
$1$ |
$223$ |
| 3.1.20292.1 |
$x^{3} - x^{2} - 16 x - 134$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 89$ |
$4$ |
$27.2756400929$ |
$142.44999122499095$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$56.4525671366$ |
$1$ |
$89$ |
| 3.3.20381.1 |
$x^{3} - 26 x - 43$ |
$3$ |
(3, 0) |
$89\cdot 229$ |
$2$ |
$27.3154586022$ |
$142.76203977248295$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$36.5161764746$ |
$3$ |
$229$ |
| 3.1.20915.1 |
$x^{3} + 23 x - 36$ |
$3$ |
(1, 1) |
$-\,5\cdot 47\cdot 89$ |
$3$ |
$27.5519678481$ |
$144.62019222777985$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$63.9456953871$ |
$1$ |
$89$ |
