| 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 $p$ |
| 3.1.679.1 |
$x^{3} + x - 5$ |
$3$ |
(1, 1) |
$-\,7\cdot 97$ |
$2$ |
$8.78934661221$ |
$26.057628441590765$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.44325590957$ |
$1$ |
$97$ |
| 3.1.1067.1 |
$x^{3} - 4 x - 7$ |
$3$ |
(1, 1) |
$-\,11\cdot 97$ |
$2$ |
$10.2185233064$ |
$32.66496594212215$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.61270164756$ |
$1$ |
$97$ |
| 3.1.1164.1 |
$x^{3} - x^{2} - x + 7$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 97$ |
$3$ |
$10.5192391032$ |
$27.07903342142803$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.88237750613$ |
$1$ |
$97$ |
| 3.1.1843.1 |
$x^{3} - x^{2} + x + 8$ |
$3$ |
(1, 1) |
$-\,19\cdot 97$ |
$2$ |
$12.2605074361$ |
$42.930175867331364$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.93352926928$ |
$1$ |
$97$ |
| 3.3.1940.1 |
$x^{3} - 8 x - 2$ |
$3$ |
(3, 0) |
$2^{2}\cdot 5\cdot 97$ |
$3$ |
$12.4719370448$ |
$34.95888182419493$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$11.0867440113$ |
$2$ |
$97$ |
| 3.1.2619.1 |
$x^{3} + 6 x - 29$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 97$ |
$2$ |
$13.7841026766$ |
$35.4835719013513$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$4.70831127318$ |
$1$ |
$97$ |
| 3.1.3783.1 |
$x^{3} - 9 x - 37$ |
$3$ |
(1, 1) |
$-\,3\cdot 13\cdot 97$ |
$3$ |
$15.5816022429$ |
$61.506097258727124$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.52129628774$ |
$1$ |
$97$ |
| 3.1.3880.1 |
$x^{3} - 2 x - 24$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 97$ |
$3$ |
$15.7136560157$ |
$62.289646009589745$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$22.0645076353$ |
$1$ |
$97$ |
| 3.1.4559.1 |
$x^{3} - x - 13$ |
$3$ |
(1, 1) |
$-\,47\cdot 97$ |
$2$ |
$16.5814764102$ |
$67.52036729757918$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$4.25969373476$ |
$1$ |
$97$ |
| 3.1.4947.1 |
$x^{3} - 6 x - 41$ |
$3$ |
(1, 1) |
$-\,3\cdot 17\cdot 97$ |
$3$ |
$17.0391255695$ |
$70.33491309442275$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$3.74441709373$ |
$1$ |
$97$ |
| 3.1.5432.1 |
$x^{3} + 11 x - 2$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 97$ |
$3$ |
$17.5786932244$ |
$73.70210309075311$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.31856543208$ |
$1$ |
$97$ |
| 3.3.5529.1 |
$x^{3} - x^{2} - 20 x + 39$ |
$3$ |
(3, 0) |
$3\cdot 19\cdot 97$ |
$3$ |
$17.6827115815$ |
$74.35724578008521$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$13.7765006432$ |
$3$ |
$97$ |
| 3.1.6596.1 |
$x^{3} - x^{2} + x + 31$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 17\cdot 97$ |
$3$ |
$18.7539843385$ |
$81.21576201698781$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.9483500234$ |
$1$ |
$97$ |
| 3.1.6887.1 |
$x^{3} - x^{2} + 4 x - 17$ |
$3$ |
(1, 1) |
$-\,71\cdot 97$ |
$2$ |
$19.0258190077$ |
$82.98795093265046$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.43467017021$ |
$1$ |
$97$ |
| 3.1.8148.1 |
$x^{3} - x^{2} + 16 x + 60$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 7\cdot 97$ |
$4$ |
$20.1225804995$ |
$90.26627277117406$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$40.0037733075$ |
$1$ |
$97$ |
| 3.1.8827.1 |
$x^{3} + 25 x - 54$ |
$3$ |
(1, 1) |
$-\,7\cdot 13\cdot 97$ |
$3$ |
$20.6666955717$ |
$93.95211546314431$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.4131938273$ |
$1$ |
$97$ |
| 3.1.9700.1 |
$x^{3} - x^{2} + 17 x - 33$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5^{2}\cdot 97$ |
$3$ |
$21.3267123551$ |
$57.59646982717597$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$6.31551166272$ |
$1$ |
$97$ |
| 3.1.10088.1 |
$x^{3} - x^{2} - 7 x - 37$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 13\cdot 97$ |
$3$ |
$21.6073591751$ |
$100.43903623591775$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.8431598226$ |
$1$ |
$97$ |
| 3.1.10476.1 |
$x^{3} + 24 x - 38$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 97$ |
$3$ |
$21.8808990893$ |
$56.3266593637943$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.71123099358$ |
$1$ |
$97$ |
| 3.1.10476.2 |
$x^{3} - 24 x - 60$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 97$ |
$3$ |
$21.8808990893$ |
$56.3266593637943$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.22710030291$ |
$1$ |
$97$ |
| 3.1.11155.1 |
$x^{3} - x^{2} + 4 x + 80$ |
$3$ |
(1, 1) |
$-\,5\cdot 23\cdot 97$ |
$3$ |
$22.3437737379$ |
$105.61723344227494$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$13.8975586392$ |
$1$ |
$97$ |
| 3.1.11252.1 |
$x^{3} - x^{2} - 16 x + 38$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 29\cdot 97$ |
$3$ |
$22.4083514777$ |
$106.07544484940895$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$11.9860429667$ |
$1$ |
$97$ |
| 3.1.12319.1 |
$x^{3} - x^{2} - 10 x + 48$ |
$3$ |
(1, 1) |
$-\,97\cdot 127$ |
$2$ |
$23.095382097$ |
$110.99099062536563$ |
|
|
|
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$9.45336488663$ |
$1$ |
$127$ |
| 3.1.13095.1 |
$x^{3} + 3 x - 44$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 5\cdot 97$ |
$3$ |
$23.5704840235$ |
$79.34367885592297$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$69.3145184854$ |
$1$ |
$97$ |
| 3.1.13580.1 |
$x^{3} + 8 x - 44$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 7\cdot 97$ |
$4$ |
$23.8579572826$ |
$92.49250741971584$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$22.4471338427$ |
$1$ |
$97$ |
| 3.1.15423.1 |
$x^{3} - x^{2} - 14 x - 27$ |
$3$ |
(1, 1) |
$-\,3\cdot 53\cdot 97$ |
$3$ |
$24.8917990444$ |
$124.18937152590796$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.5988258331$ |
$1$ |
$97$ |
| 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 |
$2$ |
$1$ |
$37.4887182057$ |
$1$ |
$163$ |
| 3.1.16684.1 |
$x^{3} - x^{2} + 33 x + 9$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 43\cdot 97$ |
$3$ |
$25.5524998097$ |
$102.51956592876812$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$23.5679655413$ |
$1$ |
$97$ |
| 3.3.16684.1 |
$x^{3} - x^{2} - 36 x - 56$ |
$3$ |
(3, 0) |
$2^{2}\cdot 43\cdot 97$ |
$3$ |
$25.5524998097$ |
$129.1665591397402$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$38.3678945092$ |
$2$ |
$97$ |
| 3.3.18333.1 |
$x^{3} - 24 x - 37$ |
$3$ |
(3, 0) |
$3^{3}\cdot 7\cdot 97$ |
$3$ |
$26.3680398366$ |
$93.88070687925487$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$46.5821817731$ |
$3$ |
$97$ |
| 3.1.18527.1 |
$x^{3} - x^{2} + 12 x - 81$ |
$3$ |
(1, 1) |
$-\,97\cdot 191$ |
$2$ |
$26.4607226368$ |
$136.11392287345186$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$5.28392456173$ |
$1$ |
$191$ |
| 3.1.18915.1 |
$x^{3} - 12 x - 81$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 13\cdot 97$ |
$4$ |
$26.644165046$ |
$137.5318145012273$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$48.1706869301$ |
$1$ |
$97$ |
| 3.1.19012.1 |
$x^{3} - 35 x - 84$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 7^{2}\cdot 97$ |
$3$ |
$26.6896329926$ |
$72.07996318263355$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$15.9168049521$ |
$1$ |
$97$ |
| 3.1.19303.1 |
$x^{3} - x^{2} + 32 x + 31$ |
$3$ |
(1, 1) |
$-\,97\cdot 199$ |
$2$ |
$26.8251156846$ |
$138.93523671121017$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.1169564738$ |
$1$ |
$199$ |
| 3.3.19885.1 |
$x^{3} - 22 x - 29$ |
$3$ |
(3, 0) |
$5\cdot 41\cdot 97$ |
$3$ |
$27.0920497914$ |
$141.01418368376991$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$38.1472934675$ |
$2$ |
$97$ |
| 3.1.20564.1 |
$x^{3} - 22 x - 68$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 53\cdot 97$ |
$3$ |
$27.3969698462$ |
$143.4015341619468$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$22.4533221963$ |
$1$ |
$97$ |
| 3.1.20952.1 |
$x^{3} - 6 x - 56$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 97$ |
$3$ |
$27.5682053532$ |
$100.36269724866376$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$50.7124074892$ |
$1$ |
$97$ |
| 3.1.22407.1 |
$x^{3} - x^{2} - 8 x + 33$ |
$3$ |
(1, 1) |
$-\,3\cdot 7\cdot 11\cdot 97$ |
$4$ |
$28.1921309969$ |
$149.68967900292927$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$12.4239985974$ |
$1$ |
$97$ |
| 3.1.22504.1 |
$x^{3} - x^{2} + 18 x - 10$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 29\cdot 97$ |
$3$ |
$28.2327537202$ |
$150.0133327407934$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$31.0098971751$ |
$1$ |
$97$ |
| 3.1.22892.1 |
$x^{3} - x^{2} + 15 x - 59$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 59\cdot 97$ |
$3$ |
$28.3940872436$ |
$120.08770268889616$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$7.90212918006$ |
$1$ |
$97$ |
| 3.3.23377.1 |
$x^{3} - x^{2} - 44 x - 95$ |
$3$ |
(3, 0) |
$97\cdot 241$ |
$2$ |
$28.5932107705$ |
$152.8953890737062$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$6.33375227157$ |
$2$ |
$241$ |
| 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 |
trivial |
$2$ |
$1$ |
$48.3704191613$ |
$1$ |
$97$ |
| 3.1.23571.2 |
$x^{3} + 18 x - 3$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 97$ |
$2$ |
$28.6720889929$ |
$73.80880389609993$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$6.47850256696$ |
$1$ |
$97$ |
| 3.1.23571.3 |
$x^{3} + 27 x - 24$ |
$3$ |
(1, 1) |
$-\,3^{5}\cdot 97$ |
$2$ |
$28.6720889929$ |
$73.80880389609993$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.7895542707$ |
$1$ |
$97$ |
| 3.3.23668.1 |
$x^{3} - x^{2} - 29 x + 25$ |
$3$ |
(3, 0) |
$2^{2}\cdot 61\cdot 97$ |
$3$ |
$28.7113658763$ |
$122.10612476225724$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$23.6182775347$ |
$3$ |
$97$ |
| 3.1.24056.1 |
$x^{3} - x^{2} + 29 x - 1$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 31\cdot 97$ |
$3$ |
$28.8674089726$ |
$155.09996776273036$ |
|
|
|
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$3.36614583666$ |
$1$ |
$97$ |
| 3.1.24347.1 |
$x^{3} - x^{2} - 28 x - 124$ |
$3$ |
(1, 1) |
$-\,97\cdot 251$ |
$2$ |
$28.9833435861$ |
$156.03525242713584$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.5543946221$ |
$1$ |
$251$ |
| 3.1.24735.1 |
$x^{3} + 27 x - 73$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 17\cdot 97$ |
$4$ |
$29.1364948763$ |
$157.27364687066935$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$5.90804603512$ |
$1$ |
$97$ |
| 3.1.25220.1 |
$x^{3} - x^{2} - 20 x - 180$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 13\cdot 97$ |
$4$ |
$29.3256981965$ |
$158.80806024884254$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$101.605022983$ |
$1$ |
$97$ |
| 3.3.25705.1 |
$x^{3} - x^{2} - 30 x - 8$ |
$3$ |
(3, 0) |
$5\cdot 53\cdot 97$ |
$3$ |
$29.5124911192$ |
$160.3277892319357$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$101.930781136$ |
$3$ |
$97$ |
