| 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 $p$ |
| 3.1.199.1 |
$x^{3} - x^{2} + 4 x - 1$ |
$3$ |
(1, 1) |
$-\,199$ |
$1$ |
$5.83827246081$ |
$14.106735979665885$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$1.33665777698$ |
$1$ |
$199$ |
| 3.1.2388.1 |
$x^{3} - x^{2} + 13 x + 3$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 199$ |
$3$ |
$13.3663072756$ |
$48.86716689148246$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.6714440459$ |
$1$ |
$199$ |
| 3.1.3980.1 |
$x^{3} - x^{2} - 5 x - 23$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 199$ |
$3$ |
$15.8475096181$ |
$50.07237650931697$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.04581689677$ |
$1$ |
$199$ |
| 3.3.5373.1 |
$x^{3} - 21 x - 24$ |
$3$ |
(3, 0) |
$3^{3}\cdot 199$ |
$2$ |
$17.5148173824$ |
$50.82390166467514$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$21.3092644592$ |
$2$ |
$199$ |
| 3.1.7960.1 |
$x^{3} - x^{2} - 10 x - 18$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5\cdot 199$ |
$3$ |
$19.9666109563$ |
$89.21883209278185$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$33.2650945864$ |
$1$ |
$199$ |
| 3.1.8756.1 |
$x^{3} + 2 x - 36$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 11\cdot 199$ |
$3$ |
$20.6111354632$ |
$93.57350052231668$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.4406638556$ |
$1$ |
$199$ |
| 3.1.10348.1 |
$x^{3} - x^{2} - 13 x - 39$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 13\cdot 199$ |
$3$ |
$21.7914170965$ |
$80.7392810975926$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.14174185195$ |
$1$ |
$199$ |
| 3.1.11144.1 |
$x^{3} - x^{2} + 13 x - 41$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 199$ |
$3$ |
$22.3364268876$ |
$105.56514576317318$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.0057688645$ |
$1$ |
$199$ |
| 3.1.11343.1 |
$x^{3} - x^{2} - 20 x + 96$ |
$3$ |
(1, 1) |
$-\,3\cdot 19\cdot 199$ |
$3$ |
$22.4685981701$ |
$106.50352106855435$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$73.6181700423$ |
$1$ |
$199$ |
| 3.1.12935.1 |
$x^{3} - x^{2} - 16 x - 65$ |
$3$ |
(1, 1) |
$-\,5\cdot 13\cdot 199$ |
$3$ |
$23.4740924689$ |
$113.7321414552632$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.0617785328$ |
$1$ |
$199$ |
| 3.3.13333.1 |
$x^{3} - 34 x - 73$ |
$3$ |
(3, 0) |
$67\cdot 199$ |
$2$ |
$23.7124244231$ |
$115.46861045323097$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$25.7079123679$ |
$2$ |
$199$ |
| 3.3.14129.1 |
$x^{3} - x^{2} - 26 x - 16$ |
$3$ |
(3, 0) |
$71\cdot 199$ |
$2$ |
$24.1752222317$ |
$118.86547017532047$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$84.292737477$ |
$2$ |
$199$ |
| 3.3.15124.1 |
$x^{3} - x^{2} - 19 x + 29$ |
$3$ |
(3, 0) |
$2^{2}\cdot 19\cdot 199$ |
$3$ |
$24.7298921808$ |
$97.60903123843116$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$29.742671954$ |
$2$ |
$199$ |
| 3.1.16716.1 |
$x^{3} - x^{2} + 23 x - 35$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 7\cdot 199$ |
$4$ |
$25.568825986$ |
$102.61783536511258$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.105372159$ |
$1$ |
$199$ |
| 3.1.17512.1 |
$x^{3} - x^{2} + 25 x + 11$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 199$ |
$3$ |
$25.9684034323$ |
$132.33291351738615$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$24.4403017887$ |
$1$ |
$199$ |
| 3.3.18109.1 |
$x^{3} - x^{2} - 26 x + 4$ |
$3$ |
(3, 0) |
$7\cdot 13\cdot 199$ |
$3$ |
$26.2602076703$ |
$134.56968455042167$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$34.3008093307$ |
$2$ |
$199$ |
| 3.1.18507.1 |
$x^{3} - x^{2} - 31 x - 62$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 199$ |
$3$ |
$26.4511977093$ |
$136.0404351654316$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$39.375431586$ |
$1$ |
$199$ |
| 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 |
$2$ |
$1$ |
$14.1169564738$ |
$1$ |
$199$ |
| 3.1.20895.1 |
$x^{3} - x^{2} + 20 x - 83$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 7\cdot 199$ |
$4$ |
$27.5431828438$ |
$144.55102905202716$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$27.0135741865$ |
$1$ |
$199$ |
| 3.3.21293.1 |
$x^{3} - 41 x - 84$ |
$3$ |
(3, 0) |
$107\cdot 199$ |
$2$ |
$27.7169614652$ |
$145.9212116177768$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$48.9950911176$ |
$2$ |
$199$ |
| 3.1.21691.1 |
$x^{3} - x^{2} - 20 x - 112$ |
$3$ |
(1, 1) |
$-\,109\cdot 199$ |
$2$ |
$27.888587891$ |
$147.27864746798838$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$38.5324084082$ |
$1$ |
$199$ |
| 3.1.22487.1 |
$x^{3} - 19 x - 43$ |
$3$ |
(1, 1) |
$-\,113\cdot 199$ |
$2$ |
$28.2256427219$ |
$149.9566604055985$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.66408753431$ |
$1$ |
$199$ |
| 3.1.23084.1 |
$x^{3} - x^{2} - 17 x - 59$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 29\cdot 199$ |
$3$ |
$28.4732487259$ |
$120.59025150436757$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.5418388412$ |
$1$ |
$199$ |
| 3.1.24079.1 |
$x^{3} - x^{2} + 4 x - 31$ |
$3$ |
(1, 1) |
$-\,11^{2}\cdot 199$ |
$2$ |
$28.8766061087$ |
$69.7731496942501$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.23149769293$ |
$1$ |
$199$ |
| 3.1.24079.2 |
$x^{3} - 11 x - 33$ |
$3$ |
(1, 1) |
$-\,11^{2}\cdot 199$ |
$2$ |
$28.8766061087$ |
$69.7731496942501$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.9057138529$ |
$1$ |
$199$ |
| 3.1.24079.3 |
$x^{3} - x^{2} + 26 x + 24$ |
$3$ |
(1, 1) |
$-\,11^{2}\cdot 199$ |
$2$ |
$28.8766061087$ |
$69.7731496942501$ |
|
|
|
$S_3$ (as 3T2) |
$[12]$ |
$[12]$ |
$2$ |
$1$ |
$9.54330713206$ |
$1$ |
$199$ |
| 3.1.26467.1 |
$x^{3} - x^{2} - 21 x - 154$ |
$3$ |
(1, 1) |
$-\,7\cdot 19\cdot 199$ |
$3$ |
$29.8012791667$ |
$162.68681569199146$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$41.8411611873$ |
$1$ |
$199$ |
| 3.3.27064.1 |
$x^{3} - x^{2} - 31 x - 13$ |
$3$ |
(3, 0) |
$2^{3}\cdot 17\cdot 199$ |
$3$ |
$30.0236849995$ |
$164.51139778143033$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$48.969475283$ |
$2$ |
$199$ |
| 3.1.27263.1 |
$x^{3} - x^{2} + 20 x + 116$ |
$3$ |
(1, 1) |
$-\,137\cdot 199$ |
$2$ |
$30.0970928345$ |
$165.1151113617406$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$33.0951068354$ |
$1$ |
$199$ |
| 3.3.27661.1 |
$x^{3} - x^{2} - 30 x + 4$ |
$3$ |
(3, 0) |
$139\cdot 199$ |
$2$ |
$30.2428437412$ |
$166.3159643570033$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$33.4306709602$ |
$2$ |
$199$ |
| 3.1.27860.1 |
$x^{3} - x^{2} - 35 x + 115$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 7\cdot 199$ |
$4$ |
$30.3151953178$ |
$166.91315106965058$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$48.621025385$ |
$1$ |
$199$ |
| 3.3.29253.1 |
$x^{3} - x^{2} - 23 x + 36$ |
$3$ |
(3, 0) |
$3\cdot 7^{2}\cdot 199$ |
$3$ |
$30.8122540771$ |
$89.40995141932365$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$25.6941001131$ |
$2$ |
$199$ |
| 3.1.29452.1 |
$x^{3} + 16 x - 22$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 37\cdot 199$ |
$3$ |
$30.8819652968$ |
$136.21159047875443$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.658234043$ |
$1$ |
$199$ |
| 3.1.29651.1 |
$x^{3} - x^{2} + 6 x - 68$ |
$3$ |
(1, 1) |
$-\,149\cdot 199$ |
$2$ |
$30.951363205$ |
$172.1946572922633$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.6640192276$ |
$1$ |
$199$ |
| 3.1.30248.1 |
$x^{3} - x^{2} - 43 x + 143$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 19\cdot 199$ |
$3$ |
$31.1577117202$ |
$173.91952161847732$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$47.2233662315$ |
$1$ |
$199$ |
| 3.1.31044.1 |
$x^{3} - x^{2} + 25 x - 57$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 13\cdot 199$ |
$4$ |
$31.4286619439$ |
$176.19307591389622$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$85.729166955$ |
$1$ |
$199$ |
| 3.1.33432.1 |
$x^{3} - x^{2} - 15 x - 69$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 7\cdot 199$ |
$4$ |
$32.2147020809$ |
$182.84419597023034$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$91.1961311547$ |
$1$ |
$199$ |
| 3.3.34228.1 |
$x^{3} - x^{2} - 43 x - 11$ |
$3$ |
(3, 0) |
$2^{2}\cdot 43\cdot 199$ |
$3$ |
$32.4683715967$ |
$146.84103257571044$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$89.8301454168$ |
$3$ |
$199$ |
| 3.1.36616.1 |
$x^{3} - x^{2} - 19 x + 87$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 23\cdot 199$ |
$3$ |
$33.2065405414$ |
$191.35307679783986$ |
|
|
|
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$7.16166232547$ |
$1$ |
$199$ |
| 3.1.36815.1 |
$x^{3} - x^{2} + 37$ |
$3$ |
(1, 1) |
$-\,5\cdot 37\cdot 199$ |
$3$ |
$33.2665886659$ |
$191.87235340194272$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$3.50559317099$ |
$1$ |
$199$ |
| 3.1.37611.1 |
$x^{3} + 18 x - 23$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 199$ |
$3$ |
$33.5046403314$ |
$134.46740446273208$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$18.0914764736$ |
$1$ |
$199$ |
| 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 |
$2$ |
$1$ |
$13.7025736369$ |
$1$ |
$199$ |
| 3.3.38805.1 |
$x^{3} - x^{2} - 21 x + 6$ |
$3$ |
(3, 0) |
$3\cdot 5\cdot 13\cdot 199$ |
$4$ |
$33.8554997766$ |
$196.98984745412642$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$95.852469156$ |
$2$ |
$199$ |
| 3.1.39203.1 |
$x^{3} - x^{2} - 23 x - 50$ |
$3$ |
(1, 1) |
$-\,197\cdot 199$ |
$2$ |
$33.970851604$ |
$197.99747473137126$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$15.2212015814$ |
$1$ |
$199$ |
| 3.1.39800.1 |
$x^{3} - x^{2} + 32 x - 148$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 199$ |
$3$ |
$34.1424244719$ |
$116.66794133585502$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$52.6938668322$ |
$1$ |
$199$ |
| 3.3.39800.1 |
$x^{3} - x^{2} - 48 x - 88$ |
$3$ |
(3, 0) |
$2^{3}\cdot 5^{2}\cdot 199$ |
$3$ |
$34.1424244719$ |
$116.66794133585502$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$51.7440642526$ |
$3$ |
$199$ |
| 3.1.39999.1 |
$x^{3} - x^{2} + 38 x + 61$ |
$3$ |
(1, 1) |
$-\,3\cdot 67\cdot 199$ |
$3$ |
$34.1992339352$ |
$199.9974999843748$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$21.7771607268$ |
$1$ |
$199$ |
| 3.1.40596.1 |
$x^{3} - x^{2} + 20 x - 26$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 17\cdot 199$ |
$4$ |
$34.3685398328$ |
$201.48449071826843$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$76.0963317523$ |
$1$ |
$199$ |
| 3.1.40795.1 |
$x^{3} - x^{2} - 30 x + 252$ |
$3$ |
(1, 1) |
$-\,5\cdot 41\cdot 199$ |
$3$ |
$34.4246060657$ |
$201.97772154373857$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$12.8259176876$ |
$1$ |
$199$ |
| 3.1.42188.1 |
$x^{3} + 14 x - 34$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 53\cdot 199$ |
$3$ |
$34.8120537801$ |
$163.02384680310564$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$8.33399834442$ |
$1$ |
$199$ |
