| 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 $p$ |
| 3.1.716.1 |
$x^{3} - 4 x - 6$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 179$ |
$2$ |
$8.94618086588$ |
$21.237978619971454$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.40536230631$ |
$1$ |
$179$ |
| 3.1.1432.1 |
$x^{3} + 10 x - 8$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 179$ |
$2$ |
$11.2714815891$ |
$37.841775856849004$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.107915335$ |
$1$ |
$179$ |
| 3.1.2148.1 |
$x^{3} - x^{2} - 7 x - 17$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 179$ |
$3$ |
$12.9026255097$ |
$46.34652090502587$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.8491253901$ |
$1$ |
$179$ |
| 3.1.2327.1 |
$x^{3} - x^{2} + 8 x - 7$ |
$3$ |
(1, 1) |
$-\,13\cdot 179$ |
$2$ |
$13.2515128212$ |
$48.23898838076935$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$2.17308027352$ |
$1$ |
$179$ |
| 3.1.3043.1 |
$x^{3} + 7 x - 20$ |
$3$ |
(1, 1) |
$-\,17\cdot 179$ |
$2$ |
$14.4910765547$ |
$55.163393659201205$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.4478237746$ |
$1$ |
$179$ |
| 3.3.3580.1 |
$x^{3} - x^{2} - 15 x + 7$ |
$3$ |
(3, 0) |
$2^{2}\cdot 5\cdot 179$ |
$3$ |
$15.2977540953$ |
$59.833101206606365$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$21.0949833862$ |
$3$ |
$179$ |
| 3.1.6623.1 |
$x^{3} + 11 x - 28$ |
$3$ |
(1, 1) |
$-\,37\cdot 179$ |
$2$ |
$18.7795386258$ |
$81.38181615078395$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$34.3450400862$ |
$1$ |
$179$ |
| 3.1.7339.1 |
$x^{3} - x^{2} + 11 x + 6$ |
$3$ |
(1, 1) |
$-\,41\cdot 179$ |
$2$ |
$19.4332585701$ |
$85.66796367370944$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$3.93374993166$ |
$1$ |
$179$ |
| 3.3.10561.1 |
$x^{3} - 19 x - 25$ |
$3$ |
(3, 0) |
$59\cdot 179$ |
$2$ |
$21.939918714$ |
$102.76672613253767$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$16.3038875847$ |
$3$ |
$179$ |
| 3.1.10740.1 |
$x^{3} - x^{2} - 20 x + 60$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 5\cdot 179$ |
$4$ |
$22.0631792706$ |
$103.63397126425292$ |
|
|
|
$S_3$ (as 3T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$10.2055531114$ |
$1$ |
$179$ |
| 3.3.10740.1 |
$x^{3} - x^{2} - 25 x + 37$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 5\cdot 179$ |
$4$ |
$22.0631792706$ |
$82.25433750225862$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$37.3794607528$ |
$2$ |
$179$ |
| 3.1.10919.1 |
$x^{3} - x^{2} - 4 x - 19$ |
$3$ |
(1, 1) |
$-\,61\cdot 179$ |
$2$ |
$22.1850777624$ |
$104.4940189675945$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.14619168058$ |
$1$ |
$179$ |
| 3.1.13067.1 |
$x^{3} - x - 44$ |
$3$ |
(1, 1) |
$-\,73\cdot 179$ |
$2$ |
$23.5536724033$ |
$114.3109793501919$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.1576187174$ |
$1$ |
$179$ |
| 3.1.13783.1 |
$x^{3} - 5 x - 23$ |
$3$ |
(1, 1) |
$-\,7\cdot 11\cdot 179$ |
$3$ |
$23.9762496526$ |
$117.40102214205803$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.1731518115$ |
$1$ |
$179$ |
| 3.3.14141.1 |
$x^{3} - x^{2} - 17 x - 10$ |
$3$ |
(3, 0) |
$79\cdot 179$ |
$2$ |
$24.1820644375$ |
$118.91593669479293$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$46.4017288084$ |
$3$ |
$179$ |
| 3.1.14499.1 |
$x^{3} + 18 x - 63$ |
$3$ |
(1, 1) |
$-\,3^{4}\cdot 179$ |
$2$ |
$24.3844342179$ |
$57.88795245071825$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.23201503743$ |
$1$ |
$179$ |
| 3.1.15752.1 |
$x^{3} - x^{2} + 17 x + 35$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 179$ |
$3$ |
$25.0675506454$ |
$125.50697191789786$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$34.1013244089$ |
$1$ |
$179$ |
| 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) |
$[8]$ |
$[8]$ |
$2$ |
$1$ |
$2.78054781595$ |
$1$ |
$179$ |
| 3.1.16468.1 |
$x^{3} - x^{2} - 27 x + 83$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 23\cdot 179$ |
$3$ |
$25.4417483603$ |
$128.32770550430644$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$43.5743291088$ |
$1$ |
$179$ |
| 3.1.18795.1 |
$x^{3} - x^{2} - 15 x - 30$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 7\cdot 179$ |
$4$ |
$26.587700421$ |
$137.09485767161362$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$50.0959443494$ |
$1$ |
$179$ |
| 3.3.19869.1 |
$x^{3} - 36 x - 17$ |
$3$ |
(3, 0) |
$3\cdot 37\cdot 179$ |
$3$ |
$27.0847815136$ |
$140.95744038538726$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$53.4526551608$ |
$3$ |
$179$ |
| 3.1.21659.1 |
$x^{3} - x^{2} + 4 x + 112$ |
$3$ |
(1, 1) |
$-\,11^{2}\cdot 179$ |
$2$ |
$27.8748667773$ |
$66.17413995157763$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$8.06181072777$ |
$1$ |
$179$ |
| 3.1.23628.1 |
$x^{3} - x^{2} + 33 x - 63$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 11\cdot 179$ |
$4$ |
$28.6951822497$ |
$122.00289866826128$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$47.522121962$ |
$1$ |
$179$ |
| 3.1.24344.1 |
$x^{3} - 22 x - 72$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 17\cdot 179$ |
$3$ |
$28.9821531095$ |
$156.0256389187367$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$79.0709219475$ |
$1$ |
$179$ |
| 3.1.24523.1 |
$x^{3} - x^{2} - 25 x + 66$ |
$3$ |
(1, 1) |
$-\,137\cdot 179$ |
$2$ |
$29.0530144016$ |
$156.59821199490113$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$17.9326319476$ |
$1$ |
$179$ |
| 3.1.25239.1 |
$x^{3} - x^{2} + 14 x + 19$ |
$3$ |
(1, 1) |
$-\,3\cdot 47\cdot 179$ |
$3$ |
$29.3330607183$ |
$158.86786962756187$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$18.2147793265$ |
$1$ |
$179$ |
| 3.3.26492.1 |
$x^{3} - 47 x - 120$ |
$3$ |
(3, 0) |
$2^{2}\cdot 37\cdot 179$ |
$3$ |
$29.8106593701$ |
$162.7636323015679$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$72.9918347421$ |
$2$ |
$179$ |
| 3.1.26671.1 |
$x^{3} - x^{2} + 18 x - 19$ |
$3$ |
(1, 1) |
$-\,149\cdot 179$ |
$2$ |
$29.8776498411$ |
$163.31258371601376$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$2.95007624192$ |
$1$ |
$179$ |
| 3.1.29356.1 |
$x^{3} - x^{2} + 3 x + 65$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 179$ |
$3$ |
$30.8483750973$ |
$135.98941565561987$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$12.8682218216$ |
$1$ |
$179$ |
| 3.1.29356.2 |
$x^{3} - x^{2} + 31 x - 19$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 179$ |
$3$ |
$30.8483750973$ |
$135.98941565561987$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.95744033269$ |
$1$ |
$179$ |
| 3.1.29356.3 |
$x^{3} - x^{2} + 21 x - 99$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 41\cdot 179$ |
$3$ |
$30.8483750973$ |
$135.98941565561987$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.95506353327$ |
$1$ |
$179$ |
| 3.1.29535.1 |
$x^{3} - x^{2} - 33$ |
$3$ |
(1, 1) |
$-\,3\cdot 5\cdot 11\cdot 179$ |
$4$ |
$30.9109480377$ |
$171.85749910900017$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$30.60982632$ |
$1$ |
$179$ |
| 3.1.30251.1 |
$x^{3} - x^{2} + 9 x - 170$ |
$3$ |
(1, 1) |
$-\,13^{2}\cdot 179$ |
$2$ |
$31.1587417613$ |
$73.96996565043275$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.4337024042$ |
$1$ |
$179$ |
| 3.3.31325.1 |
$x^{3} - 20 x - 5$ |
$3$ |
(3, 0) |
$5^{2}\cdot 7\cdot 179$ |
$3$ |
$31.5232045365$ |
$103.50361977210993$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$67.5076849717$ |
$2$ |
$179$ |
| 3.1.31683.1 |
$x^{3} + 30 x - 81$ |
$3$ |
(1, 1) |
$-\,3\cdot 59\cdot 179$ |
$3$ |
$31.6428383378$ |
$177.9971909890715$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$55.4535428161$ |
$1$ |
$179$ |
| 3.3.32757.1 |
$x^{3} - x^{2} - 29 x + 60$ |
$3$ |
(3, 0) |
$3\cdot 61\cdot 179$ |
$3$ |
$31.9964188701$ |
$180.98894993893964$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$71.9021544877$ |
$2$ |
$179$ |
| 3.1.32936.1 |
$x^{3} - x^{2} + 18 x - 26$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 23\cdot 179$ |
$3$ |
$32.0545943052$ |
$181.48278155241064$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$15.8081105719$ |
$1$ |
$179$ |
| 3.1.33831.1 |
$x^{3} - 3 x - 177$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 179$ |
$3$ |
$32.3423529117$ |
$127.53136243433082$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$26.6465975199$ |
$1$ |
$179$ |
| 3.1.35263.1 |
$x^{3} - x^{2} - 14 x - 37$ |
$3$ |
(1, 1) |
$-\,179\cdot 197$ |
$2$ |
$32.7923911559$ |
$187.78445090049388$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.5112878423$ |
$1$ |
$197$ |
| 3.3.37769.1 |
$x^{3} - x^{2} - 50 x + 149$ |
$3$ |
(3, 0) |
$179\cdot 211$ |
$2$ |
$33.5514913202$ |
$194.3424812026439$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$19.2120792803$ |
$2$ |
$211$ |
| 3.1.38127.1 |
$x^{3} - 27 x - 125$ |
$3$ |
(1, 1) |
$-\,3\cdot 71\cdot 179$ |
$3$ |
$33.6571660064$ |
$195.26136330569855$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.8424193352$ |
$1$ |
$179$ |
| 3.1.38664.1 |
$x^{3} + 21 x - 66$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 179$ |
$3$ |
$33.8144447673$ |
$136.33676122793105$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$55.1831716864$ |
$1$ |
$179$ |
| 3.3.38664.1 |
$x^{3} - 51 x - 118$ |
$3$ |
(3, 0) |
$2^{3}\cdot 3^{3}\cdot 179$ |
$3$ |
$33.8144447673$ |
$136.33676122793105$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$81.6232413985$ |
$3$ |
$179$ |
| 3.1.40812.1 |
$x^{3} - x^{2} + 11 x + 73$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 19\cdot 179$ |
$4$ |
$34.4293871829$ |
$160.34322232060444$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$8.64064640172$ |
$1$ |
$179$ |
| 3.3.41528.1 |
$x^{3} - x^{2} - 22 x + 18$ |
$3$ |
(3, 0) |
$2^{3}\cdot 29\cdot 179$ |
$3$ |
$34.6295625366$ |
$203.78419958377538$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$105.776480766$ |
$2$ |
$179$ |
| 3.1.42423.1 |
$x^{3} - 15 x - 121$ |
$3$ |
(1, 1) |
$-\,3\cdot 79\cdot 179$ |
$3$ |
$34.8765720441$ |
$205.9684441850256$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$11.035002653$ |
$1$ |
$179$ |
| 3.1.42423.2 |
$x^{3} - x^{2} - 6 x - 117$ |
$3$ |
(1, 1) |
$-\,3\cdot 79\cdot 179$ |
$3$ |
$34.8765720441$ |
$205.9684441850256$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.60941259832$ |
$1$ |
$179$ |
| 3.1.42423.3 |
$x^{3} - x^{2} - 4 x + 160$ |
$3$ |
(1, 1) |
$-\,3\cdot 79\cdot 179$ |
$3$ |
$34.8765720441$ |
$205.9684441850256$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$54.696370978$ |
$1$ |
$179$ |
| 3.1.42423.4 |
$x^{3} + 21 x - 113$ |
$3$ |
(1, 1) |
$-\,3\cdot 79\cdot 179$ |
$3$ |
$34.8765720441$ |
$205.9684441850256$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.1505134213$ |
$1$ |
$179$ |
| 3.3.43497.1 |
$x^{3} - 45 x - 84$ |
$3$ |
(3, 0) |
$3^{5}\cdot 179$ |
$2$ |
$35.1684397729$ |
$100.26487479077532$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$171.686275506$ |
$2$ |
$179$ |
