| 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 |
| 3.1.980.1 |
$x^{3} - x^{2} + 5 x - 13$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}$ |
$3$ |
$9.93288388379$ |
$16.364912636128995$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.534472002$ |
| 3.1.1176.1 |
$x^{3} - x^{2} - 2 x - 6$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 7^{2}$ |
$3$ |
$10.5552641758$ |
$17.926863604818365$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.71059897095$ |
| 3.1.2303.1 |
$x^{3} - x^{2} - 2 x - 27$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 47$ |
$2$ |
$13.2057978815$ |
$25.086936025192795$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.98312268036$ |
| 3.3.2597.1 |
$x^{3} - x^{2} - 9 x + 8$ |
$3$ |
[3,0] |
$7^{2}\cdot 53$ |
$2$ |
$13.7453979089$ |
$26.640147687438905$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$4.79599055536$ |
| 3.1.2891.1 |
$x^{3} - x^{2} + 5 x + 8$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.34123738956$ |
| 3.1.3675.1 |
$x^{3} - 35$ |
$3$ |
[1,1] |
$-\,3\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$15.4318898408$ |
$18.532726798013343$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.62790570306$ |
| 3.1.3724.1 |
$x^{3} - x^{2} - 9 x + 29$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 19$ |
$3$ |
$15.5001734285$ |
$25.319909997284967$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.74470586615$ |
| 3.3.3969.2 |
$x^{3} - 21 x - 35$ |
$3$ |
[3,0] |
$3^{4}\cdot 7^{2}$ |
$2$ |
$15.8328962637$ |
$15.83289626371223$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$4.20169004224$ |
| 3.1.5292.1 |
$x^{3} - 14$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$17.4263572007$ |
$20.927956356407396$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.46551305026$ |
| 3.3.5684.1 |
$x^{3} - 14 x - 14$ |
$3$ |
[3,0] |
$2^{2}\cdot 7^{2}\cdot 29$ |
$3$ |
$17.846430146$ |
$31.281268504572243$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$5.72985919176$ |
| 3.1.6664.1 |
$x^{3} + 7 x - 14$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 17$ |
$3$ |
$18.8182108135$ |
$42.67447112735335$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$4.01030114086$ |
| 3.1.7007.1 |
$x^{3} - x^{2} + 12 x + 1$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 11\cdot 13$ |
$3$ |
$19.1356861407$ |
$43.758931819174485$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.49234210057$ |
| 3.1.7791.1 |
$x^{3} - x^{2} + 26 x + 1$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 53$ |
$3$ |
$19.8242942278$ |
$46.14208931578271$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.25962910923$ |
| 3.3.8281.1 |
$x^{3} - x^{2} - 30 x + 64$ |
$3$ |
[3,0] |
$7^{2}\cdot 13^{2}$ |
$2$ |
$20.2314772451$ |
$20.23147724512629$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$15.6222994475$ |
| 3.1.9163.1 |
$x^{3} - x^{2} + 12 x - 76$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 11\cdot 17$ |
$3$ |
$20.9256630947$ |
$50.04025297946701$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.99172259065$ |
| 3.1.11123.1 |
$x^{3} - x^{2} - 9 x - 20$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 227$ |
$2$ |
$22.3223876464$ |
$55.13299964109813$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.98304351038$ |
| 3.1.11907.1 |
$x^{3} - 63$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7^{2}$ |
$2$ |
$22.8349878331$ |
$27.423380759717027$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.86596074415$ |
| 3.1.12152.1 |
$x^{3} - x^{2} - 2 x + 22$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 31$ |
$3$ |
$22.9905443173$ |
$57.626803948274514$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$9.23063490927$ |
| 3.3.13916.1 |
$x^{3} - x^{2} - 16 x - 6$ |
$3$ |
[3,0] |
$2^{2}\cdot 7^{2}\cdot 71$ |
$3$ |
$24.0531230681$ |
$61.66771595698603$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$17.8111271909$ |
| 3.3.14945.1 |
$x^{3} - x^{2} - 16 x + 15$ |
$3$ |
[3,0] |
$5\cdot 7^{2}\cdot 61$ |
$3$ |
$24.6319412351$ |
$63.9070268062836$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$7.43787005228$ |
| 3.1.16023.2 |
$x^{3} + 21 x - 63$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 109$ |
$3$ |
$25.2104894603$ |
$66.17174228752027$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.17180954918$ |
| 3.1.16268.3 |
$x^{3} + 14 x - 14$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 83$ |
$3$ |
$25.3383338851$ |
$52.92055660111312$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$2.82287947419$ |
| 3.1.17787.1 |
$x^{3} - x^{2} + 26 x - 20$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 11^{2}$ |
$3$ |
$26.1036298001$ |
$31.348813691136165$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$13.7836606913$ |
| 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) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$15.9168049521$ |
| 3.1.19159.1 |
$x^{3} + 7 x - 133$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 17\cdot 23$ |
$3$ |
$26.7582441763$ |
$72.35808626026554$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.96890789791$ |
| 3.1.19355.1 |
$x^{3} - 28 x - 63$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 79$ |
$3$ |
$26.8491819838$ |
$72.72726256614953$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$10.5318296748$ |
| 3.3.21021.1 |
$x^{3} - 42 x - 63$ |
$3$ |
[3,0] |
$3\cdot 7^{2}\cdot 11\cdot 13$ |
$4$ |
$27.598435114$ |
$75.79269319575262$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$19.2368989216$ |
| 3.1.21511.2 |
$x^{3} - x^{2} - 16 x - 83$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 439$ |
$2$ |
$27.811230216$ |
$76.67096924299021$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.37936171234$ |
| 3.1.22099.3 |
$x^{3} - 14 x - 35$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 11\cdot 41$ |
$3$ |
$28.0623610078$ |
$77.71179925862245$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$15.7899706789$ |
| 3.1.22540.2 |
$x^{3} - x^{2} + 5 x + 85$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 23$ |
$4$ |
$28.2478004918$ |
$62.29228720573776$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$11.8803355505$ |
| 3.1.25627.1 |
$x^{3} - x^{2} - 9 x - 90$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 523$ |
$2$ |
$29.4826096872$ |
$83.68536945087664$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.5103278426$ |
| 3.1.25676.2 |
$x^{3} - 28 x - 84$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 131$ |
$3$ |
$29.5013884245$ |
$66.48459154193077$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$8.53679583639$ |
| 3.3.26460.1 |
$x^{3} - 42 x - 84$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{3}\cdot 5\cdot 7^{2}$ |
$4$ |
$29.7986516514$ |
$58.95968505886214$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$28.4880138627$ |
| 3.1.27048.1 |
$x^{3} - x^{2} - 23 x - 69$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 7^{2}\cdot 23$ |
$4$ |
$30.0177672532$ |
$85.97421759011542$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$24.193317957$ |
| 3.1.27244.1 |
$x^{3} - x^{2} + 19 x - 13$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 139$ |
$3$ |
$30.0900995021$ |
$68.48457378187439$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$9.47661928081$ |
| 3.1.27391.1 |
$x^{3} - x^{2} + 26 x - 48$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 13\cdot 43$ |
$3$ |
$30.1441213407$ |
$86.51762663289117$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$31.7872371322$ |
| 3.1.28616.1 |
$x^{3} - x^{2} - 30 x - 62$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 73$ |
$3$ |
$30.5869595709$ |
$88.43111825128939$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$9.34145797312$ |
| 3.1.29743.1 |
$x^{3} + 49 x - 14$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 607$ |
$2$ |
$30.9833417264$ |
$90.15566868256195$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$17.2623027501$ |
| 3.3.30037.1 |
$x^{3} - x^{2} - 23 x - 20$ |
$3$ |
[3,0] |
$7^{2}\cdot 613$ |
$2$ |
$31.0850939896$ |
$90.60015289874693$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$12.8831290787$ |
| 3.1.30772.3 |
$x^{3} - x^{2} - 16 x - 132$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 157$ |
$3$ |
$31.3366024455$ |
$91.70193825360194$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$19.5785721379$ |
| 3.1.31507.2 |
$x^{3} + 28 x - 161$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 643$ |
$2$ |
$31.5841372075$ |
$92.79064205866086$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.7163684131$ |
| 3.1.31703.1 |
$x^{3} - 7 x - 35$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 647$ |
$2$ |
$31.6494951532$ |
$93.07881244824813$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.70637071785$ |
| 3.3.31752.1 |
$x^{3} - 21 x - 14$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$31.6657925274$ |
$44.78219325557628$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$29.6441677606$ |
| 3.3.32340.1 |
$x^{3} - 42 x - 14$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 5\cdot 7^{2}\cdot 11$ |
$5$ |
$31.8600660531$ |
$74.61520374725771$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$25.6501077913$ |
| 3.1.32487.1 |
$x^{3} - x^{2} + 12 x + 99$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 13\cdot 17$ |
$4$ |
$31.908265924$ |
$94.22268102344923$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$9.76904205463$ |
| 3.3.32977.1 |
$x^{3} - 49 x - 112$ |
$3$ |
[3,0] |
$7^{2}\cdot 673$ |
$2$ |
$32.0678897206$ |
$94.93059992458029$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$37.8819488439$ |
| 3.3.33369.1 |
$x^{3} - x^{2} - 44 x + 57$ |
$3$ |
[3,0] |
$3\cdot 7^{2}\cdot 227$ |
$3$ |
$32.1944539913$ |
$95.49315655205864$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$12.4737569837$ |
| 3.1.34447.1 |
$x^{3} + 7 x - 35$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 19\cdot 37$ |
$3$ |
$32.5374715726$ |
$97.02337012505248$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.18156071573$ |
| 3.1.35476.1 |
$x^{3} - x^{2} - 44 x + 134$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 181$ |
$3$ |
$32.8582842344$ |
$98.46184659191837$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$29.4991606968$ |
| 3.1.38220.2 |
$x^{3} - x^{2} + 19 x + 15$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5\cdot 7^{2}\cdot 13$ |
$5$ |
$33.6845094888$ |
$81.11527834630402$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$20.9875799861$ |