| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 3.3.49.1 |
$x^{3} - x^{2} - 2 x + 1$ |
$3$ |
[3,0] |
$7^{2}$ |
$1$ |
$3.65930571002$ |
$3.6593057100229713$ |
|
✓ |
✓ |
$C_3$ (as 3T1) |
trivial |
$2$ |
$2$ |
$0.525454682123$ |
| 3.1.1323.1 |
$x^{3} - 7$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 7^{2}$ |
$2$ |
$10.9779171301$ |
$13.183786372359444$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.44105647039$ |
| 3.1.1960.1 |
$x^{3} - x^{2} + 5 x + 15$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 5\cdot 7^{2}$ |
$3$ |
$12.5146494914$ |
$23.143481397064466$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.86047323248$ |
| 3.1.2695.1 |
$x^{3} + 7 x - 7$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 11$ |
$3$ |
$13.9161656546$ |
$27.138137470492882$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$2.27226928459$ |
| 3.1.2891.2 |
$x^{3} - x^{2} - 9 x + 36$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.74005132064$ |
| 3.1.3332.1 |
$x^{3} - x^{2} + 12 x - 20$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 17$ |
$3$ |
$14.9360238208$ |
$30.175407917701083$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.2872565788$ |
| 3.1.3724.2 |
$x^{3} - x^{2} - 9 x - 13$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 19$ |
$3$ |
$15.5001734285$ |
$25.319909997284967$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$3.44527402863$ |
| 3.1.5439.1 |
$x^{3} - x^{2} - 2 x + 15$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 37$ |
$3$ |
$17.5862409683$ |
$38.553177936638974$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.61551337389$ |
| 3.1.6468.1 |
$x^{3} - x^{2} + 12 x - 6$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 11$ |
$4$ |
$18.631879656$ |
$42.04222178812256$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.85060960228$ |
| 3.1.9555.1 |
$x^{3} - x^{2} + 5 x - 20$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 7^{2}\cdot 13$ |
$4$ |
$21.2199112802$ |
$51.09942332829512$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.9180478639$ |
| 3.3.9653.1 |
$x^{3} - 14 x - 7$ |
$3$ |
[3,0] |
$7^{2}\cdot 197$ |
$2$ |
$21.2922113661$ |
$51.36080315808082$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$10.6557094182$ |
| 3.3.9996.1 |
$x^{3} - x^{2} - 16 x + 22$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 7^{2}\cdot 17$ |
$4$ |
$21.5414739376$ |
$52.265339652574454$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$17.4715160009$ |
| 3.1.10584.2 |
$x^{3} - 21 x - 42$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$21.9558342601$ |
$37.289378982440624$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$10.4675793273$ |
| 3.1.10927.1 |
$x^{3} - x^{2} - 16 x - 27$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 223$ |
$2$ |
$22.1904945373$ |
$54.645087394089686$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$3.95013954372$ |
| 3.1.12299.1 |
$x^{3} + 14 x - 7$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 251$ |
$2$ |
$23.0828768114$ |
$57.97430541309734$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.07667939217$ |
| 3.1.14308.1 |
$x^{3} - x^{2} - 23 x + 71$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 73$ |
$3$ |
$24.2768858997$ |
$62.53024338339619$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$13.3732823976$ |
| 3.1.14651.1 |
$x^{3} - x^{2} + 5 x - 118$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 13\cdot 23$ |
$3$ |
$24.4693494259$ |
$63.27531086879471$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$8.79224642436$ |
| 3.1.14700.1 |
$x^{3} - x^{2} - 23 x + 57$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$24.4965981671$ |
$29.418870015005623$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.0997255193$ |
| 3.1.16023.3 |
$x^{3} - x^{2} - 2 x - 48$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 109$ |
$3$ |
$25.2104894603$ |
$66.17174228752027$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$10.5349457375$ |
| 3.1.16268.1 |
$x^{3} - x^{2} + 33 x - 27$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 83$ |
$3$ |
$25.3383338851$ |
$52.92055660111312$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.5561151108$ |
| 3.1.17395.1 |
$x^{3} - x^{2} - 30 x + 92$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 71$ |
$3$ |
$25.9104413708$ |
$68.94660244848463$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.87207694911$ |
| 3.3.17689.1 |
$x^{3} - x^{2} - 44 x - 69$ |
$3$ |
[3,0] |
$7^{2}\cdot 19^{2}$ |
$2$ |
$26.0556009339$ |
$26.05560093389125$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$10.8673488573$ |
| 3.3.17689.2 |
$x^{3} - x^{2} - 44 x + 64$ |
$3$ |
[3,0] |
$7^{2}\cdot 19^{2}$ |
$2$ |
$26.0556009339$ |
$26.05560093389125$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$2$ |
$2$ |
$32.4707206114$ |
| 3.3.18228.1 |
$x^{3} - x^{2} - 23 x - 27$ |
$3$ |
[3,0] |
$2^{2}\cdot 3\cdot 7^{2}\cdot 31$ |
$4$ |
$26.3176035241$ |
$56.017900959926635$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$15.454548344$ |
| 3.1.18424.1 |
$x^{3} - 14 x - 56$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 47$ |
$3$ |
$26.4115957631$ |
$70.95657033042767$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$4.11488521474$ |
| 3.1.18767.1 |
$x^{3} - x^{2} + 26 x + 8$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 383$ |
$2$ |
$26.5744907801$ |
$71.61402447155707$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$6.78791742407$ |
| 3.3.21364.1 |
$x^{3} - x^{2} - 37 x - 55$ |
$3$ |
[3,0] |
$2^{2}\cdot 7^{2}\cdot 109$ |
$3$ |
$27.7477340357$ |
$60.645503502991886$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$12.7621087328$ |
| 3.1.21511.1 |
$x^{3} + 7 x - 56$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 439$ |
$2$ |
$27.811230216$ |
$76.67096924299021$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$27.0596431446$ |
| 3.1.22099.1 |
$x^{3} - x^{2} + 33 x + 36$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 11\cdot 41$ |
$3$ |
$28.0623610078$ |
$77.71179925862245$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.6403628267$ |
| 3.1.22540.1 |
$x^{3} - x^{2} + 19 x - 55$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 23$ |
$4$ |
$28.2478004918$ |
$62.29228720573776$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.6168619465$ |
| 3.1.23912.1 |
$x^{3} + 14 x - 56$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 61$ |
$3$ |
$28.8096932392$ |
$80.83670527891697$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$12.0292340368$ |
| 3.1.24843.1 |
$x^{3} - 91$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$29.1788393635$ |
$35.04194650073235$ |
|
|
|
$S_3$ (as 3T2) |
$[3, 3]$ |
$2$ |
$1$ |
$5.49260395186$ |
| 3.1.25676.1 |
$x^{3} - x^{2} + 5 x + 29$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 131$ |
$3$ |
$29.5013884245$ |
$66.48459154193077$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.54100206504$ |
| 3.1.26999.1 |
$x^{3} - x^{2} - 2 x + 64$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 19\cdot 29$ |
$3$ |
$29.9996296251$ |
$85.89630709147573$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$20.7852739408$ |
| 3.1.27244.2 |
$x^{3} - x^{2} - 9 x + 99$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 139$ |
$3$ |
$30.0900995021$ |
$68.48457378187439$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$15.5678170603$ |
| 3.3.27881.1 |
$x^{3} - x^{2} - 30 x + 8$ |
$3$ |
[3,0] |
$7^{2}\cdot 569$ |
$2$ |
$30.322810288$ |
$87.28805703521202$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$41.859540644$ |
| 3.1.28763.1 |
$x^{3} - x^{2} + 5 x - 34$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 587$ |
$2$ |
$30.6392450736$ |
$88.65796202266182$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$3.26978044919$ |
| 3.1.28959.1 |
$x^{3} - x^{2} - 2 x + 99$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 197$ |
$3$ |
$30.7086826937$ |
$88.95952058734002$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.18992046495$ |
| 3.3.29204.1 |
$x^{3} - x^{2} - 37 x - 69$ |
$3$ |
[3,0] |
$2^{2}\cdot 7^{2}\cdot 149$ |
$3$ |
$30.7950405238$ |
$70.90526611662585$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$13.9400366732$ |
| 3.1.30772.1 |
$x^{3} - x^{2} + 5 x - 69$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 157$ |
$3$ |
$31.3366024455$ |
$91.70193825360194$ |
|
|
|
$S_3$ (as 3T2) |
$[18]$ |
$2$ |
$1$ |
$3.81206159375$ |
| 3.3.30968.1 |
$x^{3} - 35 x - 42$ |
$3$ |
[3,0] |
$2^{3}\cdot 7^{2}\cdot 79$ |
$3$ |
$31.4029937508$ |
$91.99351907925389$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$29.7049370424$ |
| 3.1.31507.3 |
$x^{3} - x^{2} + 19 x + 8$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 643$ |
$2$ |
$31.5841372075$ |
$92.79064205866086$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.4181568249$ |
| 3.1.32536.1 |
$x^{3} - x^{2} - 2 x - 34$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 83$ |
$3$ |
$31.9243002312$ |
$94.2937120784099$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$8.73761043708$ |
| 3.1.33908.1 |
$x^{3} - x^{2} + 5 x + 211$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 173$ |
$3$ |
$32.3668715898$ |
$96.26130400814988$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$18.1789993869$ |
| 3.1.34888.1 |
$x^{3} - x^{2} + 33 x - 13$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 89$ |
$3$ |
$32.6757344441$ |
$97.64245498213155$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$22.2131803237$ |
| 3.1.35623.1 |
$x^{3} - x^{2} + 12 x + 29$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 727$ |
$2$ |
$32.9036060632$ |
$98.66563124578228$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.905599368$ |
| 3.1.36652.1 |
$x^{3} - 14 x - 42$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 11\cdot 17$ |
$4$ |
$33.2174196097$ |
$79.43395022036077$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$14.1924451824$ |
| 3.3.37093.1 |
$x^{3} - x^{2} - 37 x + 92$ |
$3$ |
[3,0] |
$7^{2}\cdot 757$ |
$2$ |
$33.3501137733$ |
$100.68079428327376$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$2$ |
$15.692458166$ |
| 3.1.38024.1 |
$x^{3} - x^{2} - 16 x + 232$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 97$ |
$3$ |
$33.6268304214$ |
$101.93646150823373$ |
|
|
|
$S_3$ (as 3T2) |
$[9]$ |
$2$ |
$1$ |
$11.4159849359$ |
| 3.1.38367.1 |
$x^{3} + 21 x - 7$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 7^{2}\cdot 29$ |
$3$ |
$33.7276395097$ |
$70.99686239720955$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$5.25741412321$ |
