| 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 |
| 3.1.588.1 |
$x^{3} - x^{2} + 5 x + 1$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 7^{2}$ |
$3$ |
$8.37771872824$ |
$10.061112020813587$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$1.65400419943$ |
| 3.1.931.1 |
$x^{3} - x^{2} + 5 x - 6$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 19$ |
$2$ |
$9.7644973898$ |
$15.950543793511486$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$1.84692884153$ |
| 3.1.2548.1 |
$x^{3} - x^{2} + 12 x + 8$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 13$ |
$3$ |
$13.6583993889$ |
$26.38762874017197$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.23033576204$ |
| 3.1.2891.3 |
$x^{3} - x^{2} - 2 x - 20$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 59$ |
$2$ |
$14.2456640137$ |
$28.107660494694265$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.63060662824$ |
| 3.3.3969.1 |
$x^{3} - 21 x - 28$ |
$3$ |
[3,0] |
$3^{4}\cdot 7^{2}$ |
$2$ |
$15.8328962637$ |
$15.83289626371223$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$12.5941889569$ |
| 3.3.4312.1 |
$x^{3} - x^{2} - 16 x + 8$ |
$3$ |
[3,0] |
$2^{3}\cdot 7^{2}\cdot 11$ |
$3$ |
$16.2764460888$ |
$34.32733034460722$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$7.2288617767$ |
| 3.1.5047.1 |
$x^{3} - x^{2} - 2 x - 13$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 103$ |
$2$ |
$17.1531717027$ |
$37.13789685454593$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.96603111175$ |
| 3.1.5635.1 |
$x^{3} + 7 x - 28$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 23$ |
$3$ |
$17.7949992264$ |
$39.24168194830305$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$6.50717077051$ |
| 3.1.6419.1 |
$x^{3} - x^{2} - 9 x + 22$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 131$ |
$2$ |
$18.5847101386$ |
$41.88266818867061$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.21821079135$ |
| 3.1.8036.1 |
$x^{3} + 14 x - 28$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 41$ |
$3$ |
$20.0299551122$ |
$46.86197816804901$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$5.30367610236$ |
| 3.1.8183.1 |
$x^{3} - 7 x - 70$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 167$ |
$2$ |
$20.1513517433$ |
$47.28865141512203$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.32599903579$ |
| 3.3.8281.2 |
$x^{3} - x^{2} - 30 x - 27$ |
$3$ |
[3,0] |
$7^{2}\cdot 13^{2}$ |
$2$ |
$20.2314772451$ |
$20.23147724512629$ |
|
✓ |
|
$C_3$ (as 3T1) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$7.94957796855$ |
| 3.3.9800.1 |
$x^{3} - x^{2} - 23 x - 13$ |
$3$ |
[3,0] |
$2^{3}\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$21.3997496113$ |
$30.26381613169108$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$15.3943368652$ |
| 3.1.10535.1 |
$x^{3} - 7 x - 21$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 43$ |
$3$ |
$21.9218993772$ |
$53.655954283494445$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.70073080025$ |
| 3.1.10584.1 |
$x^{3} - 21 x - 70$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$21.9558342601$ |
$37.289378982440624$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.1834544689$ |
| 3.3.11417.1 |
$x^{3} - x^{2} - 30 x + 71$ |
$3$ |
[3,0] |
$7^{2}\cdot 233$ |
$2$ |
$22.5173528685$ |
$55.85687745570608$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$5.46737744196$ |
| 3.1.11907.2 |
$x^{3} - 21$ |
$3$ |
[1,1] |
$-\,3^{5}\cdot 7^{2}$ |
$2$ |
$22.8349878331$ |
$27.423380759717027$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$8.53993806759$ |
| 3.1.12936.1 |
$x^{3} - x^{2} - 30 x + 78$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3\cdot 7^{2}\cdot 11$ |
$4$ |
$23.4746973777$ |
$59.45668024506056$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$15.8261861221$ |
| 3.1.13279.1 |
$x^{3} + 7 x - 21$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 271$ |
$2$ |
$23.6803685343$ |
$60.23977468184307$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$2.92754418277$ |
| 3.1.13524.1 |
$x^{3} - x^{2} + 5 x + 43$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 23$ |
$4$ |
$23.8251176577$ |
$60.79295226517837$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.8787067002$ |
| 3.3.15141.1 |
$x^{3} - x^{2} - 37 x + 64$ |
$3$ |
[3,0] |
$3\cdot 7^{2}\cdot 103$ |
$3$ |
$24.7391545177$ |
$64.32472423832594$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$16.0318034619$ |
| 3.1.15239.1 |
$x^{3} - 7 x - 119$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 311$ |
$2$ |
$24.7924144334$ |
$64.53255910697709$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.86903289467$ |
| 3.1.16023.1 |
$x^{3} - x^{2} + 12 x + 15$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 109$ |
$3$ |
$25.2104894603$ |
$66.17174228752027$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$2.84696808766$ |
| 3.1.16072.1 |
$x^{3} - x^{2} + 26 x - 62$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 7^{2}\cdot 41$ |
$3$ |
$25.2361620743$ |
$66.27284508488681$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.4111413765$ |
| 3.1.16268.2 |
$x^{3} - x^{2} + 19 x - 125$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 83$ |
$3$ |
$25.3383338851$ |
$52.92055660111312$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.08068738937$ |
| 3.3.16660.1 |
$x^{3} - 28 x - 28$ |
$3$ |
[3,0] |
$2^{2}\cdot 5\cdot 7^{2}\cdot 17$ |
$4$ |
$25.5402414725$ |
$53.55435831347925$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$9.92173892171$ |
| 3.3.16905.1 |
$x^{3} - x^{2} - 16 x + 1$ |
$3$ |
[3,0] |
$3\cdot 5\cdot 7^{2}\cdot 23$ |
$4$ |
$25.6648299879$ |
$67.96858690891932$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$10.4958655338$ |
| 3.1.19796.1 |
$x^{3} - 7 x - 28$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 101$ |
$3$ |
$27.05157039$ |
$73.55113449077666$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$5.19834454456$ |
| 3.1.21511.3 |
$x^{3} - x^{2} - 2 x + 29$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 439$ |
$2$ |
$27.811230216$ |
$76.67096924299021$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$3.42345011175$ |
| 3.3.21805.1 |
$x^{3} - x^{2} - 30 x - 20$ |
$3$ |
[3,0] |
$5\cdot 7^{2}\cdot 89$ |
$3$ |
$27.9373599697$ |
$77.19313851849782$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$12.8137556432$ |
| 3.1.21903.1 |
$x^{3} + 21 x - 77$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 149$ |
$3$ |
$27.9791511464$ |
$77.36641177471529$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$7.6554034234$ |
| 3.1.22099.2 |
$x^{3} - x^{2} - 30 x - 76$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 11\cdot 41$ |
$3$ |
$28.0623610078$ |
$77.71179925862245$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$10.0612603713$ |
| 3.1.22883.1 |
$x^{3} + 14 x - 21$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 467$ |
$2$ |
$28.3903657065$ |
$79.07826525969661$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[12]$ |
$[12]$ |
$2$ |
$1$ |
$5.15865889994$ |
| 3.1.23471.1 |
$x^{3} - x^{2} - 16 x + 155$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 479$ |
$2$ |
$28.6314843913$ |
$80.08781590127066$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$4.6426304907$ |
| 3.3.25137.1 |
$x^{3} - 21 x - 21$ |
$3$ |
[3,0] |
$3^{3}\cdot 7^{2}\cdot 19$ |
$3$ |
$29.2934921694$ |
$57.466792490343515$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$8.27360516933$ |
| 3.1.26215.1 |
$x^{3} - 35 x - 175$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 107$ |
$3$ |
$29.7063951735$ |
$84.63998629183843$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$4.0079996821$ |
| 3.1.27244.3 |
$x^{3} + 28 x - 28$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 139$ |
$3$ |
$30.0900995021$ |
$68.48457378187439$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$3.4308847245$ |
| 3.1.28371.1 |
$x^{3} - x^{2} - 37 x + 106$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 193$ |
$3$ |
$30.4994177081$ |
$88.05174662535941$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.93538558687$ |
| 3.1.28420.1 |
$x^{3} - x^{2} - 16 x + 106$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 29$ |
$4$ |
$30.5169662838$ |
$88.12775159991261$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$22.4326968861$ |
| 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) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$25.6941001131$ |
| 3.1.30135.1 |
$x^{3} - x^{2} + 40 x + 15$ |
$3$ |
[1,1] |
$-\,3\cdot 5\cdot 7^{2}\cdot 41$ |
$4$ |
$31.1188638087$ |
$90.7478305075947$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$11.2229475232$ |
| 3.1.30331.1 |
$x^{3} - x^{2} + 26 x + 36$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 619$ |
$2$ |
$31.1861844377$ |
$91.04246709614564$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.2746946359$ |
| 3.1.30772.2 |
$x^{3} - x^{2} + 12 x - 34$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 7^{2}\cdot 157$ |
$3$ |
$31.3366024455$ |
$91.70193825360194$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$21.123197058$ |
| 3.1.31115.1 |
$x^{3} - x^{2} + 19 x - 20$ |
$3$ |
[1,1] |
$-\,5\cdot 7^{2}\cdot 127$ |
$3$ |
$31.4526036181$ |
$92.21159963596375$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[12]$ |
$[12]$ |
$2$ |
$1$ |
$3.00081769339$ |
| 3.1.31507.1 |
$x^{3} - x^{2} + 5 x - 104$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 643$ |
$2$ |
$31.5841372075$ |
$92.79064205866086$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$14.4411291509$ |
| 3.1.33075.1 |
$x^{3} - 175$ |
$3$ |
[1,1] |
$-\,3^{3}\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$32.099624417$ |
$38.54962520958807$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$12.3318370619$ |
| 3.1.33859.1 |
$x^{3} - x^{2} - 9 x - 34$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 691$ |
$2$ |
$32.351273095$ |
$96.19172589713757$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$6.28801054752$ |
| 3.1.34251.1 |
$x^{3} - x^{2} + 33 x - 90$ |
$3$ |
[1,1] |
$-\,3\cdot 7^{2}\cdot 233$ |
$3$ |
$32.4756424991$ |
$96.74694970543153$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$25.0097558018$ |
| 3.1.35231.1 |
$x^{3} - x^{2} - 2 x - 216$ |
$3$ |
[1,1] |
$-\,7^{2}\cdot 719$ |
$2$ |
$32.7824688191$ |
$98.1212649882452$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$29.434364437$ |
| 3.1.36260.1 |
$x^{3} - x^{2} - 16 x + 50$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 37$ |
$4$ |
$33.0985727274$ |
$99.54387739464931$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$[3]$ |
$2$ |
$1$ |
$18.0273988531$ |
