| 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 $p$ |
| 3.1.31.1 |
$x^{3} + x - 1$ |
$3$ |
(1, 1) |
$-\,31$ |
$1$ |
$3.14138065239$ |
$5.5677643628300215$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$0.38224508584$ |
$1$ |
$31$ |
| 3.1.527.1 |
$x^{3} + 5 x - 1$ |
$3$ |
(1, 1) |
$-\,17\cdot 31$ |
$2$ |
$8.07737424074$ |
$22.956480566497994$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$1.61728252844$ |
$1$ |
$31$ |
| 3.1.620.1 |
$x^{3} - x^{2} - 5 x - 5$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 5\cdot 31$ |
$3$ |
$8.52701898328$ |
$19.762983718745776$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$3.55291358919$ |
$1$ |
$31$ |
| 3.1.744.1 |
$x^{3} - x^{2} - 6 x - 6$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 31$ |
$3$ |
$9.06130979217$ |
$27.27636339397171$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.29429929653$ |
$1$ |
$31$ |
| 3.3.837.1 |
$x^{3} - 6 x - 1$ |
$3$ |
(3, 0) |
$3^{3}\cdot 31$ |
$2$ |
$9.42414195717$ |
$20.05960194310363$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$6.80136952587$ |
$3$ |
$31$ |
| 3.1.1147.1 |
$x^{3} - x^{2} - 3 x + 8$ |
$3$ |
(1, 1) |
$-\,31\cdot 37$ |
$2$ |
$10.4677772542$ |
$33.8673884437522$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$6.6038483382$ |
$1$ |
$37$ |
| 3.1.1612.1 |
$x^{3} - x^{2} - 3 x - 7$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 13\cdot 31$ |
$3$ |
$11.7252383329$ |
$31.866853723191245$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$7.12686306677$ |
$1$ |
$31$ |
| 3.1.1736.1 |
$x^{3} + 2 x - 16$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 7\cdot 31$ |
$3$ |
$12.0184900138$ |
$41.66533331199932$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.00614272602$ |
$1$ |
$31$ |
| 3.1.2387.1 |
$x^{3} - x^{2} + 6 x - 20$ |
$3$ |
(1, 1) |
$-\,7\cdot 11\cdot 31$ |
$3$ |
$13.3644412547$ |
$48.85693400122443$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.45829604356$ |
$1$ |
$31$ |
| 3.1.2604.1 |
$x^{3} - x^{2} + 9 x - 3$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 7\cdot 31$ |
$4$ |
$13.7577366928$ |
$40.50206423088982$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.6838574054$ |
$1$ |
$31$ |
| 3.1.2635.1 |
$x^{3} - x^{2} + 9 x - 4$ |
$3$ |
(1, 1) |
$-\,5\cdot 17\cdot 31$ |
$3$ |
$13.812115664$ |
$51.332251070842396$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.4683255601$ |
$1$ |
$31$ |
| 3.1.2728.1 |
$x^{3} + 10 x - 16$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 11\cdot 31$ |
$3$ |
$13.9727360556$ |
$52.230259428802384$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.8633410692$ |
$1$ |
$31$ |
| 3.1.2759.1 |
$x^{3} - x^{2} + 4 x - 11$ |
$3$ |
(1, 1) |
$-\,31\cdot 89$ |
$2$ |
$14.0254638611$ |
$52.52618394667559$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$2.44889225965$ |
$1$ |
$89$ |
| 3.1.2852.1 |
$x^{3} + 14 x - 4$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 23\cdot 31$ |
$3$ |
$14.1813151058$ |
$53.40411969127476$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.4289675336$ |
$1$ |
$31$ |
| 3.1.3348.1 |
$x^{3} + 9 x - 4$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3^{3}\cdot 31$ |
$3$ |
$14.9598928567$ |
$40.11920388620726$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.9057446337$ |
$1$ |
$31$ |
| 3.1.3596.1 |
$x^{3} - x^{2} - 9 x + 19$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 29\cdot 31$ |
$3$ |
$15.320510178$ |
$47.59556752168191$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$8.7907289844$ |
$1$ |
$31$ |
| 3.3.3596.1 |
$x^{3} - 11 x - 8$ |
$3$ |
(3, 0) |
$2^{2}\cdot 29\cdot 31$ |
$3$ |
$15.320510178$ |
$59.9666574022598$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$23.0493975608$ |
$3$ |
$31$ |
| 3.1.3720.1 |
$x^{3} - x^{2} + 10 x + 30$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 5\cdot 31$ |
$4$ |
$15.49462179$ |
$60.991802727907626$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$25.4083294222$ |
$1$ |
$31$ |
| 3.1.3999.1 |
$x^{3} + 9 x - 35$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 43$ |
$3$ |
$15.8726875752$ |
$63.23764701504951$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.3258124383$ |
$1$ |
$43$ |
| 3.1.4619.1 |
$x^{3} - x^{2} - 9 x - 14$ |
$3$ |
(1, 1) |
$-\,31\cdot 149$ |
$2$ |
$16.6539013364$ |
$67.96322535018479$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$10.0915425657$ |
$1$ |
$149$ |
| 3.1.5828.1 |
$x^{3} - x^{2} + 4 x + 28$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 31\cdot 47$ |
$3$ |
$17.9958838325$ |
$76.34133873596926$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$17.1531412128$ |
$1$ |
$47$ |
| 3.1.5859.1 |
$x^{3} - 12 x - 47$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 7\cdot 31$ |
$3$ |
$18.0277350208$ |
$53.07271814040024$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$14.4841411481$ |
$1$ |
$31$ |
| 3.1.6107.1 |
$x^{3} + 2 x - 15$ |
$3$ |
(1, 1) |
$-\,31\cdot 197$ |
$2$ |
$18.278587834$ |
$78.14729681825213$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$27.3572298903$ |
$1$ |
$197$ |
| 3.1.6200.1 |
$x^{3} + 5 x - 30$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 5^{2}\cdot 31$ |
$3$ |
$18.3709055001$ |
$46.04747738887663$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$39.5435526726$ |
$1$ |
$31$ |
| 3.1.6479.1 |
$x^{3} - x^{2} + 10 x - 32$ |
$3$ |
(1, 1) |
$-\,11\cdot 19\cdot 31$ |
$3$ |
$18.642435964$ |
$80.49223565040295$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$30.5348858915$ |
$1$ |
$31$ |
| 3.1.6572.1 |
$x^{3} - x^{2} - 9 x - 45$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 31\cdot 53$ |
$3$ |
$18.7312108075$ |
$64.34361328022038$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$24.7347346545$ |
$1$ |
$53$ |
| 3.1.6603.1 |
$x^{3} - x^{2} - 13 x - 20$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 71$ |
$3$ |
$18.7606162102$ |
$81.25884567233281$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$11.6955386435$ |
$1$ |
$71$ |
| 3.1.6851.1 |
$x^{3} - x^{2} + 18 x - 20$ |
$3$ |
(1, 1) |
$-\,13\cdot 17\cdot 31$ |
$3$ |
$18.992610238$ |
$82.77076778670111$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$16.9568298621$ |
$1$ |
$31$ |
| 3.1.7223.1 |
$x^{3} - x^{2} - 2 x - 32$ |
$3$ |
(1, 1) |
$-\,31\cdot 233$ |
$2$ |
$19.3303271849$ |
$84.98823447983844$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$32.8307014548$ |
$1$ |
$233$ |
| 3.1.7564.1 |
$x^{3} - x^{2} + 25 x + 9$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 31\cdot 61$ |
$3$ |
$19.6298586967$ |
$69.02913450639817$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$13.7144751218$ |
$1$ |
$61$ |
| 3.1.7719.1 |
$x^{3} - x^{2} + 18 x - 24$ |
$3$ |
(1, 1) |
$-\,3\cdot 31\cdot 83$ |
$3$ |
$19.7630368447$ |
$87.8578397184907$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$55.1896522956$ |
$1$ |
$83$ |
| 3.1.8215.1 |
$x^{3} - x^{2} + 4 x + 51$ |
$3$ |
(1, 1) |
$-\,5\cdot 31\cdot 53$ |
$3$ |
$20.1775851749$ |
$90.63663718386732$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$11.9396823147$ |
$1$ |
$53$ |
| 3.3.8277.1 |
$x^{3} - x^{2} - 22 x + 28$ |
$3$ |
(3, 0) |
$3\cdot 31\cdot 89$ |
$3$ |
$20.2282192271$ |
$90.97801932335085$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$35.3501486324$ |
$3$ |
$89$ |
| 3.3.8308.1 |
$x^{3} - x^{2} - 13 x + 11$ |
$3$ |
(3, 0) |
$2^{2}\cdot 31\cdot 67$ |
$3$ |
$20.2534414717$ |
$72.34439882439624$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$17.7154841799$ |
$3$ |
$67$ |
| 3.1.8463.1 |
$x^{3} - x^{2} + 6 x + 15$ |
$3$ |
(1, 1) |
$-\,3\cdot 7\cdot 13\cdot 31$ |
$4$ |
$20.3786204313$ |
$91.9945650568554$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$15.1498308669$ |
$1$ |
$31$ |
| 3.1.8556.1 |
$x^{3} - x^{2} - x - 53$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 23\cdot 31$ |
$4$ |
$20.4529956177$ |
$73.41622607741607$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$19.3671870837$ |
$1$ |
$31$ |
| 3.3.8556.1 |
$x^{3} - 27 x - 8$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 23\cdot 31$ |
$4$ |
$20.4529956177$ |
$92.49864863877742$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$45.0631901049$ |
$3$ |
$31$ |
| 3.1.8587.1 |
$x^{3} + 19 x - 16$ |
$3$ |
(1, 1) |
$-\,31\cdot 277$ |
$2$ |
$20.4776675302$ |
$92.66606714434361$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.70124989098$ |
$1$ |
$277$ |
| 3.3.8680.1 |
$x^{3} - 13 x - 2$ |
$3$ |
(3, 0) |
$2^{3}\cdot 5\cdot 7\cdot 31$ |
$4$ |
$20.551328839$ |
$93.16651759081692$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$36.4914598376$ |
$3$ |
$31$ |
| 3.1.8711.1 |
$x^{3} - x^{2} + 10 x - 17$ |
$3$ |
(1, 1) |
$-\,31\cdot 281$ |
$2$ |
$20.5757656383$ |
$93.33273809334$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$5.42553179143$ |
$1$ |
$281$ |
| 3.3.9052.1 |
$x^{3} - x^{2} - 23 x + 31$ |
$3$ |
(3, 0) |
$2^{2}\cdot 31\cdot 73$ |
$3$ |
$20.8408221966$ |
$95.14199913813037$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$30.7894192003$ |
$2$ |
$73$ |
| 3.1.9083.1 |
$x^{3} - x^{2} - 3 x - 54$ |
$3$ |
(1, 1) |
$-\,31\cdot 293$ |
$2$ |
$20.8645859825$ |
$95.30477427705287$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$36.2735074004$ |
$1$ |
$293$ |
| 3.1.9207.1 |
$x^{3} - 15 x - 29$ |
$3$ |
(1, 1) |
$-\,3^{3}\cdot 11\cdot 31$ |
$3$ |
$20.9591040835$ |
$66.53017308915885$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$9.61899932436$ |
$1$ |
$31$ |
| 3.1.9300.1 |
$x^{3} - x^{2} - 8 x - 18$ |
$3$ |
(1, 1) |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 31$ |
$4$ |
$21.0294371746$ |
$56.39641177254681$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$41.7573691838$ |
$1$ |
$31$ |
| 3.3.9300.1 |
$x^{3} - x^{2} - 13 x + 7$ |
$3$ |
(3, 0) |
$2^{2}\cdot 3\cdot 5^{2}\cdot 31$ |
$4$ |
$21.0294371746$ |
$44.76186168748628$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$36.5003883353$ |
$3$ |
$31$ |
| 3.1.9455.1 |
$x^{3} - x^{2} - 6 x + 40$ |
$3$ |
(1, 1) |
$-\,5\cdot 31\cdot 61$ |
$3$ |
$21.1456242683$ |
$97.23682430026189$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$45.7243474198$ |
$1$ |
$61$ |
| 3.3.9517.1 |
$x^{3} - 22 x - 35$ |
$3$ |
(3, 0) |
$31\cdot 307$ |
$2$ |
$21.1917435512$ |
$97.5551126287085$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$[2]$ |
$2$ |
$2$ |
$25.7313231194$ |
$2$ |
$307$ |
| 3.1.9672.1 |
$x^{3} - x^{2} - 3 x + 39$ |
$3$ |
(1, 1) |
$-\,2^{3}\cdot 3\cdot 13\cdot 31$ |
$4$ |
$21.3061720305$ |
$98.34632682515398$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$40.7586104154$ |
$1$ |
$31$ |
| 3.1.10075.1 |
$x^{3} + 10 x - 15$ |
$3$ |
(1, 1) |
$-\,5^{2}\cdot 13\cdot 31$ |
$3$ |
$21.5980736737$ |
$58.699246439401115$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$1$ |
$23.3825505148$ |
$1$ |
$31$ |
| 3.3.10261.1 |
$x^{3} - x^{2} - 22 x - 4$ |
$3$ |
(3, 0) |
$31\cdot 331$ |
$2$ |
$21.7301752681$ |
$101.29659421717987$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
trivial |
$2$ |
$2$ |
$22.8901612423$ |
$3$ |
$331$ |
