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 |
3.1.324.1 |
$x^{3} - 3 x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}$ |
$2$ |
$6.86828545532$ |
$8.65349742184445$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$4.04764172645$ |
3.1.567.1 |
$x^{3} - 3 x - 5$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 7$ |
$2$ |
$8.27677252914$ |
$11.447501074569505$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$2.46402039258$ |
3.1.1539.1 |
$x^{3} + 6 x - 5$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 19$ |
$2$ |
$11.5455033938$ |
$18.859860385004858$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$9.16356433339$ |
3.3.1620.1 |
$x^{3} - 12 x - 14$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 5$ |
$3$ |
$11.7446029235$ |
$15.357953166968596$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$10.1679428335$ |
3.3.2349.1 |
$x^{3} - 12 x - 13$ |
$3$ |
[3,0] |
$3^{4}\cdot 29$ |
$2$ |
$13.2931428651$ |
$23.300254887372947$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$11.9198361438$ |
3.1.3240.1 |
$x^{3} - 3 x - 22$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 5$ |
$3$ |
$14.797272446$ |
$27.364761579423373$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$19.0659298755$ |
3.1.3483.1 |
$x^{3} + 15 x - 4$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 43$ |
$2$ |
$15.1583230416$ |
$28.37238868197542$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$12.1861709357$ |
3.1.4212.1 |
$x^{3} + 9 x - 36$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 13$ |
$3$ |
$16.1496378363$ |
$31.200628666555602$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$19.0652515517$ |
3.1.4455.1 |
$x^{3} - 3 x - 13$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 11$ |
$3$ |
$16.4544196573$ |
$32.08802724398451$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$8.03592605573$ |
3.1.5427.1 |
$x^{3} + 6 x - 13$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 67$ |
$2$ |
$17.573298008$ |
$35.41596455414278$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$15.6284604167$ |
3.1.6156.1 |
$x^{3} + 6 x - 14$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 19$ |
$3$ |
$18.3273442329$ |
$29.938162215130085$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.71074614539$ |
3.1.6156.2 |
$x^{3} - 12 x - 22$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 19$ |
$3$ |
$18.3273442329$ |
$29.938162215130085$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$3.66160038964$ |
3.3.6237.1 |
$x^{3} - 12 x - 5$ |
$3$ |
[3,0] |
$3^{4}\cdot 7\cdot 11$ |
$3$ |
$18.407377319$ |
$37.9670658515373$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$25.5325910926$ |
3.1.6399.1 |
$x^{3} + 9 x - 45$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 79$ |
$2$ |
$18.5653882864$ |
$38.456983737546345$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$6.15496627162$ |
3.1.7128.1 |
$x^{3} + 6 x - 32$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 11$ |
$3$ |
$19.24520598$ |
$40.58850068501063$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$29.120349922$ |
3.1.7371.1 |
$x^{3} - 12 x - 23$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 7\cdot 13$ |
$3$ |
$19.4614623501$ |
$41.27455210028946$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$18.1791623418$ |
3.1.8343.1 |
$x^{3} - 21 x - 41$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 103$ |
$2$ |
$20.2818429052$ |
$43.91170349655221$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$10.2047028815$ |
3.3.9153.1 |
$x^{3} - 21 x - 4$ |
$3$ |
[3,0] |
$3^{4}\cdot 113$ |
$2$ |
$20.9180479468$ |
$45.99396969216493$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$66.0433492178$ |
3.1.9315.1 |
$x^{3} - 18 x - 63$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 23$ |
$3$ |
$21.0407372505$ |
$46.39921073529938$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$28.6286564262$ |
3.1.10287.1 |
$x^{3} + 15 x - 32$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 127$ |
$2$ |
$21.7485135726$ |
$48.75998164220662$ |
|
|
|
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$28.9918775958$ |
3.1.11016.1 |
$x^{3} + 6 x - 40$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 17$ |
$3$ |
$22.2505786156$ |
$50.45812718894282$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$42.321512895$ |
3.3.11097.1 |
$x^{3} - 21 x - 31$ |
$3$ |
[3,0] |
$3^{4}\cdot 137$ |
$2$ |
$22.3049812248$ |
$50.643295250437625$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$16.5359455291$ |
3.1.11988.1 |
$x^{3} - 30 x - 76$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 37$ |
$3$ |
$22.8866508776$ |
$52.63716987362767$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$36.611910361$ |
3.1.12231.1 |
$x^{3} + 9 x - 63$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 151$ |
$2$ |
$23.0402571586$ |
$53.16797829076763$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$6.53227072575$ |
3.1.13203.1 |
$x^{3} - 30 x - 67$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 163$ |
$2$ |
$23.6351052764$ |
$55.24022961951863$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$25.6729762536$ |
3.1.13932.1 |
$x^{3} + 24 x - 4$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 43$ |
$3$ |
$24.0623379424$ |
$45.03835964061842$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$6.76503498728$ |
3.1.13932.2 |
$x^{3} + 6 x - 22$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 43$ |
$3$ |
$24.0623379424$ |
$45.03835964061842$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.39200992801$ |
3.3.14013.1 |
$x^{3} - 30 x - 59$ |
$3$ |
[3,0] |
$3^{4}\cdot 173$ |
$2$ |
$24.1088802981$ |
$56.909494045298054$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$2$ |
$18.6925849015$ |
3.1.14175.1 |
$x^{3} + 15 x - 40$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5^{2}\cdot 7$ |
$3$ |
$24.2014296904$ |
$33.472696200252074$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$24.1479184671$ |
3.1.14175.2 |
$x^{3} + 15 x - 5$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5^{2}\cdot 7$ |
$3$ |
$24.2014296904$ |
$33.472696200252074$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$4.92709649874$ |
3.1.14904.1 |
$x^{3} - 3 x - 94$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 23$ |
$3$ |
$24.6093955782$ |
$58.69087502307282$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$33.3450416927$ |
3.1.15147.1 |
$x^{3} + 6 x - 23$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 11\cdot 17$ |
$3$ |
$24.7424219224$ |
$59.16739874454812$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$2$ |
$1$ |
$6.63193407399$ |
3.3.16200.1 |
$x^{3} - 30 x - 40$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$25.3029799591$ |
$35.783817426546634$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$55.2672272771$ |
3.3.17172.1 |
$x^{3} - 30 x - 58$ |
$3$ |
[3,0] |
$2^{2}\cdot 3^{4}\cdot 53$ |
$3$ |
$25.7992428117$ |
$50.00187286567662$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$32.6089690272$ |
3.1.18063.1 |
$x^{3} + 15 x - 13$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 223$ |
$2$ |
$26.2379536564$ |
$64.61213688514853$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[2]$ |
$2$ |
$1$ |
$6.39203493941$ |
3.1.18792.1 |
$x^{3} + 15 x - 14$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 29$ |
$3$ |
$26.5862857302$ |
$65.90307293694563$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$46.2356678197$ |
3.1.19035.1 |
$x^{3} - 12 x - 31$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 47$ |
$3$ |
$26.700391359$ |
$66.32780175578546$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$34.4028184907$ |
3.3.20088.1 |
$x^{3} - 30 x - 32$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{4}\cdot 31$ |
$3$ |
$27.1839293765$ |
$68.13770683734411$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$66.7665347768$ |
3.1.20979.1 |
$x^{3} + 36 x - 9$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 7\cdot 37$ |
$3$ |
$27.5800422827$ |
$69.63243060193999$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[4]$ |
$2$ |
$1$ |
$6.36129353382$ |
3.1.21708.1 |
$x^{3} - 18 x - 90$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 67$ |
$3$ |
$27.8958717444$ |
$56.21933938971472$ |
|
|
|
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$7.59235163296$ |
3.1.21708.2 |
$x^{3} + 36 x - 18$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 67$ |
$3$ |
$27.8958717444$ |
$56.21933938971472$ |
|
|
|
$S_3$ (as 3T2) |
$[6]$ |
$2$ |
$1$ |
$4.9902940418$ |
3.1.21951.1 |
$x^{3} - 21 x - 68$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 271$ |
$2$ |
$27.9995748235$ |
$71.22727317835208$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$78.9868795622$ |
3.1.22680.1 |
$x^{3} - 3 x - 58$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 5\cdot 7$ |
$4$ |
$28.3061638819$ |
$72.40035382572933$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$64.9121347545$ |
3.3.22761.1 |
$x^{3} - 21 x - 23$ |
$3$ |
[3,0] |
$3^{4}\cdot 281$ |
$2$ |
$28.339821659$ |
$72.52952494328268$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$14.6218678901$ |
3.1.23652.1 |
$x^{3} - 3 x - 148$ |
$3$ |
[1,1] |
$-\,2^{2}\cdot 3^{4}\cdot 73$ |
$3$ |
$28.7048946154$ |
$73.93551438233459$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$43.3533478736$ |
3.1.23895.1 |
$x^{3} + 33 x - 94$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 5\cdot 59$ |
$3$ |
$28.8028642985$ |
$74.31434955782635$ |
|
|
|
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$103.051809351$ |
3.3.23976.1 |
$x^{3} - 21 x - 22$ |
$3$ |
[3,0] |
$2^{3}\cdot 3^{4}\cdot 37$ |
$3$ |
$28.8353732022$ |
$74.44019952022074$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$2$ |
$73.6220185$ |
3.1.25839.1 |
$x^{3} - 3 x - 31$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 11\cdot 29$ |
$3$ |
$29.563685073$ |
$77.27820298106069$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$11.4765622097$ |
3.1.26568.1 |
$x^{3} + 15 x - 22$ |
$3$ |
[1,1] |
$-\,2^{3}\cdot 3^{4}\cdot 41$ |
$3$ |
$29.8391389996$ |
$78.36075194668068$ |
|
|
✓ |
$S_3$ (as 3T2) |
trivial |
$2$ |
$1$ |
$45.9622544942$ |
3.1.26811.1 |
$x^{3} + 6 x - 31$ |
$3$ |
[1,1] |
$-\,3^{4}\cdot 331$ |
$2$ |
$29.9298360285$ |
$78.7182933559387$ |
|
|
✓ |
$S_3$ (as 3T2) |
$[3]$ |
$2$ |
$1$ |
$11.6018424946$ |