| 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 |
| 6.0.1778112.1 |
$x^{6} + 3 x^{4} - 2 x^{3} + 6 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$11.0067690039$ |
$29.3133549806909$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$7.66963675212$ |
| 6.0.2177712.1 |
$x^{6} - x^{5} - 4 x^{2} + 8$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 71^{2}$ |
$3$ |
$11.3850097631$ |
$33.442143949031745$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$17.6663598699$ |
| 6.2.2299968.1 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 4 x^{2} + 4 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{3}\cdot 11^{3}$ |
$3$ |
$11.4891252931$ |
$38.94309359419253$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$8.94858785913$ |
| 6.0.2611467.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 6 x^{3} + 6 x^{2} - 7 x + 5$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 311^{2}$ |
$2$ |
$11.7349368552$ |
$40.199544816599136$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$8.73416086387$ |
| 6.0.2725888.1 |
$x^{6} - x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} + 4 x + 8$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 11^{3}$ |
$2$ |
$11.8191070971$ |
$40.63282352308103$ |
|
|
|
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$27.7367899009$ |
| 6.2.2725888.5 |
$x^{6} - x^{5} - x^{4} + 2 x^{3} - 5 x^{2} - x - 3$ |
$6$ |
[2,2] |
$2^{11}\cdot 11^{3}$ |
$2$ |
$11.8191070971$ |
$40.63282352308103$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$18.6829042442$ |
| 6.2.3200000.1 |
$x^{6} - 2 x^{5} + 4 x + 2$ |
$6$ |
[2,2] |
$2^{10}\cdot 5^{5}$ |
$2$ |
$12.1392446201$ |
$28.57900880593445$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$15.5733986742$ |
| 6.0.3421872.4 |
$x^{6} - 2 x^{5} + 6 x^{4} - 12 x^{3} + 14 x^{2} - 10 x + 4$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 89^{2}$ |
$3$ |
$12.2756348091$ |
$28.44982682753188$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$2$ |
$2$ |
$5.3725526246$ |
| 6.0.3479787.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{2} + 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 359^{2}$ |
$2$ |
$12.3100205204$ |
$43.190493395557326$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$9.57099207339$ |
| 6.0.3786752.3 |
$x^{6} - x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} - 6 x + 10$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 43^{2}$ |
$2$ |
$12.4846913645$ |
$44.11301238665728$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$14.013439558$ |
| 6.0.3895843.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - x + 3$ |
$6$ |
[0,3] |
$-\,7^{2}\cdot 43^{3}$ |
$2$ |
$12.5439286323$ |
$44.42734513579336$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$8.75310751929$ |
| 6.2.5000000.1 |
$x^{6} - 2 x^{5} - 8 x - 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{7}$ |
$2$ |
$13.0766048601$ |
$27.202271339006447$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$22.9563447187$ |
| 6.2.5256144.1 |
$x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + x^{2} + 5 x + 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{3}\cdot 23^{3}$ |
$3$ |
$13.1859434583$ |
$41.68317719787903$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$38.3435411021$ |
| 6.0.5400000.3 |
$x^{6} - 2 x^{5} + 5 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$ |
$3$ |
$13.2454167278$ |
$31.18323200079904$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$2$ |
$4.93230060794$ |
| 6.0.5400000.4 |
$x^{6} - 2 x^{5} + 5 x^{4} + 6 x + 3$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$ |
$3$ |
$13.2454167278$ |
$41.03944127612018$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$13.8203686028$ |
| 6.2.5778125.2 |
$x^{6} - 5 x^{2} - 6 x - 5$ |
$6$ |
[2,2] |
$5^{5}\cdot 43^{2}$ |
$2$ |
$13.3956714983$ |
$41.739739355256155$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$21.401504859$ |
| 6.0.5787963.1 |
$x^{6} - x^{5} + 4 x^{4} - 12 x^{3} + 15 x^{2} - 9 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 463^{2}$ |
$2$ |
$13.3994701129$ |
$49.04914445444661$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$12.1291618824$ |
| 6.0.6154544.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 2 x^{3} + 6 x^{2} + 12 x + 4$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}\cdot 17^{2}$ |
$3$ |
$13.5373184967$ |
$49.80798473323167$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$34.7329016144$ |
| 6.0.6627103.2 |
$x^{6} - 2 x^{5} - 8 x^{3} + 21 x^{2} - 8 x + 1$ |
$6$ |
[0,3] |
$-\,7^{3}\cdot 139^{2}$ |
$2$ |
$13.7052602488$ |
$50.73771797850044$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$10.0973990726$ |
| 6.0.6750000.1 |
$x^{6} - x^{5} + 5 x^{2} + 3 x + 2$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 5^{6}$ |
$3$ |
$13.74729637$ |
$32.16073334649287$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$42.3233145267$ |
| 6.0.7129088.4 |
$x^{6} - 3 x^{5} + 7 x^{4} - 4 x^{3} + 8 x^{2} - 4 x + 4$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 59^{2}$ |
$2$ |
$13.8730620665$ |
$51.6723833953922$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$20.5428136872$ |
| 6.0.8108208.2 |
$x^{6} - 3 x^{5} + 4 x^{4} - 2 x + 2$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 137^{2}$ |
$3$ |
$14.1738385061$ |
$46.45422521927823$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$44.1031162279$ |
| 6.0.9148592.2 |
$x^{6} - x^{5} + 4 x^{4} + x^{2} + 3 x + 2$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 83^{3}$ |
$2$ |
$14.4619118474$ |
$47.877621361804$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$46.6823817044$ |
| 6.2.9483264.1 |
$x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + 7 x^{2} - 2 x - 5$ |
$6$ |
[2,2] |
$2^{10}\cdot 3^{3}\cdot 7^{3}$ |
$3$ |
$14.5487709578$ |
$44.04495071120707$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$36.4613498789$ |
| 6.0.9590832.1 |
$x^{6} - x^{5} + 4 x^{4} + 4 x^{3} + x^{2} + 3 x + 10$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 149^{2}$ |
$3$ |
$14.5761461422$ |
$36.811012081445085$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$2$ |
$2$ |
$9.58735606627$ |
| 6.2.9800000.2 |
$x^{6} - 10 x^{3} - 4 x + 5$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{5}\cdot 7^{2}$ |
$3$ |
$14.628653257$ |
$47.63317368567695$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$34.6257839335$ |
| 6.0.9834496.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 5 x^{2} - 6 x + 7$ |
$6$ |
[0,3] |
$-\,2^{12}\cdot 7^{4}$ |
$2$ |
$14.6372228401$ |
$31.90883292885454$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$31.6560004442$ |
| 6.0.10209375.1 |
$x^{6} - 2 x^{5} + 5 x^{4} + 9 x + 12$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$14.7287715469$ |
$48.12301053396556$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$30.6381933629$ |
| 6.2.10368000.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} - 4 x - 6$ |
$6$ |
[2,2] |
$2^{10}\cdot 3^{4}\cdot 5^{3}$ |
$3$ |
$14.7666675706$ |
$24.1776264427508$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$3$ |
$21.9198018435$ |
| 6.0.10546875.1 |
$x^{6} - 5 x^{4} + 15 x^{2} - 11 x + 5$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 5^{8}$ |
$2$ |
$14.8088260968$ |
$29.935943327131625$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$17.5548258232$ |
| 6.2.10731125.1 |
$x^{6} - x^{5} + 2 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 293^{2}$ |
$2$ |
$14.8516330053$ |
$38.27531841800928$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$3$ |
$6.81902608276$ |
| 6.0.10784448.3 |
$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} + 4 x + 4$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 79^{2}$ |
$3$ |
$14.8639072536$ |
$45.48373790490821$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$34.1944381174$ |
| 6.0.10916416.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 7 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{2}\cdot 59^{2}$ |
$3$ |
$14.8940684767$ |
$40.64480286580315$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$2$ |
$2$ |
$5.4020629411$ |
| 6.2.11366912.2 |
$x^{6} - 2 x^{5} + 7 x^{4} - 10 x^{3} + 12 x^{2} - 8 x + 1$ |
$6$ |
[2,2] |
$2^{9}\cdot 149^{2}$ |
$2$ |
$14.9947909805$ |
$34.52535300326414$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$3$ |
$11.2091815101$ |
| 6.0.12800000.1 |
$x^{6} - 2 x^{5} + 5 x^{4} + 4 x + 2$ |
$6$ |
[0,3] |
$-\,2^{12}\cdot 5^{5}$ |
$2$ |
$15.2944898266$ |
$42.82013114405259$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$61.8109645217$ |
| 6.2.12869712.1 |
$x^{6} - x^{5} - x^{3} + 4 x^{2} + 3 x - 9$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{3}\cdot 31^{3}$ |
$3$ |
$15.3083413628$ |
$47.53887228405204$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$34.8170402258$ |
| 6.2.13203125.1 |
$x^{6} - x^{5} - 4 x - 1$ |
$6$ |
[2,2] |
$5^{7}\cdot 13^{2}$ |
$2$ |
$15.3737373026$ |
$43.68930970521314$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$18.2488150839$ |
| 6.2.13530125.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - x^{3} + 2 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 7^{2}\cdot 47^{2}$ |
$3$ |
$15.4365520444$ |
$60.64925245200599$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$20.0167357786$ |
| 6.2.13530125.2 |
$x^{6} - 3 x^{4} - 2 x^{3} + 11 x^{2} - 7 x + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 7^{2}\cdot 47^{2}$ |
$3$ |
$15.4365520444$ |
$40.55859958134649$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$3$ |
$8.49157891171$ |
| 6.0.13687488.1 |
$x^{6} - x^{5} + x^{4} + x^{3} + x^{2} - x + 4$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 89^{2}$ |
$3$ |
$15.4663306968$ |
$60.82483477139187$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$55.9028130089$ |
| 6.0.13841712.3 |
$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 12 x^{2} - 10 x + 4$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 179^{2}$ |
$3$ |
$15.4952397934$ |
$40.34698988068586$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$2$ |
$2$ |
$9.45065645161$ |
| 6.0.14625792.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 12 x^{3} + 15 x^{2} - 18 x + 15$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 3^{3}\cdot 23^{2}$ |
$3$ |
$15.6381928835$ |
$49.08361221655921$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$39.4471392322$ |
| 6.0.14697207.1 |
$x^{6} - x^{5} + 3 x^{4} + 6 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 7^{3}\cdot 23^{2}$ |
$3$ |
$15.6508934626$ |
$49.70321159788357$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$38.4305857854$ |
| 6.2.14792000.2 |
$x^{6} - 3 x^{4} - 8 x^{3} - 9 x^{2} - 8 x - 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{3}\cdot 43^{2}$ |
$3$ |
$15.6676724305$ |
$41.47288270665544$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$2$ |
$3$ |
$20.0397950081$ |
| 6.2.15000633.1 |
$x^{6} - 3 x^{5} - 3 x^{4} + 4 x^{3} - 12 x^{2} + 6 x - 5$ |
$6$ |
[2,2] |
$3^{7}\cdot 19^{3}$ |
$2$ |
$15.7042884755$ |
$32.78737625893961$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$48.9955672887$ |
| 6.0.15106608.2 |
$x^{6} - 3 x^{5} + 4 x^{4} + 6 x^{2} + 2 x + 2$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 17^{2}$ |
$4$ |
$15.7227252981$ |
$54.2732390008592$ |
|
|
✓ |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$52.8636670977$ |
| 6.0.15268608.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{2} - 18 x + 18$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 3^{3}\cdot 47^{2}$ |
$3$ |
$15.7507017366$ |
$62.510052166634665$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$2$ |
$35.9635639851$ |
| 6.0.16133283.3 |
$x^{6} - x^{5} + 3 x^{4} + 9 x^{3} + 5 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 773^{2}$ |
$2$ |
$15.8959733257$ |
$48.155996511338024$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$2$ |
$2$ |
$8.60637589824$ |
| 6.2.16200000.1 |
$x^{6} - 2 x^{5} - 6 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{4}\cdot 5^{5}$ |
$3$ |
$15.9069104351$ |
$43.356828069359494$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$77.61245252$ |
| 6.2.16200000.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{2} + 8 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{4}\cdot 5^{5}$ |
$3$ |
$15.9069104351$ |
$34.41233724365281$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$2$ |
$3$ |
$66.4566196514$ |
