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 |
6.0.9747.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 19^{2}$ |
$2$ |
$4.62180723059$ |
$12.332838034173273$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$0.601543105945$ |
6.0.10051.1 |
$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,19\cdot 23^{2}$ |
$2$ |
$4.64552582629$ |
$20.904544960366874$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.205216461048$ |
6.0.10571.1 |
$x^{6} - x^{5} - x^{4} + 2 x^{3} - x + 1$ |
$6$ |
[0,3] |
$-\,11\cdot 31^{2}$ |
$2$ |
$4.68474560175$ |
$18.466185312619388$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.21320935989$ |
6.0.10816.1 |
$x^{6} - x^{4} - 2 x^{3} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13^{2}$ |
$2$ |
$4.70266937544$ |
$11.057549627357744$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$0.434147804699$ |
6.0.11691.1 |
$x^{6} - x^{5} - x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 433$ |
$2$ |
$4.76403865609$ |
$36.0416425818802$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$0.691359666578$ |
6.0.12167.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,23^{3}$ |
$1$ |
$4.79583152331$ |
$4.795831523312719$ |
|
✓ |
✓ |
$S_3$ (as 6T2) |
trivial |
$2$ |
$2$ |
$0.237219601798$ |
6.0.14283.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 23^{2}$ |
$2$ |
$4.92572209907$ |
$8.306623862918075$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$6$ |
$2$ |
$0.803563966653$ |
6.0.14731.1 |
$x^{6} - x^{5} + x^{3} - x^{2} + 1$ |
$6$ |
[0,3] |
$-\,14731$ |
$1$ |
$4.95114187916$ |
$121.37133104650373$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.277754459978$ |
6.0.16551.1 |
$x^{6} - x^{5} - x^{4} + 3 x^{3} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 613$ |
$2$ |
$5.04820953884$ |
$42.883563284783136$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$0.932873082902$ |
6.0.16807.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,7^{5}$ |
$1$ |
$5.0611401848$ |
$5.061140184796386$ |
✓ |
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$14$ |
$2$ |
$2.10181872849$ |
6.0.18515.1 |
$x^{6} + 2 x^{4} - x^{3} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 7\cdot 23^{2}$ |
$3$ |
$5.14344325363$ |
$28.372521918222215$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.328780614749$ |
6.0.19683.1 |
$x^{6} - x^{3} + 1$ |
$6$ |
[0,3] |
$-\,3^{9}$ |
$1$ |
$5.19615242271$ |
$5.196152422706632$ |
✓ |
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$18$ |
$2$ |
$3.39714980258$ |
6.0.20627.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,20627$ |
$1$ |
$5.23688067144$ |
$143.62102910089456$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.390200557232$ |
6.0.21168.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - 2 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$5.25952638099$ |
$10.061112020813587$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$1.11901604193$ |
6.0.21296.1 |
$x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}$ |
$2$ |
$5.26481368119$ |
$5.264813681193971$ |
|
✓ |
✓ |
$S_3$ (as 6T2) |
trivial |
$2$ |
$2$ |
$0.371341380446$ |
6.0.22291.1 |
$x^{6} + x^{4} - x^{3} - x + 1$ |
$6$ |
[0,3] |
$-\,22291$ |
$1$ |
$5.30503506276$ |
$149.30170796075979$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.373661196485$ |
6.0.22592.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 353$ |
$2$ |
$5.316907603$ |
$37.57658845611187$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$0.752120362427$ |
6.0.22707.1 |
$x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 5 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 29^{2}$ |
$2$ |
$5.32140883904$ |
$9.327379053088816$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$6$ |
$2$ |
$1.25603528677$ |
6.0.22747.1 |
$x^{6} - x^{5} - 2 x^{3} + x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 43$ |
$2$ |
$5.32297003373$ |
$31.448370387032774$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.388951542699$ |
6.0.23031.1 |
$x^{6} + x^{4} - x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 853$ |
$2$ |
$5.33398920661$ |
$50.586559479766954$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.18590232532$ |
6.0.24003.1 |
$x^{6} - x^{5} + 3 x^{3} - x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7\cdot 127$ |
$3$ |
$5.3708652218$ |
$51.64300533470143$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.15781781619$ |
6.0.25747.1 |
$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,25747$ |
$1$ |
$5.43401841081$ |
$160.45871743224174$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.457055178835$ |
6.0.25947.1 |
$x^{6} - x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 31^{2}$ |
$2$ |
$5.44103089586$ |
$9.643650760992955$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$6$ |
$2$ |
$1.37763890943$ |
6.0.27556.1 |
$x^{6} - x^{5} + 2 x^{3} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 83^{2}$ |
$2$ |
$5.4958646601$ |
$18.2208671582886$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.594769419961$ |
6.0.27848.1 |
$x^{6} - x^{5} + 2 x^{4} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{3}\cdot 59^{2}$ |
$2$ |
$5.5055283296$ |
$21.72556098240043$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.599228830431$ |
6.0.27971.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,83\cdot 337$ |
$2$ |
$5.50957372539$ |
$167.24532878379594$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.436494860807$ |
6.2.28037.1 |
$x^{6} - 2 x^{5} + 3 x^{3} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 53$ |
$2$ |
$5.51173831771$ |
$34.91418050019218$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.478924705547$ |
6.2.29077.1 |
$x^{6} - x^{5} + x^{4} - x^{2} + 2 x - 1$ |
$6$ |
[2,2] |
$29077$ |
$1$ |
$5.54529854883$ |
$170.51979357247652$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$0.491602105294$ |
6.0.29095.1 |
$x^{6} - x^{5} + 3 x^{4} - x^{3} + 3 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 11\cdot 23^{2}$ |
$3$ |
$5.54587053377$ |
$35.566838487557476$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.446620658377$ |
6.2.29189.1 |
$x^{6} - 2 x^{5} + x^{4} + x^{3} - 2 x^{2} + x + 1$ |
$6$ |
[2,2] |
$17^{2}\cdot 101$ |
$2$ |
$5.54885278411$ |
$66.44464230590899$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$0.49291662671$ |
6.0.29791.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} + 7 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,31^{3}$ |
$1$ |
$5.56776436283$ |
$5.5677643628300215$ |
|
✓ |
✓ |
$S_3$ (as 6T2) |
trivial |
$2$ |
$2$ |
$0.438333916947$ |
6.2.30125.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{2} + x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 241$ |
$2$ |
$5.57811986838$ |
$34.713109915419565$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.50437245294$ |
6.0.30808.1 |
$x^{6} - x^{4} - x^{3} + x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,2^{3}\cdot 3851$ |
$2$ |
$5.59900150547$ |
$175.52207838331907$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.643679055537$ |
6.0.30976.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 2$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 11^{2}$ |
$2$ |
$5.60407866131$ |
$8.357370775943878$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$4$ |
$2$ |
$1.29138778296$ |
6.2.31133.1 |
$x^{6} - 2 x^{4} - x^{3} + 2 x + 1$ |
$6$ |
[2,2] |
$163\cdot 191$ |
$2$ |
$5.60880268418$ |
$176.44545899512406$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$0.516354684031$ |
6.0.31211.1 |
$x^{6} - x^{4} - x^{3} + 2 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 59$ |
$2$ |
$5.61114227353$ |
$36.837480912787726$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.482550424804$ |
6.2.31213.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 13$ |
$2$ |
$5.6112021989$ |
$13.193814370085985$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$0.517040346258$ |
6.0.31223.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,31223$ |
$1$ |
$5.61150177778$ |
$176.7003112617519$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.649982527739$ |
6.0.31347.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 43$ |
$2$ |
$5.61520992871$ |
$24.357295210976567$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.57963516749$ |
6.2.31709.1 |
$x^{6} - x^{5} + 2 x^{3} - 2 x^{2} + 1$ |
$6$ |
[2,2] |
$37\cdot 857$ |
$2$ |
$5.62596584169$ |
$178.07021087200408$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$0.522986177098$ |
6.0.32171.1 |
$x^{6} - x^{5} + 2 x^{4} - x^{3} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,53\cdot 607$ |
$2$ |
$5.63954535118$ |
$179.36276090649363$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.536093401482$ |
6.2.32269.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 61$ |
$2$ |
$5.64240494139$ |
$37.456641600656084$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.529910039105$ |
6.0.32911.1 |
$x^{6} - x^{3} - x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,32911$ |
$1$ |
$5.6609612195$ |
$181.41389141959334$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.518066133218$ |
6.0.33791.1 |
$x^{6} - x^{5} + x^{4} + x^{3} + x + 1$ |
$6$ |
[0,3] |
$-\,33791$ |
$1$ |
$5.68591252578$ |
$183.8232847057195$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.688322549696$ |
6.0.33856.1 |
$x^{6} - x^{4} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{2}$ |
$2$ |
$5.6877339597$ |
$16.131190144457708$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.480272990261$ |
6.0.33856.2 |
$x^{6} + x^{4} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{2}$ |
$2$ |
$5.6877339597$ |
$9.591663046625438$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$4$ |
$2$ |
$1.02428142886$ |
6.2.33856.1 |
$x^{6} + x^{4} - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 23^{2}$ |
$2$ |
$5.6877339597$ |
$13.564659966250536$ |
|
|
✓ |
$S_4$ (as 6T7) |
trivial |
$2$ |
$3$ |
$0.550118007418$ |
6.0.34371.1 |
$x^{6} - x^{5} - 2 x^{3} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 19\cdot 67$ |
$3$ |
$5.70206321806$ |
$61.7980582219215$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.68719062958$ |
6.0.34992.1 |
$x^{6} - 3 x^{5} + 5 x^{3} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{7}$ |
$2$ |
$5.71910575798$ |
$5.71910575798162$ |
|
✓ |
✓ |
$S_3$ (as 6T2) |
trivial |
$6$ |
$2$ |
$1.81542571879$ |
6.0.35099.1 |
$x^{6} + x^{4} + x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,35099$ |
$1$ |
$5.72201673807$ |
$187.34727113037968$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$2$ |
$0.585021824316$ |