| 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 |
| 6.0.10816.1 |
$x^{6} - x^{4} - 2 x^{3} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13^{2}$ |
$2$ |
$4.70266937544$ |
$11.057549627357744$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$0.434147804699$ |
| 6.0.22592.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 353$ |
$2$ |
$5.316907603$ |
$37.57658845611187$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$0.752120362427$ |
| 6.0.33856.2 |
$x^{6} + x^{4} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{2}$ |
$2$ |
$5.6877339597$ |
$9.591663046625438$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$4$ |
$2$ |
$1.02428142886$ |
| 6.0.47680.1 |
$x^{6} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 149$ |
$3$ |
$6.02174981256$ |
$54.589376255824725$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.27956995152$ |
| 6.0.60992.1 |
$x^{6} + 3 x^{4} - 2 x^{3} + 4 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 953$ |
$2$ |
$6.27401393708$ |
$61.741396161732524$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.4085735579$ |
| 6.0.61504.2 |
$x^{6} - 2 x^{4} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 31^{2}$ |
$2$ |
$6.28276130478$ |
$11.135528725660043$ |
|
|
✓ |
$D_{6}$ (as 6T3) |
trivial |
$4$ |
$2$ |
$1.34349356038$ |
| 6.0.65600.1 |
$x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{2}\cdot 41$ |
$3$ |
$6.35063725183$ |
$37.44569770046876$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.57718616336$ |
| 6.0.87616.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 4 x^{3} + 3 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 37^{2}$ |
$2$ |
$6.66444370329$ |
$22.20740493717357$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$1.99857728103$ |
| 6.0.96832.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 17\cdot 89$ |
$3$ |
$6.77646423181$ |
$77.79460135510689$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.81789725839$ |
| 6.0.106560.1 |
$x^{6} - 2 x^{5} + 3 x^{4} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 5\cdot 37$ |
$4$ |
$6.88545062961$ |
$47.11687595755899$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.14909635266$ |
| 6.0.147008.1 |
$x^{6} - 4 x^{4} - 2 x^{3} + 5 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 2297$ |
$2$ |
$7.26479719299$ |
$95.85405573057407$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.31983457795$ |
| 6.0.147520.1 |
$x^{6} - 2 x^{5} - 2 x^{3} + 3 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 461$ |
$3$ |
$7.26900806348$ |
$96.02083107326243$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.76265973544$ |
| 6.0.153664.1 |
$x^{6} + 5 x^{4} + 6 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{4}$ |
$2$ |
$7.31861142005$ |
$7.318611420045943$ |
✓ |
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$4$ |
$2$ |
$2.10181872849$ |
| 6.0.202304.1 |
$x^{6} - 4 x^{4} + 5 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 29\cdot 109$ |
$3$ |
$7.66185763869$ |
$112.44554237496477$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.05861044058$ |
| 6.0.205376.1 |
$x^{6} - x^{4} - 4 x^{3} + 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3209$ |
$2$ |
$7.68112704783$ |
$113.29607230614837$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.08571500917$ |
| 6.0.212032.1 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3313$ |
$2$ |
$7.7220670512$ |
$115.11733144926528$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.72194011798$ |
| 6.0.230464.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} - 4 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13\cdot 277$ |
$3$ |
$7.83009772813$ |
$120.01666550941998$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.24263551418$ |
| 6.0.238144.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 8 x^{3} + 12 x^{2} - 12 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 61^{2}$ |
$2$ |
$7.8729943662$ |
$30.99202014514269$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$3.91336396199$ |
| 6.0.305728.1 |
$x^{6} + 3 x^{4} - 2 x^{3} + 4 x^{2} - 2 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 17\cdot 281$ |
$3$ |
$8.20772006571$ |
$138.2316895650198$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.68439866841$ |
| 6.0.308800.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 11 x^{2} - 12 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{2}\cdot 193$ |
$3$ |
$8.22140826515$ |
$62.12889826803627$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.65289151867$ |
| 6.0.326720.1 |
$x^{6} + 2 x^{4} + 5 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 1021$ |
$3$ |
$8.29906730552$ |
$142.89856542317$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.537557793$ |
| 6.0.330304.1 |
$x^{6} - 3 x^{4} - 4 x^{3} + 6 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13\cdot 397$ |
$3$ |
$8.31417137621$ |
$143.68020044529447$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.45961938427$ |
| 6.0.341056.1 |
$x^{6} - 5 x^{4} + 10 x^{2} - 6 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 73^{2}$ |
$2$ |
$8.35867839276$ |
$34.93375223681704$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$3.47739996254$ |
| 6.0.348736.1 |
$x^{6} - 2 x^{5} + 4 x^{3} - 5 x^{2} - 2 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5449$ |
$2$ |
$8.38975857433$ |
$147.63468427168462$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.94556706438$ |
| 6.0.356416.1 |
$x^{6} + 3 x^{4} + 6 x^{2} - 2 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5569$ |
$2$ |
$8.42027351049$ |
$149.25146565444507$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.06388567033$ |
| 6.0.374336.1 |
$x^{6} + x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5849$ |
$2$ |
$8.4893987409$ |
$152.95751043999115$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.8612827457$ |
| 6.0.419904.1 |
$x^{6} + 6 x^{4} + 9 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{8}$ |
$2$ |
$8.65349742184$ |
$8.65349742184445$ |
✓ |
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$4$ |
$2$ |
$3.39714980258$ |
| 6.0.419904.3 |
$x^{6} - 2 x^{3} + 9 x^{2} - 12 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{8}$ |
$2$ |
$8.65349742184$ |
$14.100858664870902$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$5.28645643215$ |
| 6.0.424000.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 11 x^{2} - 10 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{3}\cdot 53$ |
$3$ |
$8.66750916264$ |
$55.67278331919142$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.07822815216$ |
| 6.0.470080.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 7 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 13\cdot 113$ |
$4$ |
$8.81783488501$ |
$171.40595088852663$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.44360128338$ |
| 6.2.476608.1 |
$x^{6} + x^{4} - 2 x^{3} - 4 x^{2} + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 11\cdot 677$ |
$3$ |
$8.83812666244$ |
$172.59200444980064$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$3.8032253284$ |
| 6.0.484416.2 |
$x^{6} - 3 x^{4} + 6 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 29^{2}$ |
$3$ |
$8.86209524339$ |
$18.65475810617763$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$4$ |
$2$ |
$4.96716897875$ |
| 6.0.499264.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 4 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 29\cdot 269$ |
$3$ |
$8.90680016813$ |
$176.64653973401235$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.87935730262$ |
| 6.0.516160.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 6 x^{2} - 6 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 1613$ |
$3$ |
$8.95634314303$ |
$179.61069010501575$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.91329345864$ |
| 6.2.516544.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 6 x^{3} + 7 x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 7\cdot 1153$ |
$3$ |
$8.95745331886$ |
$179.67748885155314$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$3.9721220511$ |
| 6.0.517184.1 |
$x^{6} - 5 x^{4} - 2 x^{3} + 8 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 8081$ |
$2$ |
$8.95930208451$ |
$179.78876494375282$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.93961104276$ |
| 6.4.526912.1 |
$x^{6} - 3 x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1$ |
$6$ |
[4,1] |
$-\,2^{6}\cdot 8233$ |
$2$ |
$8.98717120188$ |
$181.4717608885746$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$4$ |
$3.97729003004$ |
| 6.0.543296.1 |
$x^{6} - 3 x^{4} - 4 x^{3} + 10 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13\cdot 653$ |
$3$ |
$9.03315407583$ |
$184.27153876819935$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$3.98946463749$ |
| 6.0.549440.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 14 x^{2} - 10 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 17\cdot 101$ |
$4$ |
$9.05010001877$ |
$185.31055015837603$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$6.08682230843$ |
| 6.0.549440.2 |
$x^{6} - 2 x^{5} + 6 x^{4} - 4 x^{3} + 7 x^{2} + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 17\cdot 101$ |
$4$ |
$9.05010001877$ |
$185.31055015837603$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.6492960579$ |
| 6.0.557120.1 |
$x^{6} - 5 x^{4} - 2 x^{3} + 8 x^{2} + 10 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 1741$ |
$3$ |
$9.07106178244$ |
$186.60117898877274$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$6.15175867615$ |
| 6.0.580160.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 4 x^{3} - x^{2} + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 7^{2}\cdot 37$ |
$4$ |
$9.13253398579$ |
$71.97221686178632$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$6.35036831854$ |
| 6.0.583232.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 6 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13\cdot 701$ |
$3$ |
$9.14057586108$ |
$190.9240686765291$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$7.0451519548$ |
| 6.0.586304.1 |
$x^{6} - 3 x^{4} - 4 x^{3} + 2 x^{2} + 8 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 9161$ |
$2$ |
$9.14858251502$ |
$191.42622599842477$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.59556685363$ |
| 6.0.586816.1 |
$x^{6} - 2 x^{5} + 6 x^{3} + 3 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 53\cdot 173$ |
$3$ |
$9.14991355683$ |
$191.5097908724251$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.86960874211$ |
| 6.0.595008.1 |
$x^{6} - 2 x^{5} + x^{4} + 2 x^{3} + 2 x^{2} - 8 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 1033$ |
$3$ |
$9.17107969688$ |
$111.33732527773424$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.09441484881$ |
| 6.0.602176.1 |
$x^{6} - 2 x^{5} - 4 x^{4} + 11 x^{2} + 14 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 97^{2}$ |
$2$ |
$9.18940178441$ |
$42.222552577696334$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$6.37089333685$ |
| 6.0.603200.1 |
$x^{6} - 4 x^{4} - 4 x^{3} + 5 x^{2} + 10 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{2}\cdot 13\cdot 29$ |
$4$ |
$9.19200436987$ |
$113.54830970975435$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$5.22950198325$ |
| 6.0.609344.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 8 x^{3} - x^{2} - 12 x + 9$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 9521$ |
$2$ |
$9.20754301696$ |
$195.15122341404884$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.38441695523$ |
| 6.0.613952.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 12 x^{2} - 14 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 53\cdot 181$ |
$3$ |
$9.21911154639$ |
$195.88772294352702$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$4.83552322446$ |
