| 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 |
| 6.0.107811.1 |
$x^{6} - x^{4} - 2 x^{3} + 3 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 11^{3}$ |
$2$ |
$6.89885757355$ |
$14.350202036282921$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$1.3637383458$ |
| 6.0.489808.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + 2 x^{3} - 3 x^{2} + x + 3$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}\cdot 23$ |
$3$ |
$8.87846006706$ |
$44.98888751680797$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$3.83200713819$ |
| 6.0.752015.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 11^{3}\cdot 113$ |
$3$ |
$9.53610630729$ |
$78.835271294009$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$3.81681781935$ |
| 6.0.1044835.1 |
$x^{6} + 3 x^{4} - 2 x^{3} + 5 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 11^{3}\cdot 157$ |
$3$ |
$10.0733661172$ |
$92.92470069900683$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$5.26329524389$ |
| 6.0.1279091.2 |
$x^{6} - 2 x^{5} - 2 x^{3} + 6 x^{2} - 4 x + 5$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 31^{2}$ |
$2$ |
$10.4187809477$ |
$32.729356890496106$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$7.19083504469$ |
| 6.2.1398881.1 |
$x^{6} - x^{5} + 5 x^{3} - 5 x^{2} + 3 x + 1$ |
$6$ |
[2,2] |
$11^{3}\cdot 1051$ |
$2$ |
$10.5753998125$ |
$107.5220907534819$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$9.22899509208$ |
| 6.0.1412191.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 5 x^{3} + 7 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 1061$ |
$2$ |
$10.5921040878$ |
$108.03240254664338$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$4.86859335462$ |
| 6.0.1673067.1 |
$x^{6} - 3 x^{5} + 6 x^{4} - 6 x^{3} + 7 x^{2} - 5 x + 3$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 419$ |
$3$ |
$10.8956268739$ |
$117.58826472059191$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$6.59784148732$ |
| 6.0.1724976.1 |
$x^{6} - x^{5} - 2 x^{4} - x^{3} + 8 x^{2} - 5 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{4}\cdot 11^{3}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$2.65030466524$ |
| 6.0.1724976.2 |
$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} + 6 x^{2} - 15 x + 9$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{4}\cdot 11^{3}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$4.2524698409$ |
| 6.0.1895344.1 |
$x^{6} - 3 x^{5} + 6 x^{4} - 5 x^{3} + x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}\cdot 89$ |
$3$ |
$11.1245215278$ |
$49.66815293217739$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$2.55310574624$ |
| 6.0.1944591.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 9 x^{3} + 13 x^{2} - 10 x + 4$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 487$ |
$3$ |
$11.1721831136$ |
$126.77144788949916$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$10.0564034014$ |
| 6.0.2173523.1 |
$x^{6} - 2 x^{5} + 4 x^{2} - 5 x + 3$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 23\cdot 71$ |
$3$ |
$11.3813568409$ |
$134.02611685787215$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$8.37296526203$ |
| 6.0.2258707.1 |
$x^{6} - x^{5} + 2 x^{4} - x^{3} + x^{2} - 2 x + 4$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 1697$ |
$2$ |
$11.4545135321$ |
$136.62723008244$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$10.8005741288$ |
| 6.0.2299968.2 |
$x^{6} - 5 x^{4} - 4 x^{3} + 9 x^{2} + 10 x + 4$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 11^{3}$ |
$3$ |
$11.4891252931$ |
$47.796687326287945$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$12.0672436092$ |
| 6.0.2551527.1 |
$x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 11^{3}\cdot 71$ |
$3$ |
$11.6896101616$ |
$100.68551151824563$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$7.19882675867$ |
| 6.0.2626063.1 |
$x^{6} - x^{5} + 3 x^{2} - 6 x + 4$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 1973$ |
$2$ |
$11.7458429606$ |
$147.31938093815083$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$7.77612294696$ |
| 6.0.2759163.1 |
$x^{6} - x^{5} - 3 x^{3} - x^{2} + 4 x + 3$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 691$ |
$3$ |
$11.8430317322$ |
$151.0066223713384$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$12.3527815871$ |
| 6.0.3002736.1 |
$x^{6} - x^{5} + 3 x^{4} + 4 x^{3} - 2 x^{2} + 4$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3\cdot 11^{3}\cdot 47$ |
$4$ |
$12.0111942827$ |
$78.76547467006087$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$16.4470814778$ |
| 6.0.3195731.1 |
$x^{6} - x^{5} + 4 x^{4} - 3 x^{3} + 29 x^{2} - 4 x + 71$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 11^{3}$ |
$2$ |
$12.1365440334$ |
$12.136544033351255$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
trivial |
$2$ |
$2$ |
$2.10181872849$ |
| 6.0.3350127.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - x^{3} - 4 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 839$ |
$3$ |
$12.2323588142$ |
$166.39411047269672$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$16.6831967261$ |
| 6.0.3398043.1 |
$x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{2} + 4 x + 3$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 23\cdot 37$ |
$4$ |
$12.2613459207$ |
$167.57983172207807$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$9.19620365329$ |
| 6.0.3503192.1 |
$x^{6} - 2 x^{5} + 7 x^{4} - 13 x^{3} + 16 x^{2} - 10 x + 4$ |
$6$ |
[0,3] |
$-\,2^{3}\cdot 7\cdot 11^{3}\cdot 47$ |
$4$ |
$12.3237815106$ |
$170.15287244122564$ |
|
|
? |
$S_6$ (as 6T16) |
$[2]$ |
$2$ |
$2$ |
$11.8148720586$ |
| 6.0.3632299.1 |
$x^{6} - x^{5} + x^{4} - 4 x^{2} + x + 3$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 2729$ |
$2$ |
$12.398341618$ |
$173.2599203508994$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$5.19460528795$ |
| 6.0.3973035.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 11 x^{3} + 22 x^{2} - 25 x + 15$ |
$6$ |
[0,3] |
$-\,3\cdot 5\cdot 11^{3}\cdot 199$ |
$4$ |
$12.585014835$ |
$181.20430458463176$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$19.4285668105$ |
| 6.2.4848833.1 |
$x^{6} - 2 x^{5} + 5 x^{4} + x^{3} - x^{2} - x - 2$ |
$6$ |
[2,2] |
$11^{3}\cdot 3643$ |
$2$ |
$13.0098674293$ |
$200.18241681026834$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$21.6666638384$ |
| 6.0.4851495.1 |
$x^{6} + 6 x^{4} - x^{3} + 9 x^{2} - 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 5\cdot 11^{3}$ |
$3$ |
$13.0110575558$ |
$34.10748949793651$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$16.7406655794$ |
| 6.0.4851495.2 |
$x^{6} - x^{5} + 4 x^{4} - 4 x^{3} + 13 x^{2} - 10 x + 12$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 5\cdot 11^{3}$ |
$3$ |
$13.0110575558$ |
$55.578093501235514$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$22.2125416912$ |
| 6.4.5096399.1 |
$x^{6} - 2 x^{5} - 3 x^{4} - x^{3} + 9 x^{2} - x - 2$ |
$6$ |
[4,1] |
$-\,7\cdot 11^{3}\cdot 547$ |
$3$ |
$13.1182902885$ |
$205.22914023110852$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$2$ |
$4$ |
$30.185334882$ |
| 6.0.5160287.1 |
$x^{6} - 2 x^{5} - x^{4} + x^{3} + 13 x^{2} - 10 x + 3$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 3877$ |
$2$ |
$13.1455564987$ |
$206.51150089038626$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$16.7119879253$ |
| 6.0.5174928.1 |
$x^{6} - x^{5} - x^{4} - 4 x^{3} + 7 x^{2} + x + 9$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{5}\cdot 11^{3}$ |
$3$ |
$13.1517653575$ |
$70.30134538948258$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$19.0492800545$ |
| 6.0.5217520.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 3$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5\cdot 7^{2}\cdot 11^{3}$ |
$4$ |
$13.1697446288$ |
$39.242833740697165$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$15.9275675567$ |
| 6.0.5282739.1 |
$x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + 14 x^{2} - 8 x + 3$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 7^{2}\cdot 11^{3}$ |
$3$ |
$13.197039778$ |
$37.9670658515373$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$14.3935160569$ |
| 6.2.5439797.1 |
$x^{6} - x^{5} + 2 x^{4} + 4 x^{3} - 7 x^{2} + x + 1$ |
$6$ |
[2,2] |
$11^{3}\cdot 61\cdot 67$ |
$3$ |
$13.2616363704$ |
$212.03065816055943$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$7.38463161105$ |
| 6.2.5503685.1 |
$x^{6} - 2 x^{5} - 4 x^{3} - 3 x^{2} - 3 x - 2$ |
$6$ |
[2,2] |
$5\cdot 11^{3}\cdot 827$ |
$3$ |
$13.2874689158$ |
$213.27212663637036$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$23.6305638203$ |
| 6.0.5857731.1 |
$x^{6} - x^{5} + 4 x^{4} - 7 x^{3} + 9 x^{2} - 6 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 11^{3}\cdot 163$ |
$3$ |
$13.426255392$ |
$152.55681340422214$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$10.2016863079$ |
| 6.0.5889675.1 |
$x^{6} - 3 x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} + 10 x + 5$ |
$6$ |
[0,3] |
$-\,3\cdot 5^{2}\cdot 11^{3}\cdot 59$ |
$4$ |
$13.4384306698$ |
$98.66610360199697$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$19.6502872494$ |
| 6.4.5930936.1 |
$x^{6} - 3 x^{5} - 3 x^{4} + 7 x^{3} + 7 x^{2} - 2 x - 2$ |
$6$ |
[4,1] |
$-\,2^{3}\cdot 11^{3}\cdot 557$ |
$3$ |
$13.4540758861$ |
$221.39557357815445$ |
|
|
✓ |
$S_6$ (as 6T16) |
trivial |
$2$ |
$4$ |
$28.0610540472$ |
| 6.0.5974859.1 |
$x^{6} - x^{5} + 9 x^{4} - 20 x^{3} + 23 x^{2} - 18 x + 9$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 67^{2}$ |
$2$ |
$13.4706311172$ |
$54.711616225701704$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$37.3153135569$ |
| 6.0.6161199.1 |
$x^{6} - 3 x^{5} - x^{4} + x^{3} + 10 x^{2} + 2 x + 5$ |
$6$ |
[0,3] |
$-\,3\cdot 11^{3}\cdot 1543$ |
$3$ |
$13.5397570822$ |
$225.6523875344553$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$21.8125525845$ |
| 6.0.6209115.1 |
$x^{6} - x^{5} + 6 x^{4} - 4 x^{3} + 9 x^{2} - x + 5$ |
$6$ |
[0,3] |
$-\,3\cdot 5\cdot 11^{3}\cdot 311$ |
$4$ |
$13.5572503935$ |
$226.5281439468394$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$25.0988813191$ |
| 6.0.6219763.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 5 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 4673$ |
$2$ |
$13.5611225117$ |
$226.72229709492623$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$8.39587008098$ |
| 6.0.6241059.1 |
$x^{6} - x^{5} - 4 x^{4} + 8 x^{3} - x^{2} - 13 x + 25$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 11^{3}\cdot 521$ |
$3$ |
$13.5688502047$ |
$131.12208052040663$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$31.6319591617$ |
| 6.0.6623056.1 |
$x^{6} - x^{5} - 3 x^{4} - 6 x^{3} + 8 x^{2} + 16 x + 12$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}\cdot 311$ |
$3$ |
$13.7038649858$ |
$165.43276579928173$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$33.583038539$ |
| 6.0.7087575.1 |
$x^{6} - 2 x^{5} - x^{4} + 3 x^{3} + 11 x^{2} + 10 x + 3$ |
$6$ |
[0,3] |
$-\,3\cdot 5^{2}\cdot 11^{3}\cdot 71$ |
$4$ |
$13.859565372$ |
$141.53574889517313$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$26.9483078989$ |
| 6.0.7098223.1 |
$x^{6} - x^{5} + 6 x^{4} + 7 x^{3} - 2 x^{2} - x + 5$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 5333$ |
$2$ |
$13.8630335154$ |
$242.2044590836428$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$21.0136297506$ |
| 6.0.7204703.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 8 x^{3} + 14 x^{2} - 16 x + 9$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 5413$ |
$2$ |
$13.8974785935$ |
$244.01434384068492$ |
|
|
? |
$S_6$ (as 6T16) |
$[2]$ |
$2$ |
$2$ |
$9.16380627443$ |
| 6.0.7391043.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + 3 x + 5$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 11^{3}\cdot 617$ |
$3$ |
$13.9567496427$ |
$142.69197594819408$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$27.2380388696$ |
| 6.2.7432304.1 |
$x^{6} - x^{5} + x^{4} - 3 x^{3} + 3 x^{2} - 7 x + 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 11^{3}\cdot 349$ |
$3$ |
$13.9697052902$ |
$175.24839514243774$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$2$ |
$3$ |
$46.0527090166$ |
| 6.0.7438959.2 |
$x^{6} - x^{5} - 7 x^{4} - 7 x^{3} + 20 x^{2} + 38 x + 25$ |
$6$ |
[0,3] |
$-\,3^{5}\cdot 11^{3}\cdot 23$ |
$3$ |
$13.9717892945$ |
$82.64986388373546$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$28.7071901284$ |
