| 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 |
| 8.0.1763584.1 |
$x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 83^{2}$ |
$2$ |
$6.03669895858$ |
$18.2208671582886$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$0.781195313952$ |
| 8.0.3207681.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 2 x^{4} - x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 199^{2}$ |
$2$ |
$6.50539836897$ |
$24.43358344574123$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$1.89392987116$ |
| 8.0.4247721.1 |
$x^{8} - 2 x^{5} - x^{4} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 229^{2}$ |
$2$ |
$6.73782144697$ |
$26.210684844162312$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$2.46005711067$ |
| 8.0.4626801.1 |
$x^{8} - 3 x^{7} + 3 x^{6} + 3 x^{5} - 7 x^{4} + 3 x^{3} + 3 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 239^{2}$ |
$2$ |
$6.81020370483$ |
$26.77685567799177$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$2.44210647993$ |
| 8.0.5349969.1 |
$x^{8} - x^{6} - 2 x^{5} + x^{3} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 257^{2}$ |
$2$ |
$6.93495916539$ |
$27.76688675382964$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$2.61193154189$ |
| 8.0.5607424.1 |
$x^{8} - 2 x^{5} - 2 x^{4} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 37^{2}$ |
$2$ |
$6.97582254952$ |
$18.227692292212264$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$2.51616826897$ |
| 8.0.5817744.1 |
$x^{8} - 2 x^{7} + 2 x^{5} - x^{4} + 2 x^{3} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 67^{2}$ |
$3$ |
$7.00800375508$ |
$22.50529408956344$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.06844049959$ |
| 8.0.6487209.1 |
$x^{8} - 2 x^{5} + x^{4} + x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 283^{2}$ |
$2$ |
$7.10407006749$ |
$29.13760456866693$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$2.7918036281$ |
| 8.0.7485696.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$7.23234314192$ |
$16.948805249221287$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.41970954689$ |
| 8.0.7573504.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{4} - 6 x^{3} + 8 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 43^{2}$ |
$2$ |
$7.24289363407$ |
$19.65011309429094$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.02631405652$ |
| 8.0.7634169.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 5 x^{4} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 307^{2}$ |
$2$ |
$7.25012044064$ |
$30.347981810987037$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.03548635515$ |
| 8.0.8346321.1 |
$x^{8} + x^{6} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 107^{2}$ |
$2$ |
$7.33139949815$ |
$23.579404344249447$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.4784617434$ |
| 8.0.8661249.1 |
$x^{8} - 3 x^{7} + x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} + x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 109^{2}$ |
$2$ |
$7.36542082709$ |
$23.7987523638325$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.81221103022$ |
| 8.0.8667136.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 23^{2}$ |
$2$ |
$7.36604642023$ |
$16.131190144457708$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.34129412261$ |
| 8.0.8874441.1 |
$x^{8} - x^{7} - 3 x^{5} + 3 x^{4} - x^{3} + 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 331^{2}$ |
$2$ |
$7.3878424588$ |
$31.51190251317746$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.10205164459$ |
| 8.0.10909809.1 |
$x^{8} - 4 x^{7} + 6 x^{6} - 4 x^{5} + 2 x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 367^{2}$ |
$2$ |
$7.58101129019$ |
$33.18132004607411$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$4.30951944618$ |
| 8.0.11029041.1 |
$x^{8} - x^{7} - 2 x^{6} + x^{5} + 5 x^{4} + x^{3} - 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{8}\cdot 41^{2}$ |
$2$ |
$7.59131860331$ |
$23.06924557594881$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.48635947039$ |
| 8.0.11397376.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 3 x^{4} - 4 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 211^{2}$ |
$2$ |
$7.62255575154$ |
$29.0516780926679$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$2.84282514548$ |
| 8.0.11505664.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 53^{2}$ |
$2$ |
$7.63157120875$ |
$20.591260281974$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$2.80746400336$ |
| 8.0.11634921.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} - x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 379^{2}$ |
$2$ |
$7.6422357332$ |
$33.71943060017473$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$3.60551138703$ |
| 8.0.12730624.2 |
$x^{8} - 2 x^{7} + x^{6} + x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 223^{2}$ |
$2$ |
$7.72869575622$ |
$29.866369046136157$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.38303876122$ |
| 8.0.13220496.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 2 x^{4} - 3 x^{3} + 5 x^{2} - 6 x + 4$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 101^{2}$ |
$3$ |
$7.76525941143$ |
$27.631723729009256$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.14493710463$ |
| 8.0.13424896.3 |
$x^{8} + 2 x^{4} + x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 229^{2}$ |
$2$ |
$7.78016605232$ |
$30.265491900843113$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.18626152893$ |
| 8.0.13690000.1 |
$x^{8} - x^{7} + x^{6} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$7.79920670985$ |
$21.590988593881082$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$3$ |
$1.81112849726$ |
| 8.0.14070001.1 |
$x^{8} - x^{7} - x^{6} + x^{5} + x^{4} + x^{3} - x^{2} - x + 1$ |
$8$ |
[0,4] |
$11^{4}\cdot 31^{2}$ |
$2$ |
$7.82594454307$ |
$18.466185312619388$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$3$ |
$1.82307131825$ |
| 8.0.14220441.1 |
$x^{8} - x^{7} + x^{6} - x^{5} - 3 x^{4} + x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 419^{2}$ |
$2$ |
$7.83635556055$ |
$35.45419580247167$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.28223960374$ |
| 8.0.14258176.1 |
$x^{8} - 2 x^{7} + 3 x^{4} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 59^{2}$ |
$2$ |
$7.83895184211$ |
$21.72556098240043$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.7596262663$ |
| 8.0.14258176.2 |
$x^{8} - 2 x^{7} + x^{6} + x^{4} + x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 59^{2}$ |
$2$ |
$7.83895184211$ |
$21.72556098240043$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$3$ |
$2.14010881952$ |
| 8.0.14561856.1 |
$x^{8} - x^{7} + 6 x^{6} - 3 x^{5} + 12 x^{4} - x^{3} + 11 x^{2} + 2 x + 4$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 53^{2}$ |
$3$ |
$7.85962981609$ |
$35.66510900025401$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$6.11637071272$ |
| 8.0.15241216.1 |
$x^{8} - 2 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 61^{2}$ |
$2$ |
$7.90455548448$ |
$22.090722034374522$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.88452378495$ |
| 8.0.15610401.1 |
$x^{8} + 5 x^{6} + 11 x^{4} + 10 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 439^{2}$ |
$2$ |
$7.92823943378$ |
$36.29049462324811$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.40442420178$ |
| 8.0.15745024.1 |
$x^{8} - 2 x^{7} + 4 x^{5} - 4 x^{3} + 4 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 31^{2}$ |
$2$ |
$7.93675393294$ |
$18.727652374724588$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$5.48340868285$ |
| 8.0.16908544.2 |
$x^{8} - x^{6} + 3 x^{4} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 257^{2}$ |
$2$ |
$8.00780108192$ |
$32.0624390837628$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$5.07343395931$ |
| 8.0.16916769.1 |
$x^{8} - 2 x^{6} - 2 x^{5} + 5 x^{4} + 2 x^{3} + 3 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 457^{2}$ |
$2$ |
$8.00828789313$ |
$37.027017163147235$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.13593873638$ |
| 8.0.18122049.1 |
$x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{3} + x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 11^{2}\cdot 43^{2}$ |
$3$ |
$8.07748039384$ |
$37.66961640367472$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.77896710987$ |
| 8.0.19527561.1 |
$x^{8} - x^{7} + 2 x^{6} - 5 x^{5} + 5 x^{4} - 5 x^{3} + 8 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 491^{2}$ |
$2$ |
$8.15325452923$ |
$38.379682124790975$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$6.14534604672$ |
| 8.0.20169081.1 |
$x^{8} + x^{4} + 3 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 499^{2}$ |
$2$ |
$8.18626433186$ |
$38.691084244306204$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$8.11360683713$ |
| 8.0.20493729.1 |
$x^{8} - x^{7} - 2 x^{6} + 5 x^{5} + 3 x^{4} - 5 x^{3} - 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 503^{2}$ |
$2$ |
$8.20262058589$ |
$38.84584919911006$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$5.87602421254$ |
| 8.0.20502784.2 |
$x^{8} - 2 x^{4} + x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 283^{2}$ |
$2$ |
$8.20307353161$ |
$33.645207682521445$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$3.1797613722$ |
| 8.0.20647936.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} + 2 x^{3} + x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 71^{2}$ |
$2$ |
$8.21031048045$ |
$33.704599092705436$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$6.48292635452$ |
| 8.0.21818241.1 |
$x^{8} + 2 x^{6} + 3 x^{4} + 5 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 173^{2}$ |
$2$ |
$8.26708621579$ |
$29.98223422509149$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$9.42388493743$ |
| 8.0.22838841.1 |
$x^{8} - x^{7} - 5 x^{6} + x^{5} + 11 x^{4} + x^{3} - 5 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{8}\cdot 59^{2}$ |
$2$ |
$8.31446400743$ |
$27.67371536012528$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$9.73208560786$ |
| 8.0.24255625.2 |
$x^{8} + 2 x^{6} - x^{5} - 2 x^{4} + 4 x^{3} + x^{2} - x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 197^{2}$ |
$2$ |
$8.37725159214$ |
$31.38470965295043$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$3$ |
$2.59459471808$ |
| 8.0.25563136.1 |
$x^{8} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 79^{2}$ |
$2$ |
$8.43241100389$ |
$25.13961017995307$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$5.45844375425$ |
| 8.0.25674489.1 |
$x^{8} - x^{7} + x^{5} + x^{4} - 3 x^{3} + 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 563^{2}$ |
$2$ |
$8.43699372444$ |
$41.09744517606904$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$7.89710980427$ |
| 8.0.25765776.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{6}\cdot 47^{2}$ |
$3$ |
$8.44073767643$ |
$24.807130641975725$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$8.47189345409$ |
| 8.0.27489049.1 |
$x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} + x^{3} - 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 107^{2}$ |
$2$ |
$8.50932212515$ |
$27.367864366808018$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$2$ |
$3$ |
$2.27061409073$ |
| 8.0.28047616.2 |
$x^{8} - x^{6} + x^{4} + 3 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 331^{2}$ |
$2$ |
$8.53074566463$ |
$36.38681079732051$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$4.99797836386$ |
| 8.0.28387584.3 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{4} + 4 x^{3} - 4 x + 4$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 37^{2}$ |
$3$ |
$8.54360289126$ |
$23.651742983410834$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$6$ |
$3$ |
$9.57954084816$ |
| 8.0.31719424.1 |
$x^{8} - 4 x^{5} + 8 x^{4} - 4 x^{3} + 1$ |
$8$ |
[0,4] |
$2^{18}\cdot 11^{2}$ |
$2$ |
$8.66294708267$ |
$16.714741551887755$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$4$ |
$3$ |
$8.61236208648$ |
