| 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 |
| 8.0.1342413.1 |
$x^{8} - x^{7} + x^{6} + x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 16573$ |
$2$ |
$5.83425985742$ |
$222.97757734803739$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$0.970727427757$ |
| 8.0.1797309.1 |
$x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 10 x^{4} - 9 x^{3} + 7 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 22189$ |
$2$ |
$6.05100962346$ |
$258.005813887982$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.20014144807$ |
| 8.0.2118069.1 |
$x^{8} - x^{7} - x^{3} + 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 79\cdot 331$ |
$3$ |
$6.17650095624$ |
$280.083915996617$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.33864883478$ |
| 8.0.2217213.1 |
$x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 31\cdot 883$ |
$3$ |
$6.21192104402$ |
$286.5641289484781$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.37910404568$ |
| 8.0.2314413.1 |
$x^{8} - x^{6} - x^{5} - x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 28573$ |
$2$ |
$6.24532592023$ |
$292.77807294946115$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.42029894182$ |
| 8.0.2712933.1 |
$x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + x^{4} - 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 33493$ |
$2$ |
$6.37059334437$ |
$316.9842267369151$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.57666375612$ |
| 8.0.2824713.1 |
$x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} - 4 x^{4} + x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 43\cdot 811$ |
$3$ |
$6.40282734558$ |
$323.4486048818266$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.7400253268$ |
| 8.0.2844928.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 11113$ |
$2$ |
$6.40853720479$ |
$210.83642948978243$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.11974748455$ |
| 8.0.3057993.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 19\cdot 1987$ |
$3$ |
$6.46665305207$ |
$336.5397450524975$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.83028307754$ |
| 8.0.3167829.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 37\cdot 151$ |
$4$ |
$6.49524019945$ |
$342.53029063135426$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.77871765724$ |
| 8.0.3198933.1 |
$x^{8} - x^{7} - x^{6} + 4 x^{4} - x^{3} - 3 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 73\cdot 541$ |
$3$ |
$6.50317802496$ |
$344.20778608276714$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.04684730841$ |
| 8.0.3243888.1 |
$x^{8} - x^{7} + 2 x^{5} - 3 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 2503$ |
$3$ |
$6.51453214511$ |
$245.0958995985041$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.90341831177$ |
| 8.0.3339873.1 |
$x^{8} - x^{7} - x^{5} + 3 x^{4} - x^{3} + 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 41233$ |
$2$ |
$6.53832108405$ |
$351.7086862731712$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.79480563528$ |
| 8.0.3379725.1 |
$x^{8} - x^{7} - x^{6} + x^{5} + 2 x^{3} + x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{2}\cdot 1669$ |
$3$ |
$6.54802261285$ |
$158.22452401571636$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.12614827503$ |
| 8.0.3567321.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 9 x^{4} - 9 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 44041$ |
$2$ |
$6.59238820691$ |
$363.4872762559922$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.02666468748$ |
| 8.0.3684933.1 |
$x^{8} - x^{7} + x^{6} - 2 x^{5} - x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 67\cdot 97$ |
$4$ |
$6.61917250375$ |
$369.43064301706215$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$1.90964552544$ |
| 8.0.3707289.1 |
$x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 37\cdot 1237$ |
$3$ |
$6.62417893574$ |
$370.54959182274104$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.12456448497$ |
| 8.0.3747141.1 |
$x^{8} - x^{7} - x^{6} + x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 46261$ |
$2$ |
$6.63303829144$ |
$372.53590430990675$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.27220445923$ |
| 8.0.3853089.1 |
$x^{8} - x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{3} + 4 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 47569$ |
$2$ |
$6.65619643317$ |
$377.76580046372646$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.17718433097$ |
| 8.0.3925989.1 |
$x^{8} - 3 x^{6} - x^{5} + 4 x^{4} - 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 19\cdot 2551$ |
$3$ |
$6.67180946002$ |
$381.3226979868888$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.0361720282$ |
| 8.0.4132053.1 |
$x^{8} - 3 x^{7} + 2 x^{6} + 4 x^{5} - 6 x^{4} + x^{3} + 3 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 139\cdot 367$ |
$3$ |
$6.71460911113$ |
$391.20199385994954$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.10237243409$ |
| 8.0.4237568.1 |
$x^{8} - x^{6} - 2 x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 16553$ |
$2$ |
$6.73580622678$ |
$257.3169252109157$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.44505539112$ |
| 8.0.4243509.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 3 x^{3} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 5821$ |
$2$ |
$6.73698593943$ |
$173.91608106375702$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.16326164535$ |
| 8.0.4383801.1 |
$x^{8} - 3 x^{6} - 2 x^{5} + 4 x^{4} + 3 x^{3} - 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 54121$ |
$2$ |
$6.76443228918$ |
$402.942923997928$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.36280464787$ |
| 8.0.4473088.1 |
$x^{8} - 2 x^{5} + x^{4} - 2 x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 101\cdot 173$ |
$3$ |
$6.78150256379$ |
$264.3709515056448$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.51070781357$ |
| 8.0.4532480.1 |
$x^{8} - x^{6} - 2 x^{5} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5\cdot 3541$ |
$3$ |
$6.79269300355$ |
$266.12027356065903$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.60282681328$ |
| 8.0.4540293.1 |
$x^{8} - 2 x^{7} + 2 x^{5} + x^{4} - 3 x^{3} - x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 56053$ |
$2$ |
$6.79415553977$ |
$410.0719449072321$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.57647619218$ |
| 8.0.4631661.1 |
$x^{8} - 3 x^{6} - x^{5} + 4 x^{4} + 3 x^{3} - 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 211\cdot 271$ |
$3$ |
$6.81109747543$ |
$414.1774981816371$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.1969629745$ |
| 8.0.4705533.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 8 x^{5} + 8 x^{4} - 5 x^{3} + 5 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 43\cdot 193$ |
$4$ |
$6.82458273205$ |
$417.4673639938816$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.6972239063$ |
| 8.0.4807593.1 |
$x^{8} - x^{5} + x^{4} + x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 61\cdot 139$ |
$4$ |
$6.84291210674$ |
$421.970378107279$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.51445839838$ |
| 8.0.4830625.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 6 x^{4} - 5 x^{3} + 4 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 59\cdot 131$ |
$3$ |
$6.84700138286$ |
$196.58331567048106$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$3$ |
$0.829684010287$ |
| 8.0.4842261.1 |
$x^{8} - x^{7} - x^{5} - x^{4} + x^{3} + x^{2} + 1$ |
$8$ |
[0,4] |
$3^{5}\cdot 19927$ |
$2$ |
$6.84906084392$ |
$321.7821146789782$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.71317429153$ |
| 8.0.4900625.1 |
$x^{8} - x^{7} + 3 x^{5} - x^{4} - x^{3} + 3 x^{2} - x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 7841$ |
$2$ |
$6.85932584267$ |
$198.00252523642217$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$3$ |
$0.878208581759$ |
| 8.0.4967973.1 |
$x^{8} + x^{6} - x^{5} + x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 61333$ |
$2$ |
$6.87103883793$ |
$428.9510461579503$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.79092874997$ |
| 8.0.4987089.1 |
$x^{8} - x^{7} - x^{6} + 2 x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 6841$ |
$2$ |
$6.87433812607$ |
$188.5387989877311$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.53004735949$ |
| 8.0.5040873.1 |
$x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 3 x^{3} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 62233$ |
$2$ |
$6.88356185813$ |
$432.0867968360061$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.58949567245$ |
| 8.0.5118208.1 |
$x^{8} - 3 x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{3} - x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 19993$ |
$2$ |
$6.89667469356$ |
$282.79321066814884$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$4$ |
$3$ |
$1.64059012373$ |
| 8.0.5319837.1 |
$x^{8} - x^{7} - x^{5} - x^{3} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 65677$ |
$2$ |
$6.93006472316$ |
$443.88174100766975$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.5355373112$ |
| 8.0.5467824.1 |
$x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 7 x^{4} - 6 x^{3} + 4 x^{2} - x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 4219$ |
$3$ |
$6.95387397758$ |
$318.2074794846909$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.71658558699$ |
| 8.0.5472441.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 5 x^{5} + 3 x^{4} + x^{3} - 3 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 13\cdot 5197$ |
$3$ |
$6.95460768311$ |
$450.2032874158073$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.6579370044$ |
| 8.0.5481189.1 |
$x^{8} - x^{7} + x^{6} - 2 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 1381$ |
$3$ |
$6.95599637789$ |
$235.535384245302$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.59407059865$ |
| 8.0.5483133.1 |
$x^{8} - x^{6} - x^{5} - x^{4} - x^{3} + 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 139\cdot 487$ |
$3$ |
$6.95630471334$ |
$450.64287412539875$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.96900114986$ |
| 8.0.5662953.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} - x^{4} + 3 x^{3} + x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 151\cdot 463$ |
$3$ |
$6.98442035977$ |
$457.9727066103394$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.79658562792$ |
| 8.0.5714469.1 |
$x^{8} - x^{7} + x^{6} - x^{5} - 2 x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 70549$ |
$2$ |
$6.99233110586$ |
$460.0510841200138$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.56163841606$ |
| 8.2.5756875.1 |
$x^{8} - x^{7} - 2 x^{6} + 3 x^{5} - 3 x^{3} + 2 x^{2} - 1$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 61\cdot 151$ |
$3$ |
$6.99879624201$ |
$214.60428700284623$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$4$ |
$1.01211341069$ |
| 8.0.5765013.1 |
$x^{8} - x^{7} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 3 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 103\cdot 691$ |
$3$ |
$7.00003217752$ |
$462.08116170214083$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.58733763409$ |
| 8.2.5856875.1 |
$x^{8} - x^{7} - x^{6} + 2 x^{5} - 3 x^{3} + x^{2} + x - 1$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 9371$ |
$2$ |
$7.0138785967$ |
$216.4601579968009$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$2$ |
$4$ |
$1.02990013853$ |
| 8.0.5868288.1 |
$x^{8} - 2 x^{6} - 2 x^{5} + 2 x^{3} + 5 x^{2} + 4 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 283$ |
$3$ |
$7.01558559136$ |
$106.87720479506591$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$3.10452142763$ |
| 8.0.5923449.1 |
$x^{8} - x^{7} + 4 x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7\cdot 31\cdot 337$ |
$4$ |
$7.02379506717$ |
$468.3876599570061$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.86410363062$ |
| 8.0.5981769.1 |
$x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 73849$ |
$2$ |
$7.03240225818$ |
$470.68779461549667$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$6$ |
$3$ |
$2.89315764789$ |
