| 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 |
| 8.0.6036849.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 2 x^{5} + 7 x^{4} + 2 x^{3} + 5 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$7.04046411294$ |
$21.745111415357325$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$2.51985243048$ |
| 8.0.6036849.2 |
$x^{8} - x^{7} + 5 x^{6} - x^{5} + 4 x^{4} + x^{3} + 5 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$7.04046411294$ |
$21.745111415357325$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$2.69467727831$ |
| 8.0.9144576.1 |
$x^{8} + x^{6} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$7.41558550213$ |
$17.058268835716344$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$3.46550357899$ |
| 8.0.9144576.2 |
$x^{8} - x^{6} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$7.41558550213$ |
$17.058268835716344$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$4.87081685723$ |
| 8.0.12895281.1 |
$x^{8} + 2 x^{6} - 6 x^{5} - 3 x^{4} + 5 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$7.74112091795$ |
$26.28855781932478$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$6.06288932638$ |
| 8.0.12895281.2 |
$x^{8} - 2 x^{6} + 9 x^{4} - 12 x^{3} + 7 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$7.74112091795$ |
$26.28855781932478$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$3.93088083044$ |
| 8.0.17305600.1 |
$x^{8} - 2 x^{6} + 7 x^{4} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$8.03106854574$ |
$22.80350850198276$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$4.20402583715$ |
| 8.0.17305600.2 |
$x^{8} - 2 x^{6} + x^{4} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$8.03106854574$ |
$22.80350850198276$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$7.87267579444$ |
| 8.0.18740241.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + x^{4} + 12 x^{3} - 9 x^{2} + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 37^{2}$ |
$3$ |
$8.1114201345$ |
$37.986839826445156$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$4.86600103593$ |
| 8.0.18740241.2 |
$x^{8} - x^{7} - x^{6} + 7 x^{5} - 2 x^{4} + 3 x^{3} + 9 x^{2} - 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 37^{2}$ |
$3$ |
$8.1114201345$ |
$37.986839826445156$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$4.78989842211$ |
| 8.0.19360000.1 |
$x^{8} + 3 x^{6} + 3 x^{4} + 3 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$8.14447639858$ |
$20.97617696340303$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$1.56722467568$ |
| 8.4.19360000.1 |
$x^{8} - 3 x^{6} + 3 x^{4} - 3 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$8.14447639858$ |
$20.97617696340303$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$2.67883629025$ |
| 8.0.21381376.1 |
$x^{8} + x^{6} - 2 x^{4} + x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{4}$ |
$2$ |
$8.24621125124$ |
$16.492422502470642$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$3.62279344423$ |
| 8.0.26214400.1 |
$x^{8} - 2 x^{6} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{2}$ |
$2$ |
$8.45897010752$ |
$16.403867009982392$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$6.38718353025$ |
| 8.0.26214400.2 |
$x^{8} - 2 x^{6} + 4 x^{4} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{2}$ |
$2$ |
$8.45897010752$ |
$16.403867009982392$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$7.48015118487$ |
| 8.0.27300625.1 |
$x^{8} - x^{7} + 3 x^{6} - x^{5} + 8 x^{4} + x^{3} + 3 x^{2} + x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 11^{2}\cdot 19^{2}$ |
$3$ |
$8.50200926099$ |
$32.32645975048923$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$1.77048089836$ |
| 8.4.27300625.1 |
$x^{8} - 2 x^{7} - 3 x^{6} + 2 x^{5} + 3 x^{4} + 2 x^{3} - 3 x^{2} - 2 x + 1$ |
$8$ |
[4,2] |
$5^{4}\cdot 11^{2}\cdot 19^{2}$ |
$3$ |
$8.50200926099$ |
$32.32645975048923$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$3.32977383624$ |
| 8.0.29593600.1 |
$x^{8} - 2 x^{7} + 8 x^{5} + 3 x^{4} + 4 x^{3} + 4 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{2}\cdot 17^{2}$ |
$3$ |
$8.58815205142$ |
$26.076809620810597$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$4.51020228467$ |
| 8.0.29593600.2 |
$x^{8} - 2 x^{7} - 4 x^{6} + 11 x^{4} + 12 x^{3} + 8 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{2}\cdot 17^{2}$ |
$3$ |
$8.58815205142$ |
$26.076809620810597$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$4$ |
$3$ |
$5.6751812197$ |
| 8.0.30118144.1 |
$x^{8} - 3 x^{6} + 6 x^{4} - 3 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 7^{6}$ |
$2$ |
$8.60703414132$ |
$17.214068282635402$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$4.4862396573$ |
| 8.0.31539456.1 |
$x^{8} + 3 x^{6} + 12 x^{4} + 18 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$8.65678785583$ |
$23.246501929569742$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$7.8155843056$ |
| 8.0.31539456.2 |
$x^{8} - 3 x^{6} + 12 x^{4} - 18 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$8.65678785583$ |
$23.246501929569742$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$5.92074391065$ |
| 8.0.34327881.1 |
$x^{8} + x^{6} - 9 x^{5} + 6 x^{4} + 3 x^{3} + x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 31^{2}$ |
$3$ |
$8.74894879017$ |
$33.57923578236019$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$7.87493190457$ |
| 8.0.34327881.2 |
$x^{8} - 3 x^{7} + 2 x^{6} - 3 x^{5} + 3 x^{4} + 9 x^{3} + 8 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 31^{2}$ |
$3$ |
$8.74894879017$ |
$33.57923578236019$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$11.9563264129$ |
| 8.0.44475561.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + x^{5} + 19 x^{4} + 2 x^{3} - 16 x^{2} - 16 x + 16$ |
$8$ |
[0,4] |
$3^{6}\cdot 13^{2}\cdot 19^{2}$ |
$3$ |
$9.0368105841$ |
$35.82526550367126$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$6.96545197418$ |
| 8.0.44475561.2 |
$x^{8} - x^{7} - 4 x^{6} - 4 x^{5} + 25 x^{4} - 8 x^{3} - 16 x^{2} - 8 x + 16$ |
$8$ |
[0,4] |
$3^{6}\cdot 13^{2}\cdot 19^{2}$ |
$3$ |
$9.0368105841$ |
$35.82526550367126$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$7.19838747861$ |
| 8.0.48902049.1 |
$x^{8} - 2 x^{7} + 9 x^{6} - 5 x^{5} + 16 x^{4} + 9 x^{3} + 15 x^{2} + 9 x + 9$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 37^{2}$ |
$3$ |
$9.14462460622$ |
$36.68519425437213$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$13.9033387356$ |
| 8.0.48902049.2 |
$x^{8} - x^{7} + 6 x^{6} - 7 x^{5} + 13 x^{4} + 3 x^{3} + 24 x^{2} + 9 x + 9$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 37^{2}$ |
$3$ |
$9.14462460622$ |
$36.68519425437213$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$13.3144369605$ |
| 8.0.50936769.1 |
$x^{8} - x^{7} - 7 x^{6} + x^{5} + 22 x^{4} + 15 x^{3} - 9 x^{2} + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 61^{2}$ |
$3$ |
$9.19134196089$ |
$48.774993593028796$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$7.78254046164$ |
| 8.0.50936769.2 |
$x^{8} - x^{7} - 4 x^{6} + 7 x^{5} + 19 x^{4} + 3 x^{3} - 18 x^{2} - 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 61^{2}$ |
$3$ |
$9.19134196089$ |
$48.774993593028796$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$10.8517387603$ |
| 8.0.51380224.1 |
$x^{8} + 2 x^{6} + x^{4} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{20}\cdot 7^{2}$ |
$2$ |
$9.20130653516$ |
$17.798422345016238$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$3.41107843788$ |
| 8.4.51380224.1 |
$x^{8} - 2 x^{6} + x^{4} - 2 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{20}\cdot 7^{2}$ |
$2$ |
$9.20130653516$ |
$17.798422345016238$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$5.5294988312$ |
| 8.0.57760000.1 |
$x^{8} + 5 x^{6} + 7 x^{4} + 5 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 19^{2}$ |
$3$ |
$9.33691484757$ |
$27.568097504180443$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$2.44913195761$ |
| 8.4.57760000.1 |
$x^{8} - 5 x^{6} + 7 x^{4} - 5 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 5^{4}\cdot 19^{2}$ |
$3$ |
$9.33691484757$ |
$27.568097504180443$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$5.19308636207$ |
| 8.0.58003456.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} + 2 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$9.34182513843$ |
$30.854497241083024$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$4.37462010091$ |
| 8.0.58003456.2 |
$x^{8} - 2 x^{7} + 5 x^{6} - 10 x^{5} + 13 x^{4} - 16 x^{3} + 14 x^{2} - 8 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$9.34182513843$ |
$30.854497241083024$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$3.86485682109$ |
| 8.4.63600625.1 |
$x^{8} - 2 x^{7} - x^{6} + 3 x^{5} - 2 x^{4} - 9 x^{3} - 9 x^{2} - x + 1$ |
$8$ |
[4,2] |
$5^{4}\cdot 11^{2}\cdot 29^{2}$ |
$3$ |
$9.45001880937$ |
$39.93745109543172$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$5.51551625478$ |
| 8.4.63600625.2 |
$x^{8} - x^{7} - 4 x^{6} + 11 x^{5} - 7 x^{4} - 7 x^{3} + 4 x^{2} + 3 x + 1$ |
$8$ |
[4,2] |
$5^{4}\cdot 11^{2}\cdot 29^{2}$ |
$3$ |
$9.45001880937$ |
$39.93745109543172$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$5.66404408781$ |
| 8.0.65804544.1 |
$x^{8} + x^{6} - x^{4} + x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{2}\cdot 13^{4}$ |
$3$ |
$9.49034467201$ |
$17.663521732655695$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$5.55524804914$ |
| 8.4.65804544.1 |
$x^{8} - x^{6} - x^{4} - x^{2} + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{2}\cdot 13^{4}$ |
$3$ |
$9.49034467201$ |
$17.663521732655695$ |
|
|
✓ |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$6.04856444985$ |
| 8.0.66048129.1 |
$x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{4} - 6 x^{3} + 20 x^{2} - 24 x + 16$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 43^{2}$ |
$3$ |
$9.49472881171$ |
$39.54796934400926$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$17.6976391163$ |
| 8.0.66048129.2 |
$x^{8} - 3 x^{7} + 4 x^{6} - 12 x^{5} + 27 x^{4} - 24 x^{3} + 16 x^{2} - 24 x + 16$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{2}\cdot 43^{2}$ |
$3$ |
$9.49472881171$ |
$39.54796934400926$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$8.86118876129$ |
| 8.0.67371264.1 |
$x^{8} + x^{6} + 6 x^{4} - 5 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 19^{2}$ |
$3$ |
$9.51829886184$ |
$28.103650443517264$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$12.9192490854$ |
| 8.0.67371264.2 |
$x^{8} - x^{6} + 6 x^{4} + 5 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 19^{2}$ |
$3$ |
$9.51829886184$ |
$28.103650443517264$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$21.3015052773$ |
| 8.0.72675625.1 |
$x^{8} - 3 x^{7} + 8 x^{6} - 5 x^{5} + 11 x^{4} + 5 x^{3} + 8 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$9.60889830122$ |
$41.291645644125154$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$2.6634181565$ |
| 8.4.72675625.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 11 x^{4} - 17 x^{2} - 3 x + 1$ |
$8$ |
[4,2] |
$5^{4}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$9.60889830122$ |
$41.291645644125154$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$5$ |
$6.10402751872$ |
| 8.0.72948681.1 |
$x^{8} - x^{7} + 2 x^{6} - 12 x^{5} + 17 x^{4} + 6 x^{3} - 28 x^{2} + 8 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 73^{2}$ |
$3$ |
$9.61340370548$ |
$53.3572862878164$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$13.2433097402$ |
| 8.0.72948681.2 |
$x^{8} - x^{7} - x^{6} + 9 x^{5} + 11 x^{4} + 6 x^{3} - 16 x^{2} - 16 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{2}\cdot 73^{2}$ |
$3$ |
$9.61340370548$ |
$53.3572862878164$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$6$ |
$3$ |
$9.98862457175$ |
| 8.0.74287161.1 |
$x^{8} + 5 x^{6} + 5 x^{4} + 5 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{2}\cdot 13^{4}\cdot 17^{2}$ |
$3$ |
$9.63527734791$ |
$25.748786379167466$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$3.63728339778$ |
| 8.0.74287161.2 |
$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 33 x^{4} - 34 x^{3} + 29 x^{2} - 15 x + 3$ |
$8$ |
[0,4] |
$3^{2}\cdot 13^{4}\cdot 17^{2}$ |
$3$ |
$9.63527734791$ |
$25.748786379167466$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
trivial |
$2$ |
$3$ |
$6.18488246908$ |
