| 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 |
| 8.4.975437824.1 |
$x^{8} - 2 x^{6} - 2 x^{4} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 61^{2}$ |
$2$ |
$13.2938247421$ |
$71.15378852427706$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$5$ |
$38.8492307406$ |
| 8.0.975437824.2 |
$x^{8} - 2 x^{4} + 4 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 61^{2}$ |
$2$ |
$13.2938247421$ |
$71.15378852427706$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$3$ |
$13.7371698006$ |
| 8.4.4096000000.1 |
$x^{8} - 2 x^{6} - 4 x^{5} - 5 x^{4} - 16 x^{3} - 20 x^{2} - 8 x - 1$ |
$8$ |
[4,2] |
$2^{18}\cdot 5^{6}$ |
$2$ |
$15.9054145753$ |
$34.83438237794665$ |
|
|
✓ |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
trivial |
$2$ |
$5$ |
$94.5028335019$ |
| 8.4.7487094784.2 |
$x^{8} - 8 x^{5} - 5 x^{4} + 16 x^{2} + 20 x + 3$ |
$8$ |
[4,2] |
$2^{18}\cdot 13^{4}$ |
$2$ |
$17.1509889212$ |
$32.84768651624708$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
trivial |
$2$ |
$5$ |
$166.397152758$ |
| 8.0.7665352704.3 |
$x^{8} - 10 x^{6} + 40 x^{4} - 60 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$17.201507845$ |
$68.78132519344828$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$6$ |
$3$ |
$149.09946617$ |
| 8.0.7665352704.13 |
$x^{8} - 6 x^{6} + 8 x^{4} + 12 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$17.201507845$ |
$68.78132519344828$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$6$ |
$3$ |
$198.74814612$ |
| 8.0.9364045824.10 |
$x^{8} - 2 x^{6} + 24 x^{4} - 140 x^{2} + 196$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$17.6373340821$ |
$54.94435407942486$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$64.4011624771$ |
| 8.0.9364045824.11 |
$x^{8} - 10 x^{6} + 24 x^{4} - 28 x^{2} + 196$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$17.6373340821$ |
$54.94435407942486$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$157.332672021$ |
| 8.0.10892869632.1 |
$x^{8} - 18 x^{6} + 126 x^{4} - 288 x^{2} + 228$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{7}\cdot 19$ |
$3$ |
$17.9739193329$ |
$103.84629572415844$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$6$ |
$3$ |
$150.425730718$ |
| 8.0.10892869632.3 |
$x^{8} + 6 x^{6} + 30 x^{4} + 96 x^{2} + 228$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{7}\cdot 19$ |
$3$ |
$17.9739193329$ |
$103.84629572415844$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$6$ |
$3$ |
$99.4969479417$ |
| 8.4.12518162432.3 |
$x^{8} - 2 x^{4} - 44 x^{2} + 68$ |
$8$ |
[4,2] |
$2^{18}\cdot 17\cdot 53^{2}$ |
$3$ |
$18.2891100349$ |
$273.461068672299$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$2$ |
$5$ |
$125.445101057$ |
| 8.0.13271040000.20 |
$x^{8} - 8 x^{6} - 8 x^{5} + 25 x^{4} + 32 x^{3} - 20 x^{2} - 36 x + 39$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$18.4231174064$ |
$46.139591105102575$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
trivial |
$6$ |
$3$ |
$296.505565113$ |
| 8.0.15479341056.8 |
$x^{8} - 6 x^{6} - 8 x^{5} + 30 x^{4} + 96 x^{3} + 136 x^{2} + 96 x + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{10}$ |
$2$ |
$18.7810149609$ |
$47.33855458753409$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
trivial |
$6$ |
$3$ |
$311.970875141$ |
| 8.4.19824640000.3 |
$x^{8} + 4 x^{6} - 2 x^{4} - 12 x^{2} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$19.3709385623$ |
$67.5638604016345$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$175.493912296$ |
| 8.0.20405551104.11 |
$x^{8} + 14 x^{6} - 8 x^{5} + 54 x^{4} - 32 x^{3} + 72 x^{2} - 32 x + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$19.4409973497$ |
$87.85663907345199$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
trivial |
$6$ |
$3$ |
$242.870334902$ |
| 8.0.23123460096.25 |
$x^{8} - 2 x^{6} + 48 x^{4} - 44 x^{2} + 484$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 11^{2}$ |
$3$ |
$19.747249009$ |
$68.8763929050309$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$165.517170708$ |
| 8.0.23123460096.27 |
$x^{8} + 22 x^{6} + 168 x^{4} + 484 x^{2} + 484$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 11^{2}$ |
$3$ |
$19.747249009$ |
$68.8763929050309$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$96.0915118623$ |
| 8.4.25029771264.1 |
$x^{8} - 2 x^{4} - 12 x^{2} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 3^{2}\cdot 103^{2}$ |
$3$ |
$19.9437632514$ |
$160.14461911902742$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$5$ |
$266.062424046$ |
| 8.4.30190862336.2 |
$x^{8} - 8 x^{6} + 22 x^{4} - 68 x^{2} + 164$ |
$8$ |
[4,2] |
$2^{18}\cdot 41\cdot 53^{2}$ |
$3$ |
$20.4166479289$ |
$424.681139850153$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$5$ |
$171.810499307$ |
| 8.0.32296402944.2 |
$x^{8} - 14 x^{6} + 54 x^{4} - 104 x^{2} + 676$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$20.5894274224$ |
$74.8765332184235$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$137.478165796$ |
| 8.0.32296402944.4 |
$x^{8} + 4 x^{6} + 54 x^{4} + 364 x^{2} + 676$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$20.5894274224$ |
$74.8765332184235$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$155.024889554$ |
| 8.0.34542452736.6 |
$x^{8} + 4 x^{6} + 14 x^{4} + 20 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$20.7631932691$ |
$52.33474122820263$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$3$ |
$463.754314981$ |
| 8.0.34542452736.8 |
$x^{8} + 2 x^{6} + 8 x^{4} - 4 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$20.7631932691$ |
$52.33474122820263$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$3$ |
$183.030544208$ |
| 8.4.36864000000.2 |
$x^{8} + 2 x^{6} - 26 x^{4} - 72 x^{2} + 36$ |
$8$ |
[4,2] |
$2^{18}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$20.9327027878$ |
$52.76199905335091$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$264.415878414$ |
| 8.0.36864000000.9 |
$x^{8} + 6 x^{6} + 16 x^{4} + 36 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$20.9327027878$ |
$52.76199905335091$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$3$ |
$82.6200384467$ |
| 8.0.38411698176.2 |
$x^{8} - 12 x^{6} + 78 x^{4} - 252 x^{2} + 804$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{7}\cdot 67$ |
$3$ |
$21.0405911986$ |
$195.0076327908552$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$6$ |
$3$ |
$270.214480441$ |
| 8.0.38411698176.4 |
$x^{8} + 24 x^{6} + 198 x^{4} + 636 x^{2} + 804$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{7}\cdot 67$ |
$3$ |
$21.0405911986$ |
$195.0076327908552$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$6$ |
$3$ |
$134.662037906$ |
| 8.0.39261044736.5 |
$x^{8} - 2 x^{6} + 16 x^{4} - 12 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 43^{2}$ |
$3$ |
$21.0981915761$ |
$103.4732205123564$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$6$ |
$3$ |
$1277.99797228$ |
| 8.0.39261044736.11 |
$x^{8} - 12 x^{6} + 62 x^{4} - 156 x^{2} + 196$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 43^{2}$ |
$3$ |
$21.0981915761$ |
$103.4732205123564$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$6$ |
$3$ |
$544.551826246$ |
| 8.4.42998169600.5 |
$x^{8} + 2 x^{6} + 6 x^{4} - 40 x^{2} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 3^{8}\cdot 5^{2}$ |
$3$ |
$21.3393529205$ |
$88.14136791951549$ |
|
|
|
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$5$ |
$755.451386456$ |
| 8.0.42998169600.7 |
$x^{8} - 6 x^{6} + 44 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{8}\cdot 5^{2}$ |
$3$ |
$21.3393529205$ |
$88.14136791951549$ |
|
|
|
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$3$ |
$604.582639409$ |
| 8.4.59146240000.7 |
$x^{8} + 2 x^{6} - 10 x^{4} - 16 x^{2} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 5^{4}\cdot 19^{2}$ |
$3$ |
$22.2070511378$ |
$88.79630900143394$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$323.213713826$ |
| 8.4.67383853056.4 |
$x^{8} + 2 x^{6} - 16 x^{4} - 4 x^{2} + 4$ |
$8$ |
[4,2] |
$2^{18}\cdot 3^{2}\cdot 13^{4}$ |
$3$ |
$22.5719708156$ |
$56.893861957235075$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$292.34132236$ |
| 8.0.68988174336.11 |
$x^{8} + 6 x^{6} + 30 x^{4} - 72 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 19^{2}$ |
$3$ |
$22.6384574584$ |
$90.52131466353185$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$208.142672999$ |
| 8.0.68988174336.22 |
$x^{8} - 12 x^{6} + 102 x^{4} - 324 x^{2} + 324$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 19^{2}$ |
$3$ |
$22.6384574584$ |
$90.52131466353185$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$490.848575556$ |
| 8.0.101093474304.4 |
$x^{8} - 22 x^{6} + 240 x^{4} - 1012 x^{2} + 2116$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 23^{2}$ |
$3$ |
$23.7459959988$ |
$99.59509959238518$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$656.261578128$ |
| 8.0.101093474304.6 |
$x^{8} + 26 x^{6} + 264 x^{4} + 1196 x^{2} + 2116$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 23^{2}$ |
$3$ |
$23.7459959988$ |
$99.59509959238518$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$400.87552745$ |
| 8.0.107038900224.18 |
$x^{8} - 20 x^{6} - 8 x^{5} + 139 x^{4} + 80 x^{3} - 248 x^{2} - 108 x + 183$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 71^{2}$ |
$3$ |
$23.9162290885$ |
$132.96058366674902$ |
|
|
? |
$(A_4\wr C_2):C_2$ (as 8T45) |
trivial |
$6$ |
$3$ |
$831.506980012$ |
| 8.0.119439360000.27 |
$x^{8} - 2 x^{6} + 30 x^{4} - 8 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$24.2461860561$ |
$95.97421705995339$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$3$ |
$403.895246867$ |
| 8.0.119439360000.29 |
$x^{8} + 4 x^{6} + 30 x^{4} + 4 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$24.2461860561$ |
$95.97421705995339$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$2$ |
$3$ |
$236.219776888$ |
| 8.2.126976000000.6 |
$x^{8} + 2 x^{6} - 26 x^{4} + 48 x^{2} - 124$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 5^{6}\cdot 31$ |
$3$ |
$24.4323479794$ |
$169.6060974407857$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$2$ |
$4$ |
$329.673809401$ |
| 8.2.126976000000.8 |
$x^{8} + 4 x^{6} - 74 x^{4} + 204 x^{2} - 124$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 5^{6}\cdot 31$ |
$3$ |
$24.4323479794$ |
$169.6060974407857$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$2$ |
$4$ |
$471.620653105$ |
| 8.0.139314069504.9 |
$x^{8} - 24 x^{5} - 27 x^{4} + 144 x^{2} + 324 x + 243$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{12}$ |
$2$ |
$24.7172057269$ |
$98.46816160418916$ |
|
|
? |
$(A_4\wr C_2):C_2$ (as 8T45) |
trivial |
$6$ |
$3$ |
$1292.28199918$ |
| 8.0.183649959936.3 |
$x^{8} - 8 x^{6} + 150 x^{4} - 1364 x^{2} + 3844$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 31^{2}$ |
$3$ |
$25.5857913979$ |
$115.6258395499167$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$385.421372806$ |
| 8.0.183649959936.4 |
$x^{8} - 22 x^{6} + 150 x^{4} - 496 x^{2} + 3844$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 31^{2}$ |
$3$ |
$25.5857913979$ |
$115.6258395499167$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$717.005428075$ |
| 8.0.191633817600.7 |
$x^{8} + 16 x^{6} + 152 x^{4} + 800 x^{2} + 1600$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 5^{2}\cdot 19^{2}$ |
$4$ |
$25.7222537912$ |
$153.79971871506922$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$6$ |
$3$ |
$198.553425725$ |
| 8.0.191633817600.11 |
$x^{8} - 8 x^{6} + 38 x^{4} - 100 x^{2} + 100$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{4}\cdot 5^{2}\cdot 19^{2}$ |
$4$ |
$25.7222537912$ |
$153.79971871506922$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$349.727165572$ |
| 8.4.200704000000.2 |
$x^{8} - 6 x^{6} + 6 x^{4} - 336 x^{2} + 196$ |
$8$ |
[4,2] |
$2^{18}\cdot 5^{6}\cdot 7^{2}$ |
$3$ |
$25.8713745523$ |
$80.59528482638964$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$2$ |
$5$ |
$560.02218934$ |
| 8.0.200704000000.12 |
$x^{8} + 2 x^{6} - 16 x^{4} + 28 x^{2} + 196$ |
$8$ |
[0,4] |
$2^{18}\cdot 5^{6}\cdot 7^{2}$ |
$3$ |
$25.8713745523$ |
$80.59528482638964$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$3$ |
$66.6399351569$ |
| 8.0.261619974144.5 |
$x^{8} - 38 x^{6} + 582 x^{4} - 2960 x^{2} + 5476$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 37^{2}$ |
$3$ |
$26.7429222868$ |
$126.32081361845144$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$6$ |
$3$ |
$428.889935206$ |
