| 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 |
| 8.0.1257728.1 |
$x^{8} - 2 x^{7} + 4 x^{5} - 4 x^{4} + 3 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{3}$ |
$2$ |
$5.78693149384$ |
$16.74428805718538$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$0.618886617067$ |
| 8.0.1601613.1 |
$x^{8} - 2 x^{6} - 3 x^{5} + 3 x^{4} + 3 x^{3} - 2 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 13^{3}$ |
$2$ |
$5.9644403303$ |
$15.606246247497747$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$1.10095849199$ |
| 8.0.4917248.1 |
$x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 10 x^{4} - 9 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{11}\cdot 7^{4}$ |
$2$ |
$6.86222990392$ |
$17.798422345016238$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$1.14267657377$ |
| 8.0.8192000.1 |
$x^{8} - 2 x^{4} + 5$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{3}$ |
$2$ |
$7.31431639992$ |
$13.37480609952844$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$3.37718130353$ |
| 8.0.8719893.1 |
$x^{8} - 3 x^{7} - x^{6} + 11 x^{5} - 6 x^{4} - 10 x^{3} + 9 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 13^{3}$ |
$3$ |
$7.37163620696$ |
$31.37380273734233$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$3.28851213295$ |
| 8.0.8719893.2 |
$x^{8} - 3 x^{7} + 5 x^{5} + x^{4} - 3 x^{3} - 5 x^{2} - 2 x + 7$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 13^{3}$ |
$3$ |
$7.37163620696$ |
$31.37380273734233$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$3.59771330101$ |
| 8.4.15243125.1 |
$x^{8} - x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - 6 x^{3} - 2 x^{2} + 3 x + 1$ |
$8$ |
[4,2] |
$5^{4}\cdot 29^{3}$ |
$2$ |
$7.90467923584$ |
$27.943673649584856$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$5$ |
$2.29779629129$ |
| 8.0.16471125.1 |
$x^{8} - x^{7} + 5 x^{6} - 2 x^{5} + 9 x^{4} - 2 x^{3} + 5 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{2}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$7.98160824589$ |
$19.208102881010017$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$2.52193333176$ |
| 8.0.16471125.2 |
$x^{8} - x^{7} + x^{6} + 2 x^{5} - 3 x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{2}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$7.98160824589$ |
$19.208102881010017$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$1.69679589997$ |
| 8.0.20123648.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{3}$ |
$2$ |
$8.18395700311$ |
$23.679999262753405$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$1.81338098584$ |
| 8.0.31510377.1 |
$x^{8} + 2 x^{6} - 2 x^{5} - 6 x^{4} - 2 x^{3} + 9 x^{2} + 10 x + 4$ |
$8$ |
[0,4] |
$3^{4}\cdot 73^{3}$ |
$2$ |
$8.65578977134$ |
$43.25663903061054$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$11.1813393987$ |
| 8.0.32768000.1 |
$x^{8} + 2 x^{4} + 5$ |
$8$ |
[0,4] |
$2^{18}\cdot 5^{3}$ |
$2$ |
$8.69823710416$ |
$15.905414575341013$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$8.08249444091$ |
| 8.0.36926037.1 |
$x^{8} - x^{7} + 6 x^{6} - x^{5} + 10 x^{4} + 6 x^{3} + 6 x^{2} + 9 x + 3$ |
$8$ |
[0,4] |
$3^{6}\cdot 37^{3}$ |
$2$ |
$8.82910308645$ |
$34.197332740531884$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$11.6355557694$ |
| 8.0.45556992.2 |
$x^{8} - 7 x^{6} + 20 x^{4} - 26 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$9.06398921581$ |
$33.54000593239012$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$6.80355043106$ |
| 8.0.45556992.3 |
$x^{8} + 7 x^{6} + 20 x^{4} + 26 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$9.06398921581$ |
$33.54000593239012$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$9.41544733706$ |
| 8.0.64242477.1 |
$x^{8} - 3 x^{7} + 11 x^{6} - 22 x^{5} + 42 x^{4} - 52 x^{3} + 66 x^{2} - 43 x + 37$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 19^{2}$ |
$3$ |
$9.46188760124$ |
$51.688620557322054$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$11.654352285$ |
| 8.0.64242477.2 |
$x^{8} - 3 x^{7} - 3 x^{6} + 10 x^{5} + 16 x^{4} - 36 x^{3} - 2 x^{2} + 17 x + 7$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 19^{2}$ |
$3$ |
$9.46188760124$ |
$51.688620557322054$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$11.4012250884$ |
| 8.0.70304000.3 |
$x^{8} - 2 x^{7} - 2 x^{6} + 11 x^{4} - 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{3}\cdot 13^{3}$ |
$3$ |
$9.56913109595$ |
$45.78413496570207$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$10.0483494552$ |
| 8.0.70304000.4 |
$x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{5} + 10 x^{4} - 12 x^{3} + 19 x^{2} - 8 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{3}\cdot 13^{3}$ |
$3$ |
$9.56913109595$ |
$45.78413496570207$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$11.1507036068$ |
| 8.0.73926513.1 |
$x^{8} - x^{7} + 3 x^{6} + 6 x^{5} + 3 x^{4} + 8 x^{3} + 20 x^{2} + 8 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 97^{3}$ |
$2$ |
$9.62941774411$ |
$53.535199825186666$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$12.6437392405$ |
| 8.0.78675968.2 |
$x^{8} + 3 x^{6} + 3 x^{4} + 2 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{15}\cdot 7^{4}$ |
$2$ |
$9.70465859824$ |
$21.166010488516726$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$7.357839972$ |
| 8.4.88410125.1 |
$x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - 7 x^{4} + 11 x^{3} - 6 x^{2} + x + 1$ |
$8$ |
[4,2] |
$5^{3}\cdot 29^{4}$ |
$2$ |
$9.84719981627$ |
$18.006383777357115$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$5$ |
$7.58920427421$ |
| 8.0.101875968.1 |
$x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{4} + 8 x^{3} + 15 x^{2} + 6 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 17^{3}$ |
$3$ |
$10.0232593672$ |
$29.001957651613843$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$4$ |
$3$ |
$6.34325059$ |
| 8.0.131072000.1 |
$x^{8} - 2 x^{6} + 8 x^{4} - 10 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{3}$ |
$2$ |
$10.3440054523$ |
$24.529502540692157$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$18.510095453$ |
| 8.0.131072000.2 |
$x^{8} - 6 x^{6} + 12 x^{4} - 10 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{3}$ |
$2$ |
$10.3440054523$ |
$24.529502540692157$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$16.8944703759$ |
| 8.0.134217728.2 |
$x^{8} + 2 x^{4} + 2$ |
$8$ |
[0,4] |
$2^{27}$ |
$1$ |
$10.3747164372$ |
$15.32165249117718$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$23.9804883874$ |
| 8.0.134217728.3 |
$x^{8} - 2 x^{4} + 2$ |
$8$ |
[0,4] |
$2^{27}$ |
$1$ |
$10.3747164372$ |
$15.32165249117718$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$15.3140319207$ |
| 8.0.143982592.1 |
$x^{8} + 6 x^{4} + 13$ |
$8$ |
[0,4] |
$2^{16}\cdot 13^{3}$ |
$2$ |
$10.4661932274$ |
$27.385300168092183$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$25.2300222834$ |
| 8.0.165469149.1 |
$x^{8} - 3 x^{7} + 2 x^{6} - 6 x^{5} + 30 x^{4} - 63 x^{3} + 71 x^{2} - 36 x + 7$ |
$8$ |
[0,4] |
$3^{6}\cdot 61^{3}$ |
$2$ |
$10.6497553021$ |
$49.755181783405924$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$33.419193433$ |
| 8.0.171016677.1 |
$x^{8} - 3 x^{7} + 14 x^{6} - 23 x^{5} + 57 x^{4} - 59 x^{3} + 99 x^{2} - 62 x + 43$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 31^{2}$ |
$3$ |
$10.6937446087$ |
$66.02356770151067$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$12.1415917033$ |
| 8.0.171016677.2 |
$x^{8} - 9 x^{6} - 5 x^{5} + 37 x^{4} + 24 x^{3} - 71 x^{2} - 25 x + 67$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 31^{2}$ |
$3$ |
$10.6937446087$ |
$66.02356770151067$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$12.3756892326$ |
| 8.0.201041757.1 |
$x^{8} - x^{7} + 7 x^{6} - 13 x^{5} + 24 x^{4} - 32 x^{3} + 43 x^{2} - 29 x + 19$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 37^{3}$ |
$3$ |
$10.9121614741$ |
$68.74813805509002$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$18.9618903656$ |
| 8.0.201041757.2 |
$x^{8} - 2 x^{7} + 11 x^{6} - 14 x^{5} + 32 x^{4} - 23 x^{3} + 31 x^{2} - 12 x + 3$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 37^{3}$ |
$3$ |
$10.9121614741$ |
$68.74813805509002$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$49.1613945849$ |
| 8.0.204800000.1 |
$x^{8} + 2 x^{6} - 12 x^{5} + 4 x^{4} + 8 x^{3} + 14 x^{2} - 8 x + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{5}$ |
$2$ |
$10.9374541141$ |
$13.37480609952844$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$4$ |
$3$ |
$12.0943214968$ |
| 8.0.221445125.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 15 x^{5} + 18 x^{4} - 16 x^{3} + 13 x^{2} - 5 x + 3$ |
$8$ |
[0,4] |
$5^{3}\cdot 11^{6}$ |
$2$ |
$11.044810413$ |
$20.19630948441476$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$19.2475978728$ |
| 8.0.233644288.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 13 x^{4} - 10 x^{3} - 4 x^{2} + 6 x + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 97^{3}$ |
$2$ |
$11.1190938534$ |
$61.817124060383854$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$21.0649230094$ |
| 8.0.240945152.1 |
$x^{8} - 3 x^{7} + 11 x^{6} - 23 x^{5} + 42 x^{4} - 55 x^{3} + 57 x^{2} - 39 x + 11$ |
$8$ |
[0,4] |
$2^{11}\cdot 7^{6}$ |
$2$ |
$11.1619423227$ |
$28.950496621601552$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$11.22690469$ |
| 8.0.270672597.1 |
$x^{8} - 3 x^{7} - 5 x^{6} + 15 x^{5} + 15 x^{4} - 6 x^{3} - 71 x^{2} - 36 x + 133$ |
$8$ |
[0,4] |
$3^{6}\cdot 13^{5}$ |
$2$ |
$11.3254518034$ |
$15.606246247497747$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$6$ |
$3$ |
$13.3247028561$ |
| 8.8.282300416.1 |
$x^{8} - 4 x^{7} + 14 x^{5} - 8 x^{4} - 12 x^{3} + 7 x^{2} + 2 x - 1$ |
$8$ |
[8,0] |
$2^{12}\cdot 41^{3}$ |
$2$ |
$11.3851547954$ |
$45.82820910616052$ |
|
|
✓ |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$7$ |
$22.4468700736$ |
| 8.0.282300416.2 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 11 x^{4} - 6 x^{3} - 4 x^{2} + 4 x + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 41^{3}$ |
$2$ |
$11.3851547954$ |
$45.82820910616052$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$39.2631690627$ |
| 8.0.282300416.3 |
$x^{8} - 2 x^{7} + 3 x^{6} + 4 x^{5} - 5 x^{4} - 4 x^{3} + 13 x^{2} - 10 x + 3$ |
$8$ |
[0,4] |
$2^{12}\cdot 41^{3}$ |
$2$ |
$11.3851547954$ |
$45.82820910616052$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$20.8116000853$ |
| 8.0.314703872.3 |
$x^{8} - 2 x^{6} + 6 x^{4} - 12 x^{2} + 8$ |
$8$ |
[0,4] |
$2^{17}\cdot 7^{4}$ |
$2$ |
$11.5408490537$ |
$17.798422345016238$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$2$ |
$3$ |
$8.1839529035$ |
| 8.0.314703872.4 |
$x^{8} + 2 x^{6} + 6 x^{4} + 12 x^{2} + 8$ |
$8$ |
[0,4] |
$2^{17}\cdot 7^{4}$ |
$2$ |
$11.5408490537$ |
$21.166010488516726$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$3$ |
$13.4897264996$ |
| 8.0.321978368.5 |
$x^{8} + 2 x^{4} + 17$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$33.48857611437076$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$4$ |
$3$ |
$13.5496984016$ |
| 8.0.321978368.6 |
$x^{8} - 4 x^{7} + 6 x^{6} - 6 x^{4} + 4 x^{3} + 2 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$33.48857611437076$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$2$ |
$3$ |
$12.7171485653$ |
| 8.0.329042493.2 |
$x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + 25 x^{4} - 30 x^{3} - 26 x^{2} + 97 x + 67$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 43^{2}$ |
$3$ |
$11.6053033886$ |
$77.75930483841216$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$27.7699923883$ |
| 8.0.329042493.3 |
$x^{8} - 3 x^{7} - 7 x^{6} + 19 x^{5} + 33 x^{4} - 50 x^{3} - 84 x^{2} + 19 x + 139$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 43^{2}$ |
$3$ |
$11.6053033886$ |
$77.75930483841216$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$6$ |
$3$ |
$13.4560107035$ |
| 8.0.363483392.1 |
$x^{8} - 2 x^{7} + 10 x^{5} - 6 x^{4} - 20 x^{3} + 55 x^{2} - 62 x + 25$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{5}$ |
$2$ |
$11.7506143061$ |
$16.74428805718538$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$4$ |
$3$ |
$12.3163318913$ |
| 8.0.369381632.2 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 5 x^{4} - 6 x^{3} + 14 x^{2} - 8 x + 8$ |
$8$ |
[0,4] |
$2^{8}\cdot 113^{3}$ |
$2$ |
$11.7742814252$ |
$69.31685153955033$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
trivial |
$4$ |
$3$ |
$131.796586963$ |
| 8.4.381078125.1 |
$x^{8} - 3 x^{7} + x^{6} + 11 x^{5} - 26 x^{4} + 28 x^{3} - 21 x^{2} + 9 x + 1$ |
$8$ |
[4,2] |
$5^{6}\cdot 29^{3}$ |
$2$ |
$11.8202524613$ |
$41.78553833475025$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
$2$ |
$5$ |
$14.1926159056$ |
