| 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 |
| 8.0.5308416.1 |
$x^{8} - x^{4} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}$ |
$2$ |
$6.92820323028$ |
$6.928203230275509$ |
✓ |
✓ |
✓ |
$C_2^3$ (as 8T3) |
trivial |
$24$ |
$3$ |
$10.6435943208$ |
| 8.0.12960000.1 |
$x^{8} - 3 x^{6} + 8 x^{4} - 3 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$7.74596669241$ |
$7.745966692414834$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$12$ |
$3$ |
$10.4613900984$ |
| 8.0.40960000.1 |
$x^{8} + 7 x^{4} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{4}$ |
$2$ |
$8.94427191$ |
$8.94427190999916$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$8$ |
$3$ |
$12.3400472787$ |
| 8.0.49787136.1 |
$x^{8} + 3 x^{6} + 5 x^{4} + 12 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$9.16515138991$ |
$9.16515138991168$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$12$ |
$3$ |
$22.8515026384$ |
| 8.0.121550625.1 |
$x^{8} - x^{7} - 4 x^{6} - 9 x^{5} + 23 x^{4} + 18 x^{3} - 16 x^{2} + 8 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$10.246950766$ |
$10.246950765959598$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$6$ |
$3$ |
$26.5791049091$ |
| 8.0.157351936.1 |
$x^{8} + x^{4} + 16$ |
$8$ |
[0,4] |
$2^{16}\cdot 7^{4}$ |
$2$ |
$10.5830052443$ |
$10.583005244258363$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$8$ |
$3$ |
$33.1878601831$ |
| 8.0.207360000.1 |
$x^{8} + 6 x^{6} + 32 x^{4} + 24 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$6$ |
$3$ |
$12.3400472787$ |
| 8.0.207360000.2 |
$x^{8} - 6 x^{6} + 32 x^{4} - 24 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$6$ |
$3$ |
$27.2606592682$ |
| 8.0.303595776.1 |
$x^{8} + 5 x^{6} + 16 x^{4} + 45 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 11^{4}$ |
$3$ |
$11.4891252931$ |
$11.489125293076057$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$12$ |
$3$ |
$60.3617713091$ |
| 8.0.384160000.1 |
$x^{8} - 9 x^{6} + 37 x^{4} - 36 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$11.8321595662$ |
$11.832159566199232$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$4$ |
$3$ |
$26.4105598811$ |
| 8.0.592240896.1 |
$x^{8} - 7 x^{6} + 40 x^{4} - 63 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$12.4899959968$ |
$12.489995996796797$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$12$ |
$3$ |
$49.2380320284$ |
| 8.0.741200625.1 |
$x^{8} - 3 x^{6} - 7 x^{4} - 48 x^{2} + 256$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 11^{4}$ |
$3$ |
$12.8452325787$ |
$12.84523257866513$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$6$ |
$3$ |
$37.7123884032$ |
| 8.0.796594176.1 |
$x^{8} - 2 x^{7} - 5 x^{6} - 2 x^{5} + 63 x^{4} - 64 x^{3} + 46 x^{2} - 16 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$6$ |
$3$ |
$48.849423381$ |
| 8.0.796594176.2 |
$x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$6$ |
$3$ |
$35.9773896123$ |
| 8.0.959512576.1 |
$x^{8} + 7 x^{4} + 81$ |
$8$ |
[0,4] |
$2^{16}\cdot 11^{4}$ |
$2$ |
$13.2664991614$ |
$13.2664991614216$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$8$ |
$3$ |
$63.0659142175$ |
| 8.0.1445900625.1 |
$x^{8} + 9 x^{6} + 77 x^{4} + 36 x^{2} + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$13.9642400438$ |
$13.96424004376894$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$6$ |
$3$ |
$25.5406213931$ |
| 8.0.1731891456.1 |
$x^{8} - 9 x^{6} + 65 x^{4} - 144 x^{2} + 256$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 17^{4}$ |
$3$ |
$14.2828568571$ |
$14.2828568570857$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$12$ |
$3$ |
$101.630149443$ |
| 8.0.1871773696.1 |
$x^{8} + 31 x^{4} + 81$ |
$8$ |
[0,4] |
$2^{16}\cdot 13^{4}$ |
$2$ |
$14.4222051019$ |
$14.422205101855956$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[3]$ |
$8$ |
$3$ |
$38.9611726125$ |
| 8.0.2342560000.1 |
$x^{8} - 4 x^{7} + 24 x^{6} - 58 x^{5} + 141 x^{4} - 190 x^{3} + 186 x^{2} - 100 x + 20$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 11^{4}$ |
$3$ |
$14.8323969742$ |
$14.832396974191326$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$4$ |
$3$ |
$59.7092961698$ |
| 8.0.2702336256.1 |
$x^{8} + 9 x^{6} + 56 x^{4} + 225 x^{2} + 625$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 19^{4}$ |
$3$ |
$15.0996688705$ |
$15.0996688705415$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$12$ |
$3$ |
$175.343226021$ |
| 8.0.2847396321.1 |
$x^{8} - 9 x^{6} + 80 x^{4} - 9 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{4}\cdot 11^{4}$ |
$3$ |
$15.1986841536$ |
$15.198684153570664$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[3]$ |
$6$ |
$3$ |
$52.4137242735$ |
| 8.0.3317760000.1 |
$x^{8} - 8 x^{6} + 13 x^{4} + 12 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$2$ |
$3$ |
$59.180151618$ |
| 8.8.3317760000.1 |
$x^{8} - 12 x^{6} + 23 x^{4} - 12 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
|
✓ |
? |
$C_2^3$ (as 8T3) |
trivial |
$2$ |
$7$ |
$118.729878563$ |
| 8.0.3317760000.2 |
$x^{8} - 25 x^{4} + 625$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$12$ |
$3$ |
$59.180151618$ |
| 8.0.3317760000.3 |
$x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2, 2]$ |
$6$ |
$3$ |
$44.9422616403$ |
| 8.0.3317760000.4 |
$x^{8} + 17 x^{4} + 256$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$8$ |
$3$ |
$89.8845232807$ |
| 8.0.3317760000.5 |
$x^{8} - 7 x^{4} + 16$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$4$ |
$3$ |
$68.8142107718$ |
| 8.0.3317760000.6 |
$x^{8} + 8 x^{6} + 13 x^{4} - 12 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.0.3317760000.7 |
$x^{8} + 12 x^{6} + 23 x^{4} + 12 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$2$ |
$3$ |
$10.4613900984$ |
| 8.0.3317760000.8 |
$x^{8} + 4 x^{6} + 7 x^{4} + 36 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$6$ |
$3$ |
$68.8142107718$ |
| 8.0.3317760000.9 |
$x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} + 13 x^{4} - 44 x^{3} + 164 x^{2} - 140 x + 145$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[4]$ |
$4$ |
$3$ |
$27.2606592682$ |
| 8.0.4228250625.1 |
$x^{8} + 11 x^{6} + 112 x^{4} + 99 x^{2} + 81$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 17^{4}$ |
$3$ |
$15.9687194227$ |
$15.968719422671311$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[6]$ |
$6$ |
$3$ |
$35.6323756756$ |
| 8.0.4569760000.1 |
$x^{8} - 4 x^{7} + 14 x^{5} + 33 x^{4} - 94 x^{3} - 138 x^{2} + 188 x + 404$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$16.1245154966$ |
$16.1245154965971$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$4$ |
$3$ |
$25.5406213931$ |
| 8.0.4857532416.1 |
$x^{8} - 2 x^{7} + x^{6} - 14 x^{5} + 96 x^{4} - 82 x^{3} - 17 x^{2} + 86 x + 31$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 11^{4}$ |
$3$ |
$16.2480768093$ |
$16.24807680927192$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$6$ |
$3$ |
$131.384706296$ |
| 8.0.4857532416.2 |
$x^{8} - 2 x^{7} - 7 x^{6} - 2 x^{5} + 98 x^{4} - 98 x^{3} + 67 x^{2} - 30 x + 9$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 11^{4}$ |
$3$ |
$16.2480768093$ |
$16.24807680927192$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$6$ |
$3$ |
$209.789165086$ |
| 8.0.5473632256.1 |
$x^{8} + 49 x^{4} + 256$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{4}$ |
$2$ |
$16.4924225025$ |
$16.492422502470642$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2, 2]$ |
$8$ |
$3$ |
$125.49277292$ |
| 8.0.5554571841.1 |
$x^{8} + 3 x^{6} - 16 x^{4} + 75 x^{2} + 625$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{4}\cdot 13^{4}$ |
$3$ |
$16.5227116419$ |
$16.522711641858304$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$6$ |
$3$ |
$109.05365388$ |
| 8.0.5802782976.1 |
$x^{8} + 11 x^{6} + 85 x^{4} + 396 x^{2} + 1296$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 23^{4}$ |
$3$ |
$16.6132477258$ |
$16.61324772583615$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[6]$ |
$12$ |
$3$ |
$65.6019356369$ |
| 8.0.6146560000.1 |
$x^{8} - 4 x^{7} + 26 x^{6} - 64 x^{5} + 159 x^{4} - 216 x^{3} + 218 x^{2} - 120 x + 36$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$16.7332005307$ |
$16.73320053068151$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
trivial |
$2$ |
$3$ |
$81.3969873396$ |
| 8.0.6146560000.2 |
$x^{8} - 6 x^{6} + 39 x^{4} + 190 x^{2} + 225$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$16.7332005307$ |
$16.73320053068151$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$2$ |
$3$ |
$12.3400472787$ |
| 8.0.6597500625.1 |
$x^{8} - 7 x^{6} + 13 x^{4} - 252 x^{2} + 1296$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 19^{4}$ |
$3$ |
$16.8819430161$ |
$16.881943016134134$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$6$ |
$3$ |
$62.2070779359$ |
| 8.0.8540717056.1 |
$x^{8} + 31 x^{4} + 625$ |
$8$ |
[0,4] |
$2^{16}\cdot 19^{4}$ |
$2$ |
$17.4355957742$ |
$17.435595774162696$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[3]$ |
$8$ |
$3$ |
$88.4442860779$ |
| 8.0.8999178496.1 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 37 x^{4} - 82 x^{3} - 76 x^{2} + 118 x + 401$ |
$8$ |
[0,4] |
$2^{8}\cdot 7^{4}\cdot 11^{4}$ |
$3$ |
$17.5499287748$ |
$17.549928774784245$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[2]$ |
$4$ |
$3$ |
$72.4184469969$ |
| 8.0.9475854336.1 |
$x^{8} - 4 x^{7} - 10 x^{6} + 44 x^{5} + 29 x^{4} - 136 x^{3} + 136 x^{2} - 60 x + 75$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$17.6635217327$ |
$17.663521732655695$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[6]$ |
$6$ |
$3$ |
$102.180082696$ |
| 8.0.9475854336.2 |
$x^{8} - 2 x^{7} + 13 x^{6} - 2 x^{5} + 102 x^{4} - 94 x^{3} + 91 x^{2} - 10 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$17.6635217327$ |
$17.663521732655695$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[4]$ |
$6$ |
$3$ |
$38.9611726125$ |
| 8.0.12745506816.1 |
$x^{8} + 23 x^{4} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$18.3303027798$ |
$18.33030277982336$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[8]$ |
$4$ |
$3$ |
$48.849423381$ |
| 8.8.12745506816.1 |
$x^{8} - 16 x^{6} + 79 x^{4} - 120 x^{2} + 9$ |
$8$ |
[8,0] |
$2^{16}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$18.3303027798$ |
$18.33030277982336$ |
|
✓ |
? |
$C_2^3$ (as 8T3) |
trivial |
$2$ |
$7$ |
$255.621381332$ |
| 8.0.12745506816.2 |
$x^{8} - 4 x^{7} + 22 x^{6} - 52 x^{5} + 111 x^{4} - 140 x^{3} + 130 x^{2} - 68 x + 22$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$18.3303027798$ |
$18.33030277982336$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[2, 2]$ |
$2$ |
$3$ |
$58.329447273$ |
| 8.0.12745506816.3 |
$x^{8} + 16 x^{6} + 79 x^{4} + 120 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$18.3303027798$ |
$18.33030277982336$ |
✓ |
✓ |
|
$C_2^3$ (as 8T3) |
$[8]$ |
$2$ |
$3$ |
$22.8515026384$ |
| 8.0.12745506816.4 |
$x^{8} + 8 x^{6} + 55 x^{4} + 72 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$18.3303027798$ |
$18.33030277982336$ |
✓ |
✓ |
? |
$C_2^3$ (as 8T3) |
$[2, 2]$ |
$6$ |
$3$ |
$66.3757203661$ |
