| 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 |
| 8.0.3240000.1 |
$x^{8} - 3 x^{7} + 3 x^{6} + x^{5} - 2 x^{4} - 3 x^{3} + 7 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$6.51355562433$ |
$10.954451150103322$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$1.89812936734$ |
| 8.0.4665600.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - 8 x^{4} + 2 x^{3} + 5 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 5^{2}$ |
$3$ |
$6.8173161988$ |
$10.194265469082735$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$4.35269368866$ |
| 8.0.5308416.2 |
$x^{8} - 2 x^{6} + 5 x^{4} - 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}$ |
$2$ |
$6.92820323028$ |
$9.797958971132712$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$5.23935618746$ |
| 8.0.7290000.1 |
$x^{8} - 3 x^{7} + x^{6} + 3 x^{5} - 3 x^{3} + x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$7.2084342424$ |
$10.194265469082735$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$3.18091820359$ |
| 8.0.8294400.1 |
$x^{8} - 2 x^{7} + x^{6} + 7 x^{4} - 16 x^{3} + 15 x^{2} - 6 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$7.32568300297$ |
$10.954451150103322$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$3.47655855903$ |
| 8.0.9437184.1 |
$x^{8} - 4 x^{6} - 4 x^{5} + 6 x^{4} + 16 x^{3} + 16 x^{2} + 8 x + 2$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{2}$ |
$2$ |
$7.44483887282$ |
$9.797958971132712$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$7.01287439394$ |
| 8.0.14630625.1 |
$x^{8} - x^{7} + x^{6} + x^{4} - 8 x^{3} + 12 x^{2} - 6 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 17^{2}$ |
$3$ |
$7.86425993875$ |
$15.968719422671311$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$3.93922060224$ |
| 8.4.23040000.1 |
$x^{8} - 2 x^{7} - x^{6} - 5 x^{4} - x^{2} - 2 x + 1$ |
$8$ |
[4,2] |
$2^{12}\cdot 3^{2}\cdot 5^{4}$ |
$3$ |
$8.32358290058$ |
$10.954451150103322$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$5$ |
$3.04219016894$ |
| 8.0.31539456.5 |
$x^{8} - 2 x^{7} - x^{6} - 2 x^{5} + 10 x^{4} + 8 x^{3} - 22 x^{2} - 4 x + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$8.65678785583$ |
$16.437759153264928$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$13.2399540089$ |
| 8.0.47775744.2 |
$x^{8} - 6 x^{6} + 18 x^{4} - 18 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{6}$ |
$2$ |
$9.11802822782$ |
$12.894839181882503$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$19.2726257484$ |
| 8.0.51840000.2 |
$x^{8} + 5 x^{6} + 11 x^{4} + 10 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{10}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$9.21155870319$ |
$15.491933384829668$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$10.8918775784$ |
| 8.0.70560000.1 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} + 3 x^{4} + 8 x^{3} + 9 x^{2} + 4 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{2}\cdot 5^{4}\cdot 7^{2}$ |
$4$ |
$9.57347971738$ |
$20.493901531919196$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$4$ |
$3$ |
$5.5925397832$ |
| 8.0.70560000.2 |
$x^{8} - x^{6} - 4 x^{5} + 4 x^{4} + 2 x^{3} + 4 x^{2} - 10 x + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{2}\cdot 5^{4}\cdot 7^{2}$ |
$4$ |
$9.57347971738$ |
$20.493901531919196$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$4$ |
$3$ |
$10.2169603559$ |
| 8.4.84934656.1 |
$x^{8} - 4 x^{5} - 2 x^{4} - 8 x^{2} - 8 x - 2$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{4}$ |
$2$ |
$9.79795897113$ |
$9.797958971132712$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$5$ |
$10.5860600957$ |
| 8.0.112021056.1 |
$x^{8} - x^{7} - x^{6} - 7 x^{5} + 22 x^{4} - 23 x^{3} + 11 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$10.1429073345$ |
$17.058268835716344$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$6$ |
$3$ |
$9.55171500307$ |
| 8.4.116640000.1 |
$x^{8} - 2 x^{7} - x^{6} + 10 x^{5} + x^{4} - 16 x^{3} - 7 x^{2} + 2 x + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$10.1942654691$ |
$10.194265469082735$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$5$ |
$8.64401716304$ |
| 8.0.126877696.1 |
$x^{8} - 8 x^{6} - 12 x^{5} + 12 x^{4} + 56 x^{3} + 76 x^{2} + 52 x + 17$ |
$8$ |
[0,4] |
$2^{20}\cdot 11^{2}$ |
$2$ |
$10.3020383076$ |
$18.76166303929372$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$28.1956680358$ |
| 8.0.132710400.3 |
$x^{8} - 4 x^{5} + 13 x^{4} - 24 x^{3} + 22 x^{2} - 8 x + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$10.3600802564$ |
$15.491933384829668$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$6$ |
$3$ |
$9.97462313965$ |
| 8.0.134560000.3 |
$x^{8} - 2 x^{7} + 3 x^{6} + 6 x^{5} - 2 x^{4} + 8 x^{3} + 6 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 29^{2}$ |
$3$ |
$10.3780198565$ |
$24.08318915758459$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$4$ |
$3$ |
$14.0275412096$ |
| 8.0.142205625.1 |
$x^{8} - x^{7} - 3 x^{6} + 4 x^{5} - 7 x^{4} + 4 x^{3} + 30 x^{2} - 46 x + 19$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 53^{2}$ |
$3$ |
$10.4499592506$ |
$28.19574435974337$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$11.6363716962$ |
| 8.0.146313216.5 |
$x^{8} - 4 x^{7} + 2 x^{6} + 2 x^{5} + 10 x^{4} - 8 x^{3} - x^{2} - 2 x + 7$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$10.4872215901$ |
$17.058268835716344$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$21.4925540319$ |
| 8.0.150994944.1 |
$x^{8} - 4 x^{6} + 8 x^{4} - 12 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{2}$ |
$2$ |
$10.5285921036$ |
$13.856406460551018$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$32.9545761188$ |
| 8.0.156950784.2 |
$x^{8} - 2 x^{7} + 11 x^{6} - 8 x^{5} + 31 x^{4} + 2 x^{3} + 29 x^{2} + 20 x + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 29^{2}$ |
$3$ |
$10.5796289461$ |
$24.55104236145523$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$34.1206529467$ |
| 8.0.164480625.1 |
$x^{8} - x^{7} - 4 x^{6} + 5 x^{5} + x^{4} + 7 x^{3} + 2 x^{2} - 41 x + 31$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{4}\cdot 19^{2}$ |
$3$ |
$10.6417816426$ |
$22.21788649167895$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$13.0277878507$ |
| 8.0.169130025.1 |
$x^{8} - x^{7} + 7 x^{6} + x^{5} + 12 x^{4} + 5 x^{3} - 5 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{2}\cdot 17^{4}$ |
$3$ |
$10.6789262968$ |
$15.968719422671311$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$17.1474065936$ |
| 8.0.191102976.3 |
$x^{8} - 6 x^{6} + 18 x^{4} - 36 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}$ |
$2$ |
$10.8432240433$ |
$15.33463450191054$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$38.7136203321$ |
| 8.0.213890625.1 |
$x^{8} - x^{7} + 10 x^{6} - 9 x^{5} + 34 x^{4} - 29 x^{3} + 45 x^{2} - 36 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 13^{2}$ |
$3$ |
$10.9969935084$ |
$20.88140933013045$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$6$ |
$3$ |
$17.3886965747$ |
| 8.0.253605625.1 |
$x^{8} - 3 x^{7} + 10 x^{6} - 15 x^{5} + 23 x^{4} - 15 x^{3} + 10 x^{2} - x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 7^{4}\cdot 13^{2}$ |
$3$ |
$11.2336233977$ |
$21.330729007701542$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$3$ |
$6.41003720329$ |
| 8.0.255488256.6 |
$x^{8} - 2 x^{7} + 5 x^{6} + 4 x^{5} + 7 x^{4} + 20 x^{3} + 17 x^{2} + 56 x + 49$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 37^{2}$ |
$3$ |
$11.2440137422$ |
$27.731400227189784$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$35.3961470619$ |
| 8.0.260112384.10 |
$x^{8} - 2 x^{6} + 26 x^{4} - 70 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$11.269252989$ |
$25.92296279363144$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$35.0681550114$ |
| 8.0.260112384.11 |
$x^{8} - 10 x^{6} + 26 x^{4} - 14 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$11.269252989$ |
$25.92296279363144$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$52.5884814072$ |
| 8.0.279023616.2 |
$x^{8} - 2 x^{7} - 5 x^{6} + 20 x^{5} - 15 x^{4} - 32 x^{3} + 85 x^{2} - 82 x + 31$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 29^{2}$ |
$3$ |
$11.3685511553$ |
$26.38181191654584$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$12.7236701173$ |
| 8.0.333135504.1 |
$x^{8} - 3 x^{7} + 11 x^{6} - 21 x^{5} + 36 x^{4} - 21 x^{3} + 11 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{6}\cdot 13^{4}$ |
$3$ |
$11.6232509648$ |
$16.437759153264928$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$6$ |
$3$ |
$24.0229548498$ |
| 8.4.368640000.2 |
$x^{8} - 6 x^{6} - 4 x^{5} + x^{4} - 8 x^{3} - 12 x^{2} - 4 x + 1$ |
$8$ |
[4,2] |
$2^{16}\cdot 3^{2}\cdot 5^{4}$ |
$3$ |
$11.7713238255$ |
$15.491933384829668$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$5$ |
$17.4567463421$ |
| 8.0.378535936.1 |
$x^{8} - 4 x^{7} + 20 x^{6} - 44 x^{5} + 98 x^{4} - 128 x^{3} + 144 x^{2} - 96 x + 34$ |
$8$ |
[0,4] |
$2^{20}\cdot 19^{2}$ |
$2$ |
$11.8103668949$ |
$24.657656011875904$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$55.0761610673$ |
| 8.0.419430400.2 |
$x^{8} - 12 x^{6} + 48 x^{4} - 60 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{24}\cdot 5^{2}$ |
$2$ |
$11.9627902498$ |
$17.88854381999832$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$49.4656419524$ |
| 8.0.419430400.3 |
$x^{8} - 8 x^{4} + 25$ |
$8$ |
[0,4] |
$2^{24}\cdot 5^{2}$ |
$2$ |
$11.9627902498$ |
$17.88854381999832$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
trivial |
$8$ |
$3$ |
$68.4855111506$ |
| 8.0.428490000.1 |
$x^{8} - 3 x^{7} + 11 x^{6} - 11 x^{5} + 30 x^{4} + x^{3} + 39 x^{2} + 37 x + 19$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 23^{2}$ |
$4$ |
$11.9947882724$ |
$37.14835124201342$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$28.7463987527$ |
| 8.0.428490000.2 |
$x^{8} - 3 x^{7} + 6 x^{6} - 16 x^{5} + 40 x^{4} - 39 x^{3} + 64 x^{2} - 98 x + 49$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 5^{4}\cdot 23^{2}$ |
$4$ |
$11.9947882724$ |
$37.14835124201342$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$21.579940894$ |
| 8.8.432640000.1 |
$x^{8} - 2 x^{7} - 7 x^{6} + 16 x^{5} + 4 x^{4} - 18 x^{3} + 2 x^{2} + 4 x - 1$ |
$8$ |
[8,0] |
$2^{12}\cdot 5^{4}\cdot 13^{2}$ |
$3$ |
$12.0092485618$ |
$22.80350850198276$ |
|
|
✓ |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$7$ |
$28.9890220694$ |
| 8.0.432640000.4 |
$x^{8} - 2 x^{7} + x^{6} + 8 x^{5} - 7 x^{4} + 4 x^{3} + 11 x^{2} - 6 x + 9$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}\cdot 13^{2}$ |
$3$ |
$12.0092485618$ |
$22.80350850198276$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$3$ |
$11.5486485249$ |
| 8.0.433680625.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 12 x^{5} + 20 x^{4} - 20 x^{3} + 23 x^{2} - 21 x + 11$ |
$8$ |
[0,4] |
$5^{4}\cdot 7^{4}\cdot 17^{2}$ |
$3$ |
$12.0128554847$ |
$24.392621835300936$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$3$ |
$18.965077743$ |
| 8.0.437855625.1 |
$x^{8} - x^{7} + 8 x^{6} - 7 x^{5} + 25 x^{4} + 7 x^{3} + 32 x^{2} + 55 x + 19$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$12.0272507837$ |
$28.379633991993764$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$26.8511973661$ |
| 8.4.469805625.1 |
$x^{8} - 5 x^{6} - 4 x^{4} + 15 x^{2} + 9$ |
$8$ |
[4,2] |
$3^{2}\cdot 5^{4}\cdot 17^{4}$ |
$3$ |
$12.1336028715$ |
$15.968719422671311$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$2$ |
$5$ |
$18.2305095514$ |
| 8.0.524226816.2 |
$x^{8} - 2 x^{7} - 7 x^{6} + 4 x^{5} + 43 x^{4} + 8 x^{3} - 139 x^{2} - 16 x + 157$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 53^{2}$ |
$3$ |
$12.3009854302$ |
$33.190123736042416$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$35.0938639562$ |
| 8.0.558140625.1 |
$x^{8} - x^{7} - 10 x^{6} + 11 x^{5} + 34 x^{4} - 29 x^{3} - 55 x^{2} + 4 x + 76$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{6}\cdot 7^{2}$ |
$3$ |
$12.3977522757$ |
$20.165893269373882$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$6$ |
$3$ |
$31.3606243426$ |
| 8.0.595360000.5 |
$x^{8} + 9 x^{6} - 4 x^{5} + 29 x^{4} - 18 x^{3} + 39 x^{2} - 20 x + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 61^{2}$ |
$3$ |
$12.4981996111$ |
$34.92849839314596$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$4$ |
$3$ |
$30.6856630308$ |
| 8.0.646430625.1 |
$x^{8} - x^{7} + 7 x^{6} - 6 x^{5} + 13 x^{4} + 4 x^{3} + 30 x^{2} + 84 x + 49$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 113^{2}$ |
$3$ |
$12.6274378712$ |
$41.1703777004778$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$6$ |
$3$ |
$26.0898836625$ |
| 8.0.676000000.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 10 x^{5} - 14 x^{4} + 10 x^{3} + 33 x^{2} - 36 x + 41$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 13^{2}$ |
$3$ |
$12.6982343247$ |
$24.111774595619156$ |
|
|
|
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$4$ |
$3$ |
$16.2298586213$ |
| 8.0.694427904.6 |
$x^{8} - 4 x^{7} - x^{6} + 8 x^{5} + 31 x^{4} - 50 x^{3} - 43 x^{2} + 58 x + 97$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 61^{2}$ |
$3$ |
$12.7409964721$ |
$35.60703850561597$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
trivial |
$12$ |
$3$ |
$40.7339437812$ |
