| 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 |
| 8.2.107171875.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + x^{4} + 5 x^{3} - 7 x^{2} - 6 x + 1$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 19^{3}$ |
$2$ |
$10.0869554704$ |
$14.574857044323968$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$6.79191421448$ |
| 8.2.143327232.1 |
$x^{8} + 6 x^{4} - 3$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{7}$ |
$2$ |
$10.4602265145$ |
$10.460226514460828$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$14.5416008641$ |
| 8.2.257298363.1 |
$x^{8} - 2 x^{7} + x^{6} - 5 x^{5} + 7 x^{4} - 2 x^{3} + x^{2} - 5 x + 1$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 7^{6}$ |
$2$ |
$11.253940842$ |
$11.253940841985125$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$14.5040303146$ |
| 8.2.268435456.2 |
$x^{8} - 2 x^{4} - 1$ |
$8$ |
[2,3] |
$-\,2^{28}$ |
$1$ |
$11.313708499$ |
$12.337686603263526$ |
|
|
✓ |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$17.0368939674$ |
| 8.2.573308928.1 |
$x^{8} - 6 x^{4} - 3$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 3^{7}$ |
$2$ |
$12.4393757955$ |
$12.43937579553693$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$31.8596637081$ |
| 8.2.2147483648.2 |
$x^{8} - 2$ |
$8$ |
[2,3] |
$-\,2^{31}$ |
$1$ |
$14.6720646913$ |
$16.0$ |
|
|
✓ |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$49.1721882065$ |
| 8.2.3209046875.2 |
$x^{8} - x^{7} - 4 x^{6} + 14 x^{5} + 6 x^{4} - 15 x^{3} + 5 x^{2} + 10 x - 5$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 59^{3}$ |
$2$ |
$15.4275515986$ |
$25.683458749990002$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$37.9441053114$ |
| 8.2.5754585088.2 |
$x^{8} + 4 x^{6} + 4 x^{4} - 4 x^{2} - 7$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 7^{3}$ |
$2$ |
$16.5959360243$ |
$21.166010488516726$ |
|
|
✓ |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$117.703504989$ |
| 8.2.5754585088.3 |
$x^{8} - 4 x^{6} + 4 x^{4} + 4 x^{2} - 7$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 7^{3}$ |
$2$ |
$16.5959360243$ |
$21.166010488516726$ |
|
|
✓ |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$72.2696726962$ |
| 8.2.7703734375.1 |
$x^{8} - 2 x^{7} - x^{6} + 2 x^{5} - 4 x^{4} - 20 x^{3} - 30 x^{2} - 20 x - 5$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 79^{3}$ |
$2$ |
$17.2122506778$ |
$29.719469226626792$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$54.3587636703$ |
| 8.2.8680921875.1 |
$x^{8} - 3 x^{7} - x^{6} - 7 x^{5} + 21 x^{4} + 80 x^{3} - 45 x^{2} - 190 x - 95$ |
$8$ |
[2,3] |
$-\,3^{4}\cdot 5^{6}\cdot 19^{3}$ |
$3$ |
$17.4711193685$ |
$25.24439291382227$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$32.4987605988$ |
| 8.2.14206147659.1 |
$x^{8} - 2 x^{7} - x^{6} - 5 x^{5} + 16 x^{4} - x^{3} - 4 x^{2} - 28 x + 16$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 11^{7}$ |
$2$ |
$18.5805917232$ |
$18.580591723225652$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$453.969657745$ |
| 8.2.15160921875.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 39 x^{4} + 105 x^{3} - 137 x^{2} + 96 x - 29$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 5^{6}\cdot 11^{3}$ |
$3$ |
$18.7322826082$ |
$25.279285039815186$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$44.1424347177$ |
| 8.2.15160921875.2 |
$x^{8} - x^{7} - 4 x^{6} - 16 x^{5} - 14 x^{4} - 5 x^{3} + 5 x^{2} + 10 x - 5$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 5^{6}\cdot 11^{3}$ |
$3$ |
$18.7322826082$ |
$25.279285039815186$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$59.767275922$ |
| 8.8.16098453125.1 |
$x^{8} - 3 x^{7} - 8 x^{6} + 35 x^{5} - 19 x^{4} - 45 x^{3} + 53 x^{2} - 14 x + 1$ |
$8$ |
[8,0] |
$5^{6}\cdot 101^{3}$ |
$2$ |
$18.8733076114$ |
$33.60378443921746$ |
|
|
✓ |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$7$ |
$297.817403022$ |
| 8.2.21743271936.2 |
$x^{8} - 18 x^{4} - 81$ |
$8$ |
[2,3] |
$-\,2^{28}\cdot 3^{4}$ |
$2$ |
$19.5959179423$ |
$21.36950004471431$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$148.574136203$ |
| 8.2.24716870656.1 |
$x^{8} - 4 x^{7} + 11 x^{6} - 2 x^{5} - 15 x^{4} + 6 x^{3} - 54 x^{2} - 96 x - 38$ |
$8$ |
[2,3] |
$-\,2^{10}\cdot 17^{6}$ |
$2$ |
$19.9124264933$ |
$23.679999262753405$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$90.5528158363$ |
| 8.2.26261675072.2 |
$x^{8} - 3 x^{7} + 5 x^{6} + 9 x^{5} - 26 x^{4} + 18 x^{3} + 20 x^{2} - 24 x + 16$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 17^{7}$ |
$2$ |
$20.063897614$ |
$23.86012979730628$ |
|
|
|
$QD_{16}$ (as 8T8) |
$[4]$ |
$2$ |
$4$ |
$447.727402788$ |
| 8.2.27436000000.3 |
$x^{8} - 5 x^{6} - 35 x^{4} + 275 x^{2} - 475$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 5^{6}\cdot 19^{3}$ |
$3$ |
$20.1739109409$ |
$29.149714088647936$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$48.666090797$ |
| 8.2.36691771392.3 |
$x^{8} - 12 x^{4} - 12$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 3^{7}$ |
$2$ |
$20.9204530289$ |
$20.920453028921656$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$388.9771078$ |
| 8.2.36691771392.4 |
$x^{8} + 12 x^{4} - 12$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 3^{7}$ |
$2$ |
$20.9204530289$ |
$20.920453028921656$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$238.793786001$ |
| 8.2.41962796875.1 |
$x^{8} - x^{7} + x^{6} - 21 x^{5} - 9 x^{4} + 5 x^{3} + 10 x - 5$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 139^{3}$ |
$2$ |
$21.2744358964$ |
$39.42165958407071$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$95.7145574713$ |
| 8.2.58727785103.1 |
$x^{8} - x^{7} - 3 x^{6} - 2 x^{5} + 9 x^{4} + 22 x^{3} - 12 x^{2} - 34 x - 23$ |
$8$ |
[2,3] |
$-\,13^{6}\cdot 23^{3}$ |
$2$ |
$22.1873509412$ |
$32.8338214553794$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$139.066436843$ |
| 8.2.63589515264.1 |
$x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} + 4 x^{4} - 16 x^{3} - 2 x^{2} + 8 x - 23$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{6}\cdot 11^{3}$ |
$3$ |
$22.4090367741$ |
$30.241078459545175$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$147.010268954$ |
| 8.2.63589515264.2 |
$x^{8} - 4 x^{7} + 10 x^{6} - 4 x^{5} - 20 x^{4} - 4 x^{3} + 40 x^{2} - 52 x + 22$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{6}\cdot 11^{3}$ |
$3$ |
$22.4090367741$ |
$30.241078459545175$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$167.487578545$ |
| 8.2.65536000000.1 |
$x^{8} - 10 x^{4} - 100$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}$ |
$2$ |
$22.4936530076$ |
$26.74961219905688$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$252.251816204$ |
| 8.2.65536000000.2 |
$x^{8} + 10 x^{4} - 100$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}$ |
$2$ |
$22.4936530076$ |
$26.74961219905688$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$229.735788956$ |
| 8.2.65868380928.1 |
$x^{8} - 42 x^{4} - 147 x^{2} - 147$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 3^{7}\cdot 7^{6}$ |
$3$ |
$22.507881684$ |
$22.50788168397025$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$136.572708011$ |
| 8.2.69274613043.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 8 x^{5} - 33 x^{4} + 75 x^{3} - 126 x^{2} + 99 x - 27$ |
$8$ |
[2,3] |
$-\,3^{3}\cdot 37^{6}$ |
$2$ |
$22.6501855225$ |
$25.9843537703577$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$790.820751811$ |
| 8.2.89579520000.3 |
$x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} - 20 x^{4} + 32 x^{3} - 212 x^{2} - 196 x - 74$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{7}\cdot 5^{4}$ |
$3$ |
$23.3897775464$ |
$23.3897775463801$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$229.918263427$ |
| 8.2.89614671875.1 |
$x^{8} + 4 x^{6} - 25 x^{5} + 16 x^{4} - 55 x^{3} + 179 x^{2} - 80 x - 29$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 179^{3}$ |
$2$ |
$23.3909246465$ |
$44.735677482992386$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$212.523955733$ |
| 8.8.92652203125.1 |
$x^{8} - 3 x^{7} - 11 x^{6} + 38 x^{5} + 11 x^{4} - 115 x^{3} + 95 x^{2} - 10 x - 5$ |
$8$ |
[8,0] |
$5^{6}\cdot 181^{3}$ |
$2$ |
$23.4885911679$ |
$44.98490324139099$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$7$ |
$683.588849591$ |
| 8.2.97844723712.4 |
$x^{8} - 12 x^{6} + 18 x^{4} - 18$ |
$8$ |
[2,3] |
$-\,2^{27}\cdot 3^{6}$ |
$2$ |
$23.6492393325$ |
$28.12384367863563$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$555.362918561$ |
| 8.2.97844723712.5 |
$x^{8} - 12 x^{6} + 54 x^{4} - 72 x^{2} - 18$ |
$8$ |
[2,3] |
$-\,2^{27}\cdot 3^{6}$ |
$2$ |
$23.6492393325$ |
$28.12384367863563$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$264.922671515$ |
| 8.2.102889341747.1 |
$x^{8} - 2 x^{7} + 4 x^{6} + 10 x^{5} - 26 x^{4} - 8 x^{3} + 169 x^{2} + 136 x - 356$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 19^{6}$ |
$2$ |
$23.7983199288$ |
$23.79831992881347$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$1607.97747874$ |
| 8.8.104963309568.1 |
$x^{8} - 4 x^{7} - 10 x^{6} + 32 x^{5} + 16 x^{4} - 68 x^{3} + 14 x^{2} + 28 x - 11$ |
$8$ |
[8,0] |
$2^{16}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$23.8577613212$ |
$32.875518306529855$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$7$ |
$1175.00623379$ |
| 8.0.104963309568.1 |
$x^{8} - 4 x^{7} + 14 x^{6} - 16 x^{5} + 52 x^{4} - 80 x^{3} + 92 x^{2} - 140 x + 118$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$23.8577613212$ |
$32.875518306529855$ |
✓ |
|
? |
$QD_{16}$ (as 8T8) |
$[2, 2]$ |
$2$ |
$3$ |
$45.8849989593$ |
| 8.2.123134359375.1 |
$x^{8} - x^{7} + 3 x^{6} - 20 x^{5} + x^{4} + 20 x^{3} + 132 x^{2} - 262 x + 121$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 199^{3}$ |
$2$ |
$24.3387016426$ |
$47.16871460631815$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$239.786264622$ |
| 8.2.124952510464.2 |
$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} - 124$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 31^{3}$ |
$2$ |
$24.3833360014$ |
$37.455304749449176$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$595.966172184$ |
| 8.2.124952510464.3 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} - 124$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 31^{3}$ |
$2$ |
$24.3833360014$ |
$37.455304749449176$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$254.059519483$ |
| 8.2.160811476875.1 |
$x^{8} - 2 x^{7} + x^{6} - 26 x^{5} - 14 x^{4} + 145 x^{3} + 169 x^{2} - 320 x - 335$ |
$8$ |
[2,3] |
$-\,3^{7}\cdot 5^{4}\cdot 7^{6}$ |
$3$ |
$25.1645767374$ |
$25.16457673743996$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2, 2]$ |
$2$ |
$4$ |
$100.900935051$ |
| 8.2.167772160000.4 |
$x^{8} - 50 x^{4} - 625$ |
$8$ |
[2,3] |
$-\,2^{28}\cdot 5^{4}$ |
$2$ |
$25.2982212813$ |
$27.587905929985723$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$256.759217366$ |
| 8.2.173946175488.4 |
$x^{8} - 162$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 3^{4}$ |
$2$ |
$25.4127614972$ |
$27.712812921102035$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$542.965430586$ |
| 8.2.204128387072.1 |
$x^{8} - 4 x^{6} - 28 x^{4} - 44 x^{2} - 23$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 23^{3}$ |
$2$ |
$25.9261437983$ |
$38.36665218650175$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$405.809364686$ |
| 8.2.204128387072.4 |
$x^{8} + 4 x^{6} - 28 x^{4} + 44 x^{2} - 23$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 23^{3}$ |
$2$ |
$25.9261437983$ |
$38.36665218650175$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[3]$ |
$2$ |
$4$ |
$211.206492089$ |
| 8.2.208176611328.1 |
$x^{8} - 4 x^{7} + 8 x^{6} + 4 x^{5} - 30 x^{4} + 44 x^{3} - 96 x^{2} + 276 x - 227$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{3}\cdot 7^{6}$ |
$3$ |
$25.9898630983$ |
$29.815640870484444$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$356.443562103$ |
| 8.2.208176611328.2 |
$x^{8} - 4 x^{7} + 8 x^{6} + 4 x^{5} - 72 x^{4} + 240 x^{3} - 432 x^{2} + 360 x - 108$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 3^{3}\cdot 7^{6}$ |
$3$ |
$25.9898630983$ |
$29.815640870484444$ |
|
|
|
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$1175.39154558$ |
| 8.2.210093400576.2 |
$x^{8} - 17 x^{6} + 17 x^{4} + 17 x^{2} - 34$ |
$8$ |
[2,3] |
$-\,2^{9}\cdot 17^{7}$ |
$2$ |
$26.0196560464$ |
$33.74331915933294$ |
|
|
|
$QD_{16}$ (as 8T8) |
$[4]$ |
$2$ |
$4$ |
$217.459624065$ |
| 8.2.213311234375.1 |
$x^{8} - 3 x^{7} - x^{6} - 12 x^{5} - 59 x^{4} - 60 x^{3} - 60 x^{2} - 30 x - 5$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 239^{3}$ |
$2$ |
$26.0691407041$ |
$51.6923711306828$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$2$ |
$4$ |
$248.890865982$ |
| 8.2.254358061056.1 |
$x^{8} - 4 x^{7} + 14 x^{6} - 16 x^{5} - 8 x^{4} + 52 x^{3} - 52 x^{2} + 40 x - 26$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 3^{6}\cdot 11^{3}$ |
$3$ |
$26.6489859721$ |
$35.96290566944665$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$2$ |
$4$ |
$185.581769671$ |
