| 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 |
| 8.0.4102893.1 |
$x^{8} - 3 x^{7} + 3 x^{6} - 3 x^{5} + 5 x^{4} - 6 x^{3} + 6 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 37^{3}$ |
$2$ |
$6.70866759738$ |
$10.535653752852738$ |
|
|
✓ |
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$2.02888107198$ |
| 8.2.4286875.1 |
$x^{8} - x^{7} + x^{5} - 2 x^{4} - x^{3} + 2 x^{2} + 2 x - 1$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 19^{3}$ |
$2$ |
$6.74555367758$ |
$9.746794344808963$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$0.831403828897$ |
| 8.0.16290125.1 |
$x^{8} - x^{7} - x^{6} + 4 x^{5} + x^{4} - 4 x^{3} - x^{2} + x + 1$ |
$8$ |
[0,4] |
$5^{3}\cdot 19^{4}$ |
$2$ |
$7.97059150708$ |
$9.746794344808963$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$1.7277294231$ |
| 8.0.17643776.1 |
$x^{8} + 3 x^{6} - 2 x^{3} - x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 41^{3}$ |
$2$ |
$8.05052016066$ |
$12.806248474865697$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$4.07400798672$ |
| 8.0.18385461.1 |
$x^{8} + 5 x^{4} - 9 x^{3} + 6 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 61^{3}$ |
$2$ |
$8.09206412202$ |
$13.527749258468683$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$5.25530723012$ |
| 8.0.20123648.2 |
$x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{3}$ |
$2$ |
$8.18395700311$ |
$11.661903789690601$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$4.51285164721$ |
| 8.2.50602347.1 |
$x^{8} - x^{7} + x^{6} - 6 x^{5} + 9 x^{4} - 6 x^{3} + x^{2} - x + 1$ |
$8$ |
[2,3] |
$-\,3^{3}\cdot 37^{4}$ |
$2$ |
$9.18377706106$ |
$10.535653752852738$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$5.05552497857$ |
| 8.2.85525504.1 |
$x^{8} - x^{4} - 4$ |
$8$ |
[2,3] |
$-\,2^{10}\cdot 17^{4}$ |
$2$ |
$9.80645309178$ |
$11.661903789690601$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$9.45312696934$ |
| 8.2.122023936.2 |
$x^{8} - 2 x^{7} - 3 x^{6} + 6 x^{5} + 6 x^{4} - 6 x^{3} - 5 x^{2} - 2 x + 1$ |
$8$ |
[2,3] |
$-\,2^{12}\cdot 31^{3}$ |
$2$ |
$10.2519299178$ |
$15.748015748023622$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$8.12751463084$ |
| 8.2.128361875.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 10 x^{5} + 7 x^{4} + x^{3} - 9 x^{2} + 8 x - 1$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 59^{3}$ |
$2$ |
$10.3170255611$ |
$17.175564037317667$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$7.18947143168$ |
| 8.0.134217728.1 |
$x^{8} - 4 x^{6} + 10 x^{4} - 8 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{27}$ |
$1$ |
$10.3747164372$ |
$12.337686603263526$ |
|
|
✓ |
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$19.6078940119$ |
| 8.2.180848704.1 |
$x^{8} - 3 x^{7} + x^{6} + 4 x^{5} - 4 x^{4} + 4 x^{3} + x^{2} - 3 x + 1$ |
$8$ |
[2,3] |
$-\,2^{6}\cdot 41^{4}$ |
$2$ |
$10.7687284354$ |
$12.806248474865697$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$16.9443171642$ |
| 8.0.190563597.3 |
$x^{8} - x^{7} + 2 x^{6} - 6 x^{5} + 17 x^{4} + 3 x^{3} - 7 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{3}\cdot 19^{3}$ |
$3$ |
$10.839393751$ |
$19.974984355438178$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$16.9080915061$ |
| 8.0.190563597.4 |
$x^{8} - 3 x^{7} + 7 x^{6} - 6 x^{5} + x^{4} + 6 x^{3} - 3 x^{2} - 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{3}\cdot 19^{3}$ |
$3$ |
$10.839393751$ |
$19.974984355438178$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$50.7926829502$ |
| 8.2.268435456.1 |
$x^{8} - 6 x^{4} - 8 x^{2} - 1$ |
$8$ |
[2,3] |
$-\,2^{28}$ |
$1$ |
$11.313708499$ |
$12.337686603263526$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$17.2818798792$ |
| 8.2.308149375.1 |
$x^{8} - x^{7} + 4 x^{6} - 7 x^{5} + 8 x^{4} - 11 x^{3} + 11 x^{2} - 2 x - 4$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 79^{3}$ |
$2$ |
$11.5105257676$ |
$19.87460691435179$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$18.8834568302$ |
| 8.0.313461333.1 |
$x^{8} - 3 x^{7} + 4 x^{6} + x^{4} + 3 x^{3} - 3 x^{2} + 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 157^{3}$ |
$2$ |
$11.5351433776$ |
$21.702534414210707$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$71.6095771145$ |
| 8.0.321978368.4 |
$x^{8} - 4 x^{6} + 11 x^{4} - 20 x^{2} + 17$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$16.492422502470642$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$20.282622579$ |
| 8.2.347236875.1 |
$x^{8} - 3 x^{7} + 9 x^{6} - 19 x^{5} + 19 x^{4} - 3 x^{3} - 14 x^{2} + 10 x - 5$ |
$8$ |
[2,3] |
$-\,3^{4}\cdot 5^{4}\cdot 19^{3}$ |
$3$ |
$11.6836416948$ |
$16.881943016134134$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$16.3440776664$ |
| 8.2.347501687.1 |
$x^{8} - x^{7} - 5 x^{6} + 6 x^{5} + 2 x^{4} - 10 x^{3} - 7 x^{2} - x - 1$ |
$8$ |
[2,3] |
$-\,13^{4}\cdot 23^{3}$ |
$2$ |
$11.684755105$ |
$17.291616465790582$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$20.5349656678$ |
| 8.0.357453677.2 |
$x^{8} - 3 x^{7} + 4 x^{6} - 6 x^{5} + 8 x^{4} - 2 x^{3} + 9 x^{2} + 3 x + 2$ |
$8$ |
[0,4] |
$7^{4}\cdot 53^{3}$ |
$2$ |
$11.7260696945$ |
$19.261360284258224$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$37.1686299445$ |
| 8.0.369381632.1 |
$x^{8} - 2 x^{7} + 7 x^{6} - 10 x^{5} + 3 x^{2} + 4 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 113^{3}$ |
$2$ |
$11.7742814252$ |
$21.2602916254693$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$27.6764764112$ |
| 8.2.373837707.1 |
$x^{8} - 2 x^{6} - 7 x^{5} + 10 x^{4} + 7 x^{3} - 12 x^{2} - x + 5$ |
$8$ |
[2,3] |
$-\,3^{3}\cdot 61^{4}$ |
$2$ |
$11.7919434562$ |
$13.527749258468683$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$19.2565937702$ |
| 8.0.421654016.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 14 x^{5} + 21 x^{4} - 21 x^{3} + 21 x^{2} - 10 x + 2$ |
$8$ |
[0,4] |
$2^{9}\cdot 7^{7}$ |
$2$ |
$11.9706995351$ |
$15.524076653923595$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$21.4874875952$ |
| 8.2.425259008.1 |
$x^{8} - 2 x^{7} - x^{6} + 2 x^{5} + 6 x^{4} - 14 x^{3} + 9 x^{2} - 6 x + 1$ |
$8$ |
[2,3] |
$-\,2^{12}\cdot 47^{3}$ |
$2$ |
$11.9834450902$ |
$19.390719429665317$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$19.1084119867$ |
| 8.0.472842752.1 |
$x^{8} - 3 x^{7} + 3 x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 3 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$2^{9}\cdot 31^{4}$ |
$2$ |
$12.1433801826$ |
$15.748015748023622$ |
|
|
|
$D_{8}$ (as 8T6) |
$[3]$ |
$2$ |
$3$ |
$9.22141842067$ |
| 8.0.582313617.2 |
$x^{8} - 3 x^{7} + 6 x^{6} - 15 x^{5} + 29 x^{4} - 30 x^{3} + 24 x^{2} - 24 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 193^{3}$ |
$2$ |
$12.4636320189$ |
$24.06241883103193$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$6$ |
$3$ |
$68.4258233412$ |
| 8.2.606436875.1 |
$x^{8} + x^{6} - 3 x^{5} + 9 x^{4} + 6 x^{3} + 16 x^{2} - 5$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$12.5270323843$ |
$16.90527678711191$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$24.5134587485$ |
| 8.2.606436875.2 |
$x^{8} - x^{7} - x^{6} + 8 x^{5} - 2 x^{4} - 11 x^{3} + 11 x^{2} + 13 x + 1$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$12.5270323843$ |
$16.90527678711191$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$16.4184768178$ |
| 8.0.614810677.1 |
$x^{8} - x^{7} + x^{6} - x^{4} - x^{3} + 7 x^{2} + 2 x + 8$ |
$8$ |
[0,4] |
$13^{3}\cdot 23^{4}$ |
$2$ |
$12.5485248522$ |
$17.291616465790582$ |
|
|
|
$D_{8}$ (as 8T6) |
$[3]$ |
$2$ |
$3$ |
$17.1874772932$ |
| 8.0.643938125.1 |
$x^{8} - 2 x^{7} + 8 x^{6} - 9 x^{5} + 18 x^{4} - 17 x^{3} + 6 x^{2} - 5 x + 5$ |
$8$ |
[0,4] |
$5^{4}\cdot 101^{3}$ |
$2$ |
$12.6213414879$ |
$22.47220505424423$ |
✓ |
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$16.7289510053$ |
| 8.0.658266368.1 |
$x^{8} - 4 x^{7} + 12 x^{6} - 18 x^{5} + 17 x^{4} - 6 x^{3} + 2 x^{2} + 12 x + 4$ |
$8$ |
[0,4] |
$2^{8}\cdot 137^{3}$ |
$2$ |
$12.6561090537$ |
$23.40939982143925$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$4$ |
$3$ |
$38.7298997714$ |
| 8.0.741610573.1 |
$x^{8} - x^{7} - x^{6} - x^{5} + 9 x^{4} - 15 x^{3} + 20 x^{2} - 8 x + 1$ |
$8$ |
[0,4] |
$11^{4}\cdot 37^{3}$ |
$2$ |
$12.8461204293$ |
$20.174241001832016$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$15.9941542144$ |
| 8.0.843308032.1 |
$x^{8} - 4 x^{7} + 7 x^{6} - 14 x^{4} + 14 x^{3} + 7 x^{2} - 18 x + 9$ |
$8$ |
[0,4] |
$2^{10}\cdot 7^{7}$ |
$2$ |
$13.0541404084$ |
$15.524076653923595$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$33.7643922139$ |
| 8.0.1050340608.4 |
$x^{8} + 8 x^{6} + 18 x^{4} + 17 x^{2} + 37$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 37^{3}$ |
$3$ |
$13.4173351948$ |
$21.071307505705477$ |
|
|
|
$D_{8}$ (as 8T6) |
$[2]$ |
$6$ |
$3$ |
$66.5492709743$ |
| 8.0.1096135733.1 |
$x^{8} - 2 x^{7} + 7 x^{2} - 2 x + 4$ |
$8$ |
[0,4] |
$7^{7}\cdot 11^{3}$ |
$2$ |
$13.4891021018$ |
$18.203593448567553$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$77.5391266455$ |
| 8.2.1097440000.5 |
$x^{8} + 5 x^{6} + 2 x^{4} - 20 x^{2} - 19$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 5^{4}\cdot 19^{3}$ |
$3$ |
$13.4911073552$ |
$19.493588689617926$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$17.5387650122$ |
| 8.0.1124864000.1 |
$x^{8} - 2 x^{7} - 6 x^{6} + 14 x^{5} + 11 x^{4} - 46 x^{3} + 44 x^{2} - 12 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{3}\cdot 13^{3}$ |
$3$ |
$13.532794976$ |
$22.80350850198276$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$4$ |
$3$ |
$32.1335288983$ |
| 8.0.1124864000.2 |
$x^{8} - 4 x^{7} + 12 x^{6} - 18 x^{5} + 19 x^{4} - 10 x^{3} + 6 x^{2} + 6 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{3}\cdot 13^{3}$ |
$3$ |
$13.532794976$ |
$22.80350850198276$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$4$ |
$3$ |
$19.8901652499$ |
| 8.0.1258815488.2 |
$x^{8} - 4 x^{6} + 5 x^{4} - 2 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{19}\cdot 7^{4}$ |
$2$ |
$13.7244598078$ |
$17.798422345016238$ |
|
|
✓ |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$41.9007892479$ |
| 8.0.1258815488.3 |
$x^{8} + 4 x^{6} + 5 x^{4} + 2 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{19}\cdot 7^{4}$ |
$2$ |
$13.7244598078$ |
$17.798422345016238$ |
|
|
✓ |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$63.0005010115$ |
| 8.0.1319500125.1 |
$x^{8} - x^{7} + 3 x^{5} + 9 x^{4} + 2 x^{3} + 8 x^{2} - 4 x + 7$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{3}\cdot 19^{4}$ |
$3$ |
$13.8054694566$ |
$16.881943016134134$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$2$ |
$3$ |
$16.9822070191$ |
| 8.0.1334161125.1 |
$x^{8} - x^{7} + 3 x^{6} - 7 x^{5} + 10 x^{4} - 6 x^{3} + 15 x^{2} - 9 x + 3$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$13.824551008$ |
$16.90527678711191$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$2$ |
$3$ |
$17.0595109709$ |
| 8.0.1334161125.2 |
$x^{8} - 2 x^{7} + 6 x^{6} + x^{5} + 4 x^{4} + 3 x^{3} + 6 x^{2} + 3 x + 3$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$13.824551008$ |
$16.90527678711191$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$2$ |
$3$ |
$25.4705490098$ |
| 8.2.1368408064.1 |
$x^{8} + x^{4} - 4$ |
$8$ |
[2,3] |
$-\,2^{14}\cdot 17^{4}$ |
$2$ |
$13.8684189612$ |
$16.492422502470642$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$42.4862640075$ |
| 8.0.1429145856.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 2 x^{5} + 21 x^{4} - 30 x^{3} + 75 x^{2} - 62 x + 58$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 41^{3}$ |
$3$ |
$13.9439099456$ |
$22.181073012818835$ |
|
|
|
$D_{8}$ (as 8T6) |
$[2]$ |
$4$ |
$3$ |
$152.32463607$ |
| 8.2.1438646272.4 |
$x^{8} - 4 x^{7} + 4 x^{6} - 8 x^{5} + 14 x^{4} - 8 x^{3} + 4 x^{2} - 8 x - 2$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 7^{3}$ |
$2$ |
$13.9554631106$ |
$17.798422345016238$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$55.5269775606$ |
| 8.2.1438646272.5 |
$x^{8} - 4 x^{7} + 8 x^{6} - 22 x^{4} + 48 x^{3} - 44 x^{2} + 16 x - 2$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 7^{3}$ |
$2$ |
$13.9554631106$ |
$17.798422345016238$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$4$ |
$36.9302489183$ |
| 8.0.1514670125.1 |
$x^{8} - 4 x^{7} + 5 x^{6} - x^{5} + 11 x^{4} - 25 x^{3} + 14 x^{2} - x + 1$ |
$8$ |
[0,4] |
$5^{3}\cdot 59^{4}$ |
$2$ |
$14.0455825784$ |
$17.175564037317667$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[3]$ |
$2$ |
$3$ |
$14.9403465528$ |
| 8.0.1593413632.1 |
$x^{8} - 8 x^{5} - x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 73^{3}$ |
$2$ |
$14.1348455071$ |
$24.166091947189145$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$2$ |
$3$ |
$163.699695598$ |
