| 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 |
| 8.2.7486875.1 |
$x^{8} - 2 x^{7} - x^{6} + 6 x^{5} - 2 x^{4} - 5 x^{3} + 3 x^{2} + 2 x - 1$ |
$8$ |
[2,3] |
$-\,3^{2}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$7.23248551921$ |
$23.393227447460962$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$1.21226030586$ |
| 8.0.18753525.1 |
$x^{8} - 3 x^{7} + 6 x^{5} - 9 x^{3} + 6 x^{2} - 3 x + 3$ |
$8$ |
[0,4] |
$3^{7}\cdot 5^{2}\cdot 7^{3}$ |
$3$ |
$8.11213863316$ |
$25.16457673743996$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$6.35067346522$ |
| 8.2.22478848.1 |
$x^{8} - 2 x^{6} - x^{4} - 8 x^{3} - 8 x^{2} - 4 x - 1$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 7^{3}$ |
$2$ |
$8.29796801214$ |
$20.471092479852693$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$2.72428328845$ |
| 8.2.37786203.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 5 x^{4} - 3 x^{3} + x^{2} - 3 x - 1$ |
$8$ |
[2,3] |
$-\,3^{3}\cdot 7^{2}\cdot 13^{4}$ |
$3$ |
$8.85455330317$ |
$21.745111415357325$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$4.13180616592$ |
| 8.0.45556992.1 |
$x^{8} - 7 x^{4} + 13$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$9.06398921581$ |
$39.88601369203181$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$9.0540399082$ |
| 8.0.51429573.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - x^{5} + 7 x^{4} + 21 x^{2} + 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 17^{2}$ |
$3$ |
$9.20241076494$ |
$48.892540286148204$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$9.74521666059$ |
| 8.2.67381875.1 |
$x^{8} - x^{7} - 5 x^{6} + 9 x^{5} + x^{4} - 8 x^{3} + 3 x + 1$ |
$8$ |
[2,3] |
$-\,3^{4}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$9.51848624089$ |
$23.393227447460962$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$5.48804517253$ |
| 8.0.78675968.1 |
$x^{8} + x^{4} + 2$ |
$8$ |
[0,4] |
$2^{15}\cdot 7^{4}$ |
$2$ |
$9.70465859824$ |
$23.081698107401436$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$3$ |
$6.97751430231$ |
| 8.0.80494592.1 |
$x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 2 x^{4} - 2 x^{3} + x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 17^{3}$ |
$2$ |
$9.73241989697$ |
$33.48857611437076$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$3$ |
$7.63635280528$ |
| 8.2.89915392.1 |
$x^{8} + 2 x^{6} - 4 x^{5} - 4 x^{3} + 2 x^{2} + 1$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 7^{3}$ |
$2$ |
$9.8680026001$ |
$20.471092479852693$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$9.71299304082$ |
| 8.0.94139253.1 |
$x^{8} - x^{7} + 6 x^{6} + 9 x^{4} + 5 x^{3} + 29 x^{2} + 23 x + 19$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 23^{2}$ |
$3$ |
$9.92479039407$ |
$56.86984696736222$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$11.5614305416$ |
| 8.0.149661837.1 |
$x^{8} - 2 x^{7} + 12 x^{6} - 17 x^{5} + 50 x^{4} - 49 x^{3} + 85 x^{2} - 42 x + 43$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 29^{2}$ |
$3$ |
$10.5169275943$ |
$63.85826878760316$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$20.3431203334$ |
| 8.2.163840000.1 |
$x^{8} + 2 x^{6} - 2 x^{4} - 8 x^{2} - 4$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 5^{4}$ |
$2$ |
$10.6365917939$ |
$20.371270394561137$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$8.80059213993$ |
| 8.2.163840000.2 |
$x^{8} - 2 x^{6} - 2 x^{4} + 8 x^{2} - 4$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 5^{4}$ |
$2$ |
$10.6365917939$ |
$20.371270394561137$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$7.8694086544$ |
| 8.2.169996288.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 6 x^{5} + 3 x^{4} + 4 x^{3} - 10 x^{2} + 16 x - 4$ |
$8$ |
[2,3] |
$-\,2^{12}\cdot 7^{3}\cdot 11^{2}$ |
$3$ |
$10.685748042$ |
$40.37056858177486$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$10.4759482119$ |
| 8.2.187171875.1 |
$x^{8} - x^{7} + 4 x^{6} - 2 x^{5} - x^{4} + 11 x^{3} - 19 x^{2} + 27 x - 9$ |
$8$ |
[2,3] |
$-\,3^{2}\cdot 5^{6}\cdot 11^{3}$ |
$3$ |
$10.8150884064$ |
$34.98103415239156$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$8.44394434842$ |
| 8.0.190563597.1 |
$x^{8} - 3 x^{7} + 3 x^{6} - 3 x^{5} - x^{4} + 6 x^{3} + 6 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{3}\cdot 19^{3}$ |
$3$ |
$10.839393751$ |
$41.703724995169544$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$23.0819036353$ |
| 8.0.190563597.2 |
$x^{8} - 4 x^{7} + 11 x^{6} - 19 x^{5} + 20 x^{4} - 13 x^{3} - 2 x^{2} + 6 x + 3$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{3}\cdot 19^{3}$ |
$3$ |
$10.839393751$ |
$41.703724995169544$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$35.6009335362$ |
| 8.0.192036096.1 |
$x^{8} + 9 x^{4} + 21$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$10.8498281271$ |
$37.85359404601065$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$21.3133303867$ |
| 8.0.192036096.2 |
$x^{8} - 9 x^{6} + 30 x^{4} - 42 x^{2} + 21$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$10.8498281271$ |
$37.85359404601065$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$23.9639546164$ |
| 8.2.197413632.1 |
$x^{8} + x^{4} - 3$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$10.8873489409$ |
$27.64490549356882$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$11.0978087659$ |
| 8.2.197413632.2 |
$x^{8} - x^{6} - 2 x^{4} + 6 x^{2} - 3$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$10.8873489409$ |
$27.64490549356882$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$10.5819927239$ |
| 8.2.210056875.1 |
$x^{8} - x^{7} + 4 x^{6} + 2 x^{5} + 8 x^{4} + 3 x^{3} - 9 x^{2} - 6 x - 1$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 7^{2}\cdot 19^{3}$ |
$3$ |
$10.9721595076$ |
$53.83927746036854$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$9.69842582741$ |
| 8.2.212960000.1 |
$x^{8} - 6 x^{4} - 11$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$10.9910011869$ |
$45.42887775768084$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$7.29685200131$ |
| 8.2.212960000.2 |
$x^{8} + x^{4} - 11$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$10.9910011869$ |
$45.42887775768084$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$9.53857309856$ |
| 8.0.216790749.1 |
$x^{8} - x^{7} + 7 x^{6} - 13 x^{5} + 25 x^{4} - 40 x^{3} + 49 x^{2} - 40 x + 25$ |
$8$ |
[0,4] |
$3^{7}\cdot 7^{3}\cdot 17^{2}$ |
$3$ |
$11.0155222802$ |
$46.40118679595722$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$24.9633488528$ |
| 8.0.240010128.1 |
$x^{8} - x^{7} - 5 x^{6} - x^{5} + 7 x^{4} + 8 x^{3} + 10 x^{2} + 8 x + 4$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{7}\cdot 19^{3}$ |
$3$ |
$11.1565186577$ |
$47.59663985762694$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$26.096907407$ |
| 8.2.278384067.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 9 x^{5} + 9 x^{4} - 7 x^{3} + 2 x^{2} + 6 x - 9$ |
$8$ |
[2,3] |
$-\,3^{3}\cdot 13^{4}\cdot 19^{2}$ |
$3$ |
$11.3652906576$ |
$35.82526550367126$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$12.6200885783$ |
| 8.0.282300416.1 |
$x^{8} - 2 x^{7} - x^{6} + 12 x^{5} - 11 x^{4} - 12 x^{3} + 24 x^{2} - 12 x + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 41^{3}$ |
$2$ |
$11.3851547954$ |
$64.81087485720239$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$4$ |
$3$ |
$26.7883110629$ |
| 8.2.297910000.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 5 x^{5} + x^{4} - 4 x^{3} - 2 x^{2} + 8 x - 4$ |
$8$ |
[2,3] |
$-\,2^{4}\cdot 5^{4}\cdot 31^{3}$ |
$3$ |
$11.4620060984$ |
$58.753841618694295$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$16.4725408236$ |
| 8.0.314703872.1 |
$x^{8} + 2 x^{4} + 8$ |
$8$ |
[0,4] |
$2^{17}\cdot 7^{4}$ |
$2$ |
$11.5408490537$ |
$23.081698107401436$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$3$ |
$14.58404685$ |
| 8.0.314703872.2 |
$x^{8} - 2 x^{4} + 8$ |
$8$ |
[0,4] |
$2^{17}\cdot 7^{4}$ |
$2$ |
$11.5408490537$ |
$23.081698107401436$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$3$ |
$24.8772028034$ |
| 8.0.321978368.1 |
$x^{8} - 2 x^{6} + 2 x^{4} + 2 x^{2} + 17$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$23.323807579381203$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$4$ |
$3$ |
$27.9842017441$ |
| 8.4.321978368.1 |
$x^{8} - 4 x^{7} + 4 x^{6} - x^{4} + 4 x^{2} - 4 x + 1$ |
$8$ |
[4,2] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$33.48857611437076$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$5$ |
$18.115319142$ |
| 8.0.321978368.2 |
$x^{8} - 6 x^{6} + 18 x^{4} - 26 x^{2} + 17$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$23.323807579381203$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$4$ |
$3$ |
$14.5979840845$ |
| 8.0.321978368.3 |
$x^{8} - 8 x^{6} + 25 x^{4} - 34 x^{2} + 17$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{3}$ |
$2$ |
$11.5738629877$ |
$47.35999852550681$ |
|
|
✓ |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$4$ |
$3$ |
$11.1314106477$ |
| 8.0.329042493.1 |
$x^{8} - x^{7} - 10 x^{6} + 16 x^{5} + 34 x^{4} - 57 x^{3} - 45 x^{2} + 36 x + 63$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{3}\cdot 43^{2}$ |
$3$ |
$11.6053033886$ |
$77.75930483841216$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$25.8657507813$ |
| 8.2.340075827.1 |
$x^{8} - x^{7} - 3 x^{6} + 5 x^{5} - 8 x^{4} + 6 x^{3} + 3 x^{2} + 9 x - 3$ |
$8$ |
[2,3] |
$-\,3^{5}\cdot 7^{2}\cdot 13^{4}$ |
$3$ |
$11.6532474986$ |
$21.745111415357325$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$13.7962449739$ |
| 8.2.359661568.3 |
$x^{8} + 2 x^{4} - 7$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 7^{3}$ |
$2$ |
$11.7350989029$ |
$28.950496621601552$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$13.4816261279$ |
| 8.0.410012928.1 |
$x^{8} + 21 x^{4} + 117$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$11.9288806606$ |
$52.49294610035036$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$6$ |
$3$ |
$13.2971521173$ |
| 8.2.440061875.1 |
$x^{8} - 8 x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + 19 x^{2} - 12 x - 9$ |
$8$ |
[2,3] |
$-\,5^{4}\cdot 11^{3}\cdot 23^{2}$ |
$3$ |
$12.0348094425$ |
$64.77291378191644$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$13.8012880775$ |
| 8.2.448524288.1 |
$x^{8} - 2 x^{7} - x^{6} + 2 x^{5} + 5 x^{4} - 20 x^{3} + 26 x^{2} - 16 x + 4$ |
$8$ |
[2,3] |
$-\,2^{12}\cdot 3^{2}\cdot 23^{3}$ |
$3$ |
$12.0634976982$ |
$51.45190959399487$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$18.9668477341$ |
| 8.0.454039808.1 |
$x^{8} - 2 x^{7} - 3 x^{6} - 2 x^{5} + 15 x^{4} + 6 x^{3} - 6 x^{2} - 4 x + 20$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{3}\cdot 19^{2}$ |
$3$ |
$12.0819418574$ |
$72.98665952280606$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$4$ |
$3$ |
$19.9634957566$ |
| 8.0.459636525.1 |
$x^{8} - x^{7} - 6 x^{6} + 7 x^{5} + 9 x^{4} - 13 x^{3} + 13 x^{2} - 30 x + 21$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{2}\cdot 61^{3}$ |
$3$ |
$12.1004582224$ |
$84.53625526041823$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$52.4062430655$ |
| 8.0.468512000.1 |
$x^{8} - 3 x^{4} + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$12.1294215482$ |
$37.301503595352386$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$3$ |
$19.5756707013$ |
| 8.0.468838125.1 |
$x^{8} - 4 x^{7} + 13 x^{6} - 25 x^{5} + 40 x^{4} - 43 x^{3} + 10 x^{2} + 8 x + 1$ |
$8$ |
[0,4] |
$3^{7}\cdot 5^{4}\cdot 7^{3}$ |
$3$ |
$12.1304766182$ |
$25.16457673743996$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$6$ |
$3$ |
$22.3835917465$ |
| 8.2.488095744.1 |
$x^{8} - 2 x^{6} + x^{4} - 8 x^{3} - 2 x^{2} - 4 x - 2$ |
$8$ |
[2,3] |
$-\,2^{14}\cdot 31^{3}$ |
$2$ |
$12.1916680007$ |
$52.551033519462685$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$61.8892710819$ |
| 8.0.496450053.1 |
$x^{8} - 3 x^{7} - 5 x^{6} + 15 x^{5} + 13 x^{4} - 24 x^{3} - 12 x^{2} + 9 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 11^{2}\cdot 37^{3}$ |
$3$ |
$12.2175590059$ |
$86.18035187613314$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$6$ |
$3$ |
$85.9305347542$ |
| 8.0.504166032.1 |
$x^{8} - x^{7} - 2 x^{6} + 2 x^{5} + 15 x^{4} + 28 x^{3} + 28 x^{2} + 16 x + 4$ |
$8$ |
[0,4] |
$2^{4}\cdot 3^{4}\cdot 73^{3}$ |
$3$ |
$12.2411352877$ |
$86.51327806122109$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$6$ |
$3$ |
$21.9942954384$ |
| 8.2.534534400.1 |
$x^{8} - 4 x^{7} + 10 x^{6} - 6 x^{5} - 11 x^{4} + 34 x^{3} - 32 x^{2} + 10 x - 1$ |
$8$ |
[2,3] |
$-\,2^{8}\cdot 5^{2}\cdot 17^{4}$ |
$3$ |
$12.3309619442$ |
$26.076809620810597$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$2$ |
$4$ |
$17.9445202168$ |
