| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 8.0.30122769620000000.1 |
$x^{8} - 985 x^{6} + 388090 x^{4} - 76453730 x^{2} + 7530692405$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{7}\cdot 197^{4}$ |
$3$ |
$114.778848261$ |
$193.03424409861876$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$[2]$ |
$10$ |
$3$ |
$175334.887268$ |
| 8.8.618026865647775713.1 |
$x^{8} - x^{7} - 840 x^{6} + 839 x^{5} + 166615 x^{4} - 289061 x^{3} - 10165942 x^{2} + 22451853 x + 81878903$ |
$8$ |
[8,0] |
$17^{7}\cdot 197^{4}$ |
$2$ |
$167.446440248$ |
$167.44644024808923$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$893249.104151$ |
| 8.6.3234407759571058688.1 |
$x^{8} - 310472 x^{4} + 61162984 x^{2} - 3012276962$ |
$8$ |
[6,1] |
$-\,2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$297.60932268990877$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$2170859.84899$ |
| 8.2.3234407759571058688.1 |
$x^{8} - 310472 x^{4} - 61162984 x^{2} - 3012276962$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$297.60932268990877$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$766155.464612$ |
| 8.2.3234407759571058688.2 |
$x^{8} - 310472 x^{4} - 3012276962$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$224.57070156189118$ |
|
|
|
$D_{8}$ (as 8T6) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1640732.30822$ |
| 8.2.3234407759571058688.3 |
$x^{8} - 3012276962$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$224.57070156189118$ |
|
|
? |
$QD_{16}$ (as 8T8) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$878070.138401$ |
| 8.0.3234407759571058688.1 |
$x^{8} + 3012276962$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$224.57070156189118$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1861562.82919$ |
| 8.4.3234407759571058688.1 |
$x^{8} - 155236 x^{4} - 61162984 x^{2} + 3012276962$ |
$8$ |
[4,2] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$297.60932268990877$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$1918555.16096$ |
| 8.8.3234407759571058688.1 |
$x^{8} - 1576 x^{6} + 776180 x^{4} - 122325968 x^{2} + 3012276962$ |
$8$ |
[8,0] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$205.9322413175638$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[34]$ |
$[34]$ |
$2$ |
$7$ |
$223995.868511$ |
| 8.4.3234407759571058688.2 |
$x^{8} - 1576 x^{6} - 465708 x^{4} + 3012276962$ |
$8$ |
[4,2] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$224.57070156189118$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$928406.609937$ |
| 8.0.3234407759571058688.2 |
$x^{8} + 155236 x^{4} + 3012276962$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$255.73856263801852$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$875757.132922$ |
| 8.0.3234407759571058688.3 |
$x^{8} - 155236 x^{4} + 61162984 x^{2} + 3012276962$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$297.60932268990877$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$677110.280249$ |
| 8.4.3234407759571058688.3 |
$x^{8} - 155236 x^{4} + 3012276962$ |
$8$ |
[4,2] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$255.73856263801852$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$1213117.47123$ |
| 8.0.3234407759571058688.4 |
$x^{8} + 1576 x^{6} + 776180 x^{4} + 122325968 x^{2} + 3012276962$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$205.9322413175638$ |
✓ |
✓ |
? |
$C_8$ (as 8T1) |
$[73586]$ |
$[73586]$ |
$2$ |
$3$ |
$19.534360053$ |
| 8.0.3234407759571058688.5 |
$x^{8} - 1576 x^{6} + 931416 x^{4} - 244651936 x^{2} + 27110492658$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$255.73856263801852$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[74]$ |
$[74]$ |
$2$ |
$3$ |
$20326.6748615$ |
| 8.0.3234407759571058688.6 |
$x^{8} + 1576 x^{6} + 931416 x^{4} + 244651936 x^{2} + 27110492658$ |
$8$ |
[0,4] |
$2^{31}\cdot 197^{4}$ |
$2$ |
$205.932241318$ |
$255.73856263801852$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1779662.05731$ |
| 8.0.166...657.1 |
$x^{8} - x^{7} + 3582 x^{6} + 17 x^{5} + 4034810 x^{4} + 4796893 x^{3} + 1470394133 x^{2} + 3593446534 x + 148357810364$ |
$8$ |
[0,4] |
$73^{7}\cdot 197^{4}$ |
$2$ |
$599.29494667$ |
$599.2949466695865$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[44146]$ |
$[44146]$ |
$2$ |
$3$ |
$2046.25577237$ |
| 8.0.666...449.1 |
$x^{8} - x^{7} + 4367 x^{6} - 8768 x^{5} + 1460792 x^{4} + 3319296 x^{3} + 119052099 x^{2} + 301977429 x + 2589479453$ |
$8$ |
[0,4] |
$89^{7}\cdot 197^{4}$ |
$2$ |
$712.769928834$ |
$712.7699288340602$ |
✓ |
✓ |
|
$C_8$ (as 8T1) |
$[103282]$ |
$[103282]$ |
$2$ |
$3$ |
$2970.52387144$ |
| 8.8.354...977.1 |
$x^{8} - x^{7} - 5586 x^{6} - 11090 x^{5} + 7719089 x^{4} + 17585879 x^{3} - 2375003520 x^{2} + 4618266940 x + 37911729632$ |
$8$ |
[8,0] |
$113^{7}\cdot 197^{4}$ |
$2$ |
$878.368496738$ |
$878.3684967375395$ |
|
✓ |
|
$C_8$ (as 8T1) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$293376441455$ |
| 8.8.711...161.1 |
$x^{8} - x^{7} - 11914 x^{6} - 35461 x^{5} + 40177763 x^{4} + 285936385 x^{3} - 28653675856 x^{2} - 320702815139 x - 781105608509$ |
$8$ |
[8,0] |
$197^{4}\cdot 241^{7}$ |
$2$ |
$1704.11157098$ |
$1704.1115709804792$ |
|
✓ |
? |
$C_8$ (as 8T1) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$4237528184.71$ |
