| 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 |
| 8.0.327680000000.2 |
$x^{8} + 20 x^{6} + 130 x^{4} + 280 x^{2} + 20$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{7}$ |
$2$ |
$27.5062408773$ |
$32.7106173583177$ |
✓ |
|
? |
$C_8:C_2$ (as 8T7) |
$[10]$ |
$2$ |
$3$ |
$36.02606833$ |
| 8.6.720896000000.2 |
$x^{8} - 8 x^{6} + 4 x^{4} + 48 x^{2} - 44$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 5^{6}\cdot 11$ |
$3$ |
$30.3552683814$ |
$88.71842695178528$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$6$ |
$1448.72963637$ |
| 8.6.720896000000.7 |
$x^{8} - 16 x^{6} + 16 x^{4} + 384 x^{2} - 704$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 5^{6}\cdot 11$ |
$3$ |
$30.3552683814$ |
$88.71842695178528$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$6$ |
$2009.26884828$ |
| 8.0.746405756928.4 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$30.4875041579$ |
$49.95998398718719$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$6$ |
$3$ |
$789.949646855$ |
| 8.0.746405756928.9 |
$x^{8} + 16 x^{6} + 80 x^{4} + 128 x^{2} + 832$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$30.4875041579$ |
$49.95998398718719$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$6$ |
$3$ |
$789.949646855$ |
| 8.0.746405756928.21 |
$x^{8} + 28 x^{6} + 290 x^{4} + 1352 x^{2} + 2548$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$30.4875041579$ |
$94.86546254332036$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[10]$ |
$6$ |
$3$ |
$150.68081534$ |
| 8.0.746405756928.22 |
$x^{8} - 8 x^{6} + 212 x^{4} - 208 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$30.4875041579$ |
$94.86546254332036$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$6$ |
$3$ |
$1387.06680829$ |
| 8.4.1585971200000.7 |
$x^{8} - 8 x^{6} + 36 x^{4} - 80 x^{2} + 20$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$33.4993910151$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$2$ |
$5$ |
$2619.1890324$ |
| 8.4.1585971200000.9 |
$x^{8} - 16 x^{6} + 144 x^{4} - 640 x^{2} + 320$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$33.4993910151$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$2$ |
$5$ |
$1888.49629443$ |
| 8.4.1900544000000.3 |
$x^{8} + 12 x^{6} - 6 x^{4} - 152 x^{2} + 116$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{6}\cdot 29$ |
$3$ |
$34.2657104776$ |
$144.05107021885692$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$5$ |
$2043.4985137$ |
| 8.4.1900544000000.12 |
$x^{8} - 24 x^{6} + 116 x^{4} + 336 x^{2} + 116$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{6}\cdot 29$ |
$3$ |
$34.2657104776$ |
$144.05107021885692$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$5$ |
$1712.51333411$ |
| 8.0.3146319396864.10 |
$x^{8} + 12 x^{6} + 162 x^{4} + 648 x^{2} + 756$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$36.4943263128$ |
$55.35031602933466$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$917.933324575$ |
| 8.0.3146319396864.24 |
$x^{8} + 36 x^{6} + 378 x^{4} + 1176 x^{2} + 4116$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$36.4943263128$ |
$55.35031602933466$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$917.933324575$ |
| 8.0.7676100608000.6 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$40.7983483961$ |
$59.329587896765304$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$2$ |
$3$ |
$3142.36653781$ |
| 8.0.7676100608000.7 |
$x^{8} - 24 x^{6} + 180 x^{4} - 432 x^{2} + 500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$40.7983483961$ |
$59.329587896765304$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$2$ |
$3$ |
$3142.36653781$ |
| 8.0.7676100608000.23 |
$x^{8} + 12 x^{6} + 106 x^{4} + 200 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$40.7983483961$ |
$88.71842695178528$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$2$ |
$3$ |
$1755.89461128$ |
| 8.0.7676100608000.29 |
$x^{8} + 12 x^{6} + 50 x^{4} + 40 x^{2} + 500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$40.7983483961$ |
$88.71842695178528$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$2$ |
$3$ |
$3529.56452813$ |
| 8.0.11023155200000.1 |
$x^{8} - 24 x^{6} + 244 x^{4} - 1200 x^{2} + 2420$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 29^{2}$ |
$3$ |
$42.6862732633$ |
$144.05107021885692$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[6]$ |
$2$ |
$3$ |
$436.730709676$ |
| 8.0.11023155200000.10 |
$x^{8} + 12 x^{6} + 66 x^{4} + 200 x^{2} + 500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 29^{2}$ |
$3$ |
$42.6862732633$ |
$144.05107021885692$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[6]$ |
$2$ |
$3$ |
$365.993495331$ |
| 8.0.14015841435648.3 |
$x^{8} + 24 x^{6} + 196 x^{4} + 624 x^{2} + 468$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 13^{5}$ |
$3$ |
$43.9873092914$ |
$94.86546254332036$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$2$ |
$3$ |
$2381.05132655$ |
| 8.0.14015841435648.9 |
$x^{8} - 4 x^{6} - 22 x^{4} + 104 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 13^{5}$ |
$3$ |
$43.9873092914$ |
$94.86546254332036$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$2$ |
$3$ |
$963.929373064$ |
| 8.2.17980456960000.9 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} - 76$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{4}\cdot 19^{3}$ |
$3$ |
$45.378495251$ |
$77.9743547584717$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$2645.38106917$ |
| 8.2.17980456960000.18 |
$x^{8} + 16 x^{6} + 80 x^{4} + 128 x^{2} - 1216$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{4}\cdot 19^{3}$ |
$3$ |
$45.378495251$ |
$77.9743547584717$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$2645.38106917$ |
| 8.2.22024235778048.26 |
$x^{8} + 12 x^{6} - 30 x^{4} - 984 x^{2} - 3468$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{4}$ |
$3$ |
$46.5438823322$ |
$55.35031602933466$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$2$ |
$4$ |
$2886.15030308$ |
| 8.2.22024235778048.48 |
$x^{8} - 24 x^{6} + 180 x^{4} - 432 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{4}$ |
$3$ |
$46.5438823322$ |
$55.35031602933466$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$2$ |
$4$ |
$2886.15030308$ |
| 8.8.26542080000000.1 |
$x^{8} - 60 x^{6} + 1170 x^{4} - 7560 x^{2} + 1620$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{4}\cdot 5^{7}$ |
$3$ |
$47.6422067248$ |
$56.65645121155071$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$2$ |
$7$ |
$8029.88481006$ |
| 8.4.39649280000000.3 |
$x^{8} - 20 x^{6} - 750 x^{4} - 3960 x^{2} + 2420$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$50.093273526$ |
$108.48884443842614$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$2$ |
$5$ |
$3631.31606943$ |
| 8.4.39649280000000.4 |
$x^{8} + 60 x^{6} + 610 x^{4} - 3960 x^{2} + 2420$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$50.093273526$ |
$108.48884443842614$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$2$ |
$5$ |
$4792.7077793$ |
| 8.4.39649280000000.12 |
$x^{8} - 20 x^{6} - 30 x^{4} + 1320 x^{2} + 2420$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$50.093273526$ |
$108.48884443842614$ |
|
|
? |
$(C_8:C_2):C_2$ (as 8T16) |
$[2]$ |
$2$ |
$5$ |
$3525.4582558$ |
| 8.4.39649280000000.16 |
$x^{8} - 20 x^{6} - 470 x^{4} + 8360 x^{2} + 2420$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 11^{2}$ |
$3$ |
$50.093273526$ |
$108.48884443842614$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$2$ |
$5$ |
$4241.53819375$ |
| 8.2.60735312887808.6 |
$x^{8} + 24 x^{6} + 164 x^{4} + 240 x^{2} - 108$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 13^{6}$ |
$3$ |
$52.8360276944$ |
$94.86546254332036$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$4$ |
$13578.0256938$ |
| 8.2.60735312887808.16 |
$x^{8} - 4 x^{6} - 46 x^{4} - 56 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 13^{6}$ |
$3$ |
$52.8360276944$ |
$94.86546254332036$ |
|
|
|
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
trivial |
$2$ |
$4$ |
$33539.7768689$ |
| 8.0.68325736448000.5 |
$x^{8} - 40 x^{6} + 548 x^{4} - 2960 x^{2} + 5780$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 19^{4}$ |
$3$ |
$53.6195346061$ |
$116.59885635459175$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[10]$ |
$2$ |
$3$ |
$312.880829588$ |
| 8.0.68325736448000.8 |
$x^{8} + 36 x^{6} + 522 x^{4} + 3640 x^{2} + 10580$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{3}\cdot 19^{4}$ |
$3$ |
$53.6195346061$ |
$116.59885635459175$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2]$ |
$2$ |
$3$ |
$1741.98201392$ |
| 8.2.87228416000000.12 |
$x^{8} + 48 x^{6} - 176 x^{4} - 15488 x^{2} - 85184$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}\cdot 11^{3}$ |
$3$ |
$55.2818092724$ |
$88.71842695178528$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2, 2]$ |
$2$ |
$4$ |
$1592.9598618$ |
| 8.2.87228416000000.20 |
$x^{8} + 24 x^{6} - 44 x^{4} - 1936 x^{2} - 5324$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}\cdot 11^{3}$ |
$3$ |
$55.2818092724$ |
$88.71842695178528$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2, 4]$ |
$2$ |
$4$ |
$1361.44463666$ |
| 8.4.118292480000000.2 |
$x^{8} - 20 x^{6} - 1270 x^{4} - 9880 x^{2} + 7220$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 19^{2}$ |
$3$ |
$57.427464512$ |
$142.58227544573424$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$2$ |
$5$ |
$8301.9120638$ |
| 8.4.118292480000000.6 |
$x^{8} - 20 x^{6} - 910 x^{4} + 17480 x^{2} + 7220$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 19^{2}$ |
$3$ |
$57.427464512$ |
$142.58227544573424$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$2$ |
$5$ |
$5505.35230541$ |
| 8.4.126142572920832.5 |
$x^{8} - 28 x^{6} + 274 x^{4} - 936 x^{2} + 468$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$57.8905546581$ |
$94.86546254332036$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$2$ |
$5$ |
$9136.51079172$ |
| 8.4.126142572920832.18 |
$x^{8} + 12 x^{6} - 198 x^{4} - 2808 x^{2} + 4212$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$57.8905546581$ |
$94.86546254332036$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$2$ |
$5$ |
$14948.0399653$ |
| 8.0.126142572920832.24 |
$x^{8} - 104 x^{6} + 2756 x^{4} - 2704 x^{2} + 8788$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$57.8905546581$ |
$94.86546254332036$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2, 2, 2]$ |
$6$ |
$3$ |
$1830.65093193$ |
| 8.0.126142572920832.33 |
$x^{8} - 104 x^{6} + 4004 x^{4} - 67600 x^{2} + 430612$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 13^{5}$ |
$3$ |
$57.8905546581$ |
$94.86546254332036$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2, 2, 4]$ |
$6$ |
$3$ |
$733.998300665$ |
| 8.0.191902515200000.1 |
$x^{8} + 24 x^{6} - 76 x^{4} + 880 x^{2} + 2420$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$61.0077605499$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2, 4]$ |
$2$ |
$3$ |
$1038.25404018$ |
| 8.0.191902515200000.5 |
$x^{8} - 40 x^{6} + 420 x^{4} - 400 x^{2} + 4500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$61.0077605499$ |
$88.71842695178528$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
$[2, 2, 2]$ |
$2$ |
$3$ |
$1295.05947185$ |
| 8.0.191902515200000.12 |
$x^{8} - 40 x^{6} + 580 x^{4} - 3600 x^{2} + 12500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$61.0077605499$ |
$88.71842695178528$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[2, 2, 4]$ |
$2$ |
$3$ |
$2406.05022969$ |
| 8.0.191902515200000.21 |
$x^{8} + 48 x^{6} - 304 x^{4} + 7040 x^{2} + 38720$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{5}\cdot 11^{4}$ |
$3$ |
$61.0077605499$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2, 4]$ |
$2$ |
$3$ |
$1774.71564525$ |
| 8.2.212241626431488.11 |
$x^{8} - 8 x^{6} - 316 x^{4} + 1328 x^{2} - 1452$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{3}\cdot 37^{4}$ |
$3$ |
$61.7808416731$ |
$84.2852300228219$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$28291.3027781$ |
| 8.2.212241626431488.18 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} - 588$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{3}\cdot 37^{4}$ |
$3$ |
$61.7808416731$ |
$84.2852300228219$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$2$ |
$4$ |
$28291.3027781$ |
| 8.0.263186355847168.1 |
$x^{8} + 52 x^{6} + 338 x^{4} + 728 x^{2} + 468$ |
$8$ |
[0,4] |
$2^{22}\cdot 13^{7}$ |
$2$ |
$63.464800814$ |
$75.47279268029754$ |
✓ |
|
|
$C_8:C_2$ (as 8T7) |
$[3, 30]$ |
$2$ |
$3$ |
$450.484818009$ |
| 8.0.273271140384768.1 |
$x^{8} - 24 x^{6} + 180 x^{4} - 432 x^{2} + 372$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 31^{3}$ |
$3$ |
$63.7638044383$ |
$116.48015282868938$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$6$ |
$3$ |
$6924.73508975$ |
