| 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 |
| 8.4.41943040000.3 |
$x^{8} - 4 x^{6} + 18 x^{4} - 28 x^{2} + 9$ |
$8$ |
[4,2] |
$2^{26}\cdot 5^{4}$ |
$2$ |
$21.2731835878$ |
$24.225659694856393$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$5$ |
$409.363165081$ |
| 8.0.440301256704.4 |
$x^{8} - 4 x^{6} + 18 x^{4} + 36 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{8}$ |
$2$ |
$28.5409707601$ |
$46.87618753574779$ |
|
|
|
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$3$ |
$1563.95154404$ |
| 8.0.440301256704.5 |
$x^{8} + 4 x^{6} - 30 x^{4} + 28 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{8}$ |
$2$ |
$28.5409707601$ |
$46.87618753574779$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$3$ |
$277.974030455$ |
| 8.2.629145600000.4 |
$x^{8} + 4 x^{6} - 26 x^{4} - 140 x^{2} - 135$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3\cdot 5^{5}$ |
$3$ |
$29.8430973391$ |
$62.74494467601174$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$4$ |
$376.392537777$ |
| 8.2.629145600000.11 |
$x^{8} + 8 x^{6} - 44 x^{4} + 80 x^{2} - 60$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3\cdot 5^{5}$ |
$3$ |
$29.8430973391$ |
$62.74494467601174$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$4$ |
$1051.48546227$ |
| 8.4.1916696264704.14 |
$x^{8} - 20 x^{6} + 130 x^{4} - 300 x^{2} + 121$ |
$8$ |
[4,2] |
$2^{26}\cdot 13^{4}$ |
$2$ |
$34.3019778423$ |
$39.06270251649997$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$5$ |
$1595.47433241$ |
| 8.0.1916696264704.16 |
$x^{8} + 28 x^{4} + 64 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{26}\cdot 13^{4}$ |
$2$ |
$34.3019778423$ |
$59.89899167351678$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$3$ |
$294.117359285$ |
| 8.0.1916696264704.17 |
$x^{8} + 8 x^{6} + 52 x^{4} + 80 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{26}\cdot 13^{4}$ |
$2$ |
$34.3019778423$ |
$59.89899167351678$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$3$ |
$817.743361135$ |
| 8.0.2397195730944.4 |
$x^{8} + 12 x^{6} + 66 x^{4} + 180 x^{2} + 441$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$35.2746681642$ |
$65.34021680048083$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$1555.7225005$ |
| 8.0.2397195730944.5 |
$x^{8} + 12 x^{6} + 54 x^{4} - 36 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$35.2746681642$ |
$65.34021680048083$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$382.649111339$ |
| 8.2.3082108796928.4 |
$x^{8} - 8 x^{6} + 24 x^{4} - 160 x^{2} - 112$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{8}\cdot 7$ |
$3$ |
$36.400386551$ |
$124.02273463041433$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$4$ |
$3783.68607556$ |
| 8.2.3082108796928.19 |
$x^{8} - 4 x^{6} + 6 x^{4} - 20 x^{2} - 7$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{8}\cdot 7$ |
$3$ |
$36.400386551$ |
$124.02273463041433$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$2$ |
$4$ |
$2025.05613913$ |
| 8.0.3397386240000.19 |
$x^{8} + 12 x^{6} + 162 x^{4} + 756 x^{2} + 729$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$36.8462348128$ |
$41.960073438364816$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 4]$ |
$2$ |
$3$ |
$357.780354327$ |
| 8.4.3962711310336.14 |
$x^{8} + 12 x^{6} + 54 x^{4} - 228 x^{2} + 9$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{10}$ |
$2$ |
$37.5620299218$ |
$56.29534592944024$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$5$ |
$6190.70707726$ |
| 8.4.3962711310336.18 |
$x^{8} - 12 x^{6} + 18 x^{4} + 12 x^{2} + 9$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{10}$ |
$2$ |
$37.5620299218$ |
$56.29534592944024$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$5$ |
$3943.66324158$ |
| 8.0.5223821082624.22 |
$x^{8} + 12 x^{6} + 34 x^{4} - 12 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$38.8819946995$ |
$104.47974028637516$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$3$ |
$3808.16327119$ |
| 8.0.5223821082624.27 |
$x^{8} + 4 x^{6} + 38 x^{4} + 116 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$38.8819946995$ |
$104.47974028637516$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$3$ |
$3274.71451681$ |
| 8.2.5662310400000.3 |
$x^{8} - 28 x^{6} + 66 x^{4} - 900 x^{2} - 135$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{3}\cdot 5^{5}$ |
$3$ |
$39.2757248739$ |
$62.74494467601174$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$4$ |
$3057.90425613$ |
| 8.2.5662310400000.9 |
$x^{8} + 4 x^{6} - 126 x^{4} + 540 x^{2} - 135$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{3}\cdot 5^{5}$ |
$3$ |
$39.2757248739$ |
$62.74494467601174$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$4$ |
$1033.47544623$ |
| 8.0.6658877030400.13 |
$x^{8} - 12 x^{6} + 22 x^{4} - 60 x^{2} + 1225$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$40.0797611139$ |
$111.01591931192023$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$2942.98964218$ |
| 8.0.6658877030400.17 |
$x^{8} + 12 x^{6} + 118 x^{4} + 540 x^{2} + 1225$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$40.0797611139$ |
$111.01591931192023$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$1334.36914189$ |
| 8.0.6658877030400.29 |
$x^{8} + 4 x^{6} + 98 x^{4} - 100 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$40.0797611139$ |
$111.01591931192023$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$898.680026699$ |
| 8.0.6658877030400.31 |
$x^{8} - 20 x^{6} + 98 x^{4} + 20 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$40.0797611139$ |
$111.01591931192023$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$564.222762334$ |
| 8.4.8842867900416.1 |
$x^{8} - 32 x^{5} - 62 x^{4} + 40 x^{3} + 440 x^{2} + 552 x - 321$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$41.5263865382$ |
$92.81390120498207$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$5$ |
$5617.47141844$ |
| 8.4.8842867900416.21 |
$x^{8} - 12 x^{6} - 32 x^{5} - 32 x^{4} + 184 x^{3} + 752 x^{2} + 1008 x + 330$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$41.5263865382$ |
$92.81390120498207$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$2$ |
$5$ |
$9505.05632164$ |
| 8.0.8842867900416.48 |
$x^{8} + 8 x^{6} + 84 x^{4} + 720 x^{2} + 324$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$41.5263865382$ |
$92.81390120498207$ |
|
|
|
$C_2^3:S_4$ (as 8T39) |
$[4]$ |
$2$ |
$3$ |
$2422.36500641$ |
| 8.0.8842867900416.49 |
$x^{8} - 16 x^{5} - 30 x^{4} + 24 x^{3} + 152 x^{2} + 408 x + 495$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{2}\cdot 11^{4}$ |
$3$ |
$41.5263865382$ |
$92.81390120498207$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[4]$ |
$2$ |
$3$ |
$1334.56834078$ |
| 8.4.9437184000000.3 |
$x^{8} - 20 x^{6} + 150 x^{4} - 900 x^{2} + 2025$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$41.8654055757$ |
$62.74494467601174$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 2]$ |
$2$ |
$5$ |
$3828.15825838$ |
| 8.0.9437184000000.13 |
$x^{8} + 20 x^{6} + 50 x^{4} + 300 x^{2} + 2025$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$41.8654055757$ |
$62.74494467601174$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 2, 4]$ |
$2$ |
$3$ |
$314.998614608$ |
| 8.0.11007531417600.12 |
$x^{8} + 24 x^{6} - 16 x^{5} + 168 x^{4} - 288 x^{3} + 208 x^{2} - 96 x + 24$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{8}\cdot 5^{2}$ |
$3$ |
$42.6787058409$ |
$87.28046997321255$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$[2]$ |
$2$ |
$3$ |
$6600.28879294$ |
| 8.0.13051398979584.7 |
$x^{8} - 4 x^{6} + 70 x^{4} - 84 x^{2} + 441$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$43.5970529718$ |
$80.75599406866377$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$2496.3984297$ |
| 8.0.13051398979584.32 |
$x^{8} + 20 x^{6} + 210 x^{4} + 812 x^{2} + 1225$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$43.5970529718$ |
$80.75599406866377$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$4540.9392373$ |
| 8.2.27738979172352.3 |
$x^{8} - 36 x^{4} - 192 x^{2} - 252$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{10}\cdot 7$ |
$3$ |
$47.9056028012$ |
$148.94348529965117$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 2]$ |
$2$ |
$4$ |
$3647.18553844$ |
| 8.2.27738979172352.9 |
$x^{8} - 8 x^{5} - 30 x^{4} - 24 x^{3} + 64 x^{2} + 48 x - 57$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{10}\cdot 7$ |
$3$ |
$47.9056028012$ |
$148.94348529965117$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 2]$ |
$2$ |
$4$ |
$3401.29642772$ |
| 8.0.32228964827136.46 |
$x^{8} - 28 x^{6} + 230 x^{4} - 44 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$48.812471152670035$ |
$164.66321856891938$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$2040.5588592283755$ |
| 8.0.32228964827136.48 |
$x^{8} + 4 x^{6} + 230 x^{4} + 308 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$48.812471152670035$ |
$164.66321856891938$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$1563.252645715907$ |
| 8.0.32228964827136.51 |
$x^{8} - 12 x^{6} + 178 x^{4} - 1716 x^{2} + 5929$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$48.812471152670035$ |
$164.66321856891938$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$5220.389252564239$ |
| 8.0.32228964827136.53 |
$x^{8} - 12 x^{6} - 14 x^{4} + 396 x^{2} + 5929$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$48.812471152670035$ |
$164.66321856891938$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$3654.381541167535$ |
| 8.4.32583836499968.10 |
$x^{8} + 16 x^{6} + 124 x^{4} - 352 x^{2} + 68$ |
$8$ |
[4,2] |
$2^{26}\cdot 13^{4}\cdot 17$ |
$3$ |
$48.87933370631753$ |
$161.05964849761017$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$5$ |
$3550.7850973890813$ |
| 8.4.32583836499968.11 |
$x^{8} - 24 x^{6} + 84 x^{4} - 112 x^{2} + 68$ |
$8$ |
[4,2] |
$2^{26}\cdot 13^{4}\cdot 17$ |
$3$ |
$48.87933370631753$ |
$161.05964849761017$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$2$ |
$5$ |
$2935.15976600881$ |
| 8.4.40307261440000.19 |
$x^{8} - 12 x^{6} + 82 x^{4} - 2356 x^{2} + 8649$ |
$8$ |
[4,2] |
$2^{26}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$50.19643931280166$ |
$134.88276471506904$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 2]$ |
$2$ |
$5$ |
$7413.052769547799$ |
| 8.4.47464824438784.7 |
$x^{8} - 20 x^{6} + 162 x^{4} - 620 x^{2} + 729$ |
$8$ |
[4,2] |
$2^{26}\cdot 29^{4}$ |
$2$ |
$51.2326104329$ |
$58.34311448984995$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$2$ |
$5$ |
$21608.7332388$ |
| 8.2.50960793600000.4 |
$x^{8} + 20 x^{6} - 110 x^{4} + 300 x^{2} - 375$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{5}\cdot 5^{5}$ |
$3$ |
$51.6897608465$ |
$82.57699113224089$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$4087.6168808$ |
| 8.2.50960793600000.10 |
$x^{8} + 4 x^{6} - 26 x^{4} + 180 x^{2} - 135$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{5}\cdot 5^{5}$ |
$3$ |
$51.6897608465$ |
$82.57699113224089$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$6157.11182922$ |
| 8.2.50960793600000.11 |
$x^{8} + 12 x^{6} + 66 x^{4} + 180 x^{2} - 135$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{5}\cdot 5^{5}$ |
$3$ |
$51.6897608465$ |
$82.57699113224089$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$6723.11461274$ |
| 8.2.50960793600000.14 |
$x^{8} + 16 x^{6} + 124 x^{4} + 1440 x^{2} - 60$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 3^{5}\cdot 5^{5}$ |
$3$ |
$51.6897608465$ |
$82.57699113224089$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$8308.40922311$ |
| 8.4.57420021760000.9 |
$x^{8} - 184 x^{5} + 590 x^{4} - 680 x^{3} + 624 x^{2} + 720 x + 135$ |
$8$ |
[4,2] |
$2^{26}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$52.46659971309024$ |
$147.35893506362828$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 4]$ |
$2$ |
$5$ |
$9815.805369923364$ |
| 8.4.57420021760000.12 |
$x^{8} - 36 x^{6} + 358 x^{4} - 1332 x^{2} + 1369$ |
$8$ |
[4,2] |
$2^{26}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$52.46659971309024$ |
$147.35893506362828$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2, 2]$ |
$2$ |
$5$ |
$5181.033277591456$ |
| 8.0.59929893273600.51 |
$x^{8} - 16 x^{6} + 60 x^{4} + 224 x^{2} + 196$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{6}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$52.747932047317$ |
$146.10516643044895$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$6281.89072469743$ |
| 8.0.59929893273600.53 |
$x^{8} - 8 x^{6} + 126 x^{4} - 456 x^{3} + 784 x^{2} - 744 x + 319$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{6}\cdot 5^{2}\cdot 7^{2}$ |
$4$ |
$52.747932047317$ |
$146.10516643044895$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[4]$ |
$2$ |
$3$ |
$1979.152554661318$ |
