| 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 |
| 8.0.822083584.2 |
$x^{8} + 4 x^{4} + 8 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{2}$ |
$2$ |
$13.0126124936$ |
$21.166010488516726$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$3$ |
$16.1711726289$ |
| 8.0.1358954496.3 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$10.6435943208$ |
| 8.0.2701131776.1 |
$x^{8} + 4 x^{6} - 8 x^{5} + 20 x^{4} - 8 x^{3} + 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 7\cdot 23$ |
$3$ |
$15.0988274321$ |
$101.50862032359616$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$24.0353525305$ |
| 8.0.4311744512.2 |
$x^{8} - 8 x^{5} + 6 x^{4} + 28 x^{2} + 8 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 257$ |
$2$ |
$16.0077991811$ |
$128.2497563350512$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$41.773635566$ |
| 8.0.4848615424.8 |
$x^{8} - 4 x^{6} - 8 x^{5} + 20 x^{4} + 8 x^{3} - 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 17^{2}$ |
$2$ |
$16.244345479$ |
$32.984845004941285$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$2$ |
$3$ |
$35.8929101459$ |
| 8.0.5653921792.3 |
$x^{8} + 4 x^{6} + 10 x^{4} - 8 x^{3} + 4 x^{2} - 8 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 337$ |
$2$ |
$16.5593667414$ |
$146.86047800548656$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$43.1400846201$ |
| 8.0.5922357248.4 |
$x^{8} - 4 x^{6} + 28 x^{4} - 40 x^{3} + 36 x^{2} - 24 x + 17$ |
$8$ |
[0,4] |
$2^{24}\cdot 353$ |
$2$ |
$16.6556591705$ |
$150.30635382444748$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$30.6539455778$ |
| 8.0.8875147264.3 |
$x^{8} - 12 x^{4} + 24 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 23^{2}$ |
$2$ |
$17.5195096248$ |
$38.36665218650175$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$3$ |
$50.9006176071$ |
| 8.0.9948889088.1 |
$x^{8} - 4 x^{6} + 2 x^{4} - 24 x^{3} + 20 x^{2} + 40 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 593$ |
$2$ |
$17.7714074289$ |
$194.81273059017474$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$65.2529491635$ |
| 8.0.10485760000.1 |
$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 5^{4}$ |
$2$ |
$17.88854382$ |
$17.88854381999832$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$78.6242549932$ |
| 8.0.13975420928.5 |
$x^{8} - 8 x^{5} + 38 x^{4} - 80 x^{3} + 92 x^{2} - 56 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{2}\cdot 17$ |
$3$ |
$18.5425992457$ |
$87.26969691708571$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$71.8002062134$ |
| 8.0.13975420928.10 |
$x^{8} + 8 x^{6} - 8 x^{5} + 30 x^{4} - 48 x^{3} + 44 x^{2} - 72 x + 46$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{2}\cdot 17$ |
$3$ |
$18.5425992457$ |
$87.26969691708571$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$72.7361130571$ |
| 8.0.14780727296.4 |
$x^{8} - 8 x^{5} + 12 x^{4} - 16 x^{3} + 8 x + 17$ |
$8$ |
[0,4] |
$2^{24}\cdot 881$ |
$2$ |
$18.6729087767$ |
$237.45315327449327$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$56.7867283832$ |
| 8.0.19344130048.3 |
$x^{8} - 8 x^{6} - 8 x^{5} + 62 x^{4} - 64 x^{3} + 12 x^{2} - 8 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 1153$ |
$2$ |
$19.3116174786$ |
$271.64682954159434$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$86.3857625901$ |
| 8.0.20149436416.3 |
$x^{8} + 4 x^{6} - 8 x^{5} - 6 x^{4} + 8 x^{3} + 12 x^{2} - 24 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 1201$ |
$2$ |
$19.4103274933$ |
$277.2435752186153$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$71.7998830202$ |
| 8.0.20954742784.4 |
$x^{8} + 4 x^{6} - 8 x^{5} + 4 x^{4} + 8 x^{3} + 52 x^{2} + 96 x + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 1249$ |
$2$ |
$19.5056439192$ |
$282.72955275315667$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$91.8353836573$ |
| 8.0.26055016448.3 |
$x^{8} + 12 x^{6} - 8 x^{5} + 34 x^{4} - 24 x^{3} + 44 x^{2} - 24 x + 14$ |
$8$ |
[0,4] |
$2^{24}\cdot 1553$ |
$2$ |
$20.0440934549$ |
$315.2649679238085$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$100.707501065$ |
| 8.0.26860322816.4 |
$x^{8} - 8 x^{6} + 30 x^{4} - 32 x^{3} + 20 x^{2} - 40 x + 46$ |
$8$ |
[0,4] |
$2^{24}\cdot 1601$ |
$2$ |
$20.1205062371$ |
$320.0999843798809$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$111.59741346$ |
| 8.0.28202500096.12 |
$x^{8} - 8 x^{6} + 36 x^{4} - 64 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 41^{2}$ |
$2$ |
$20.2435162755$ |
$51.22499389946279$ |
✓ |
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$3$ |
$99.1962811037$ |
| 8.0.35718692864.4 |
$x^{8} - 8 x^{5} - 4 x^{4} + 64 x^{2} - 56 x + 17$ |
$8$ |
[0,4] |
$2^{24}\cdot 2129$ |
$2$ |
$20.8502825517$ |
$369.12870384189847$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$98.2805561268$ |
| 8.0.38134611968.3 |
$x^{8} + 4 x^{6} - 16 x^{5} + 28 x^{4} - 40 x^{3} + 76 x^{2} - 24 x + 17$ |
$8$ |
[0,4] |
$2^{24}\cdot 2273$ |
$2$ |
$21.0215587793$ |
$381.40791811392694$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$2$ |
$3$ |
$95.2796587184$ |
| 8.4.40282095616.4 |
$x^{8} - 16 x^{6} + 36 x^{4} - 56 x^{2} + 49$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{4}$ |
$2$ |
$21.1660104885$ |
$21.166010488516726$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$5$ |
$214.979015423$ |
| 8.2.51791265792.4 |
$x^{8} - 8 x^{6} - 8 x^{5} + 46 x^{4} - 84 x^{2} + 72 x - 18$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 3^{2}\cdot 7^{3}$ |
$3$ |
$21.8414801222$ |
$59.63128174096889$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$[2]$ |
$2$ |
$4$ |
$170.723498602$ |
| 8.6.63870861312.3 |
$x^{8} - 8 x^{6} - 12 x^{4} + 112 x^{2} - 47$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 3^{4}\cdot 47$ |
$3$ |
$22.4214061947$ |
$94.99473669630333$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$[2]$ |
$2$ |
$6$ |
$327.706910567$ |
| 8.4.66588770304.12 |
$x^{8} - 76 x^{4} + 168 x^{2} + 49$ |
$8$ |
[4,2] |
$2^{24}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$22.5385059781$ |
$36.66060555964672$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
$[2]$ |
$2$ |
$5$ |
$199.638535516$ |
| 8.0.66588770304.16 |
$x^{8} + 36 x^{4} + 216 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$22.5385059781$ |
$36.66060555964672$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2, 2]$ |
$2$ |
$3$ |
$36.7111848923$ |
| 8.0.84573945856.8 |
$x^{8} - 8 x^{6} + 20 x^{4} + 144 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{24}\cdot 71^{2}$ |
$2$ |
$23.2222648655$ |
$67.40919818541087$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$3$ |
$156.438616966$ |
| 8.0.89405784064.13 |
$x^{8} + 16 x^{6} + 68 x^{4} + 104 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 73^{2}$ |
$2$ |
$23.3841022855$ |
$68.35202996254024$ |
✓ |
|
? |
$C_2^2:C_4$ (as 8T10) |
$[6]$ |
$2$ |
$3$ |
$42.225035074$ |
| 8.4.126986747904.2 |
$x^{8} - 8 x^{5} - 36 x^{4} - 16 x^{3} - 64 x^{2} - 56 x + 1$ |
$8$ |
[4,2] |
$2^{24}\cdot 3^{2}\cdot 29^{2}$ |
$3$ |
$24.4326064798$ |
$74.61903242471053$ |
|
|
? |
$V_4^2:(S_3\times C_2)$ (as 8T41) |
$[2]$ |
$2$ |
$5$ |
$421.862711638$ |
| 8.0.132355457024.3 |
$x^{8} + 4 x^{6} - 16 x^{5} + 26 x^{4} - 40 x^{3} + 100 x^{2} - 200 x + 142$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{3}\cdot 23$ |
$3$ |
$24.5593988102$ |
$101.50862032359616$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2, 2]$ |
$2$ |
$3$ |
$83.6719926741$ |
| 8.0.132892327936.16 |
$x^{8} + 16 x^{6} + 84 x^{4} + 152 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 89^{2}$ |
$2$ |
$24.5718292451$ |
$75.47184905645283$ |
✓ |
|
? |
$C_2^2:C_4$ (as 8T10) |
$[10]$ |
$2$ |
$3$ |
$44.9362221742$ |
| 8.2.143864627200.1 |
$x^{8} - 4 x^{6} - 14 x^{4} - 60 x^{2} - 175$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 5^{2}\cdot 7^{3}$ |
$3$ |
$24.8167127071$ |
$47.32863826479693$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$[4]$ |
$2$ |
$4$ |
$135.977558653$ |
| 8.2.143864627200.6 |
$x^{8} + 12 x^{6} - 8 x^{5} + 48 x^{4} + 48 x^{3} + 120 x^{2} + 208 x + 68$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 5^{2}\cdot 7^{3}$ |
$3$ |
$24.8167127071$ |
$47.32863826479693$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$[4]$ |
$2$ |
$4$ |
$174.513256564$ |
| 8.6.150307078144.1 |
$x^{8} - 16 x^{6} - 8 x^{5} + 54 x^{4} + 80 x^{3} + 16 x^{2} - 200 x - 127$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 17^{2}\cdot 31$ |
$3$ |
$24.9529806066$ |
$183.65184453198395$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$2$ |
$6$ |
$645.464274636$ |
| 8.0.153561858048.3 |
$x^{8} + 12 x^{6} - 32 x^{5} + 76 x^{4} - 72 x^{3} + 148 x^{2} + 56 x + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}\cdot 113$ |
$3$ |
$25.0198913713$ |
$147.29562111617574$ |
|
|
? |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2, 2]$ |
$2$ |
$3$ |
$106.027060758$ |
| 8.0.157856825344.14 |
$x^{8} - 4 x^{6} - 8 x^{5} + 4 x^{4} + 8 x^{3} + 124 x^{2} + 272 x + 289$ |
$8$ |
[0,4] |
$2^{24}\cdot 97^{2}$ |
$2$ |
$25.1063119417$ |
$78.79086241436883$ |
|
|
? |
$C_2^3: C_4$ (as 8T20) |
$[2]$ |
$2$ |
$3$ |
$206.886885816$ |
| 8.0.177989484544.6 |
$x^{8} + 8 x^{6} + 4 x^{4} + 32 x^{2} + 289$ |
$8$ |
[0,4] |
$2^{24}\cdot 103^{2}$ |
$2$ |
$25.4858600044$ |
$81.19113252073775$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2]$ |
$2$ |
$3$ |
$186.625901388$ |
| 8.2.235937988608.2 |
$x^{8} - 4 x^{6} - 24 x^{5} - 28 x^{4} - 24 x^{3} - 4 x^{2} + 1$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 7^{3}\cdot 41$ |
$3$ |
$26.3997451293$ |
$135.52859476877933$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$228.77797015$ |
| 8.2.235937988608.4 |
$x^{8} + 4 x^{6} - 24 x^{5} + 10 x^{4} + 72 x^{3} - 116 x^{2} + 72 x - 18$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 7^{3}\cdot 41$ |
$3$ |
$26.3997451293$ |
$135.52859476877933$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$2$ |
$4$ |
$192.067847657$ |
| 8.4.237582155776.4 |
$x^{8} - 8 x^{6} + 20 x^{4} - 32 x^{2} + 1$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[2]$ |
$2$ |
$5$ |
$628.330821225$ |
| 8.4.237582155776.10 |
$x^{8} - 8 x^{6} + 4 x^{4} - 272 x^{2} + 289$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[2]$ |
$2$ |
$5$ |
$556.050449341$ |
| 8.0.237582155776.12 |
$x^{8} - 8 x^{6} - 28 x^{4} + 288 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2, 2]$ |
$2$ |
$3$ |
$87.1931234205$ |
| 8.4.237582155776.12 |
$x^{8} - 16 x^{6} + 4 x^{4} - 136 x^{2} + 289$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[2]$ |
$2$ |
$5$ |
$327.950874133$ |
| 8.0.237582155776.13 |
$x^{8} - 12 x^{4} + 120 x^{2} + 289$ |
$8$ |
[0,4] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
? |
$C_2^2:C_4$ (as 8T10) |
$[2, 2]$ |
$2$ |
$3$ |
$181.430149567$ |
| 8.4.237582155776.15 |
$x^{8} + 4 x^{4} - 72 x^{2} + 49$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$26.4226716162$ |
$87.26969691708571$ |
|
|
|
$C_2^2 \wr C_2$ (as 8T18) |
$[2]$ |
$2$ |
$5$ |
$771.099077727$ |
| 8.0.245635219456.1 |
$x^{8} + 24 x^{6} + 180 x^{4} + 432 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 11^{4}$ |
$2$ |
$26.5329983228$ |
$26.5329983228432$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[10]$ |
$2$ |
$3$ |
$63.0659142175$ |
| 8.6.259560308736.1 |
$x^{8} - 8 x^{6} - 28 x^{4} + 176 x^{2} - 191$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 3^{4}\cdot 191$ |
$3$ |
$26.716513691$ |
$191.4993472573732$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$[2]$ |
$2$ |
$6$ |
$556.48519396$ |
| 8.6.281303580672.2 |
$x^{8} - 60 x^{4} + 216 x^{2} - 207$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 3^{6}\cdot 23$ |
$3$ |
$26.9865214329$ |
$87.45705441086021$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$[2]$ |
$2$ |
$6$ |
$615.857958058$ |
| 8.4.290195505152.3 |
$x^{8} - 16 x^{6} - 40 x^{5} - 42 x^{4} - 32 x^{3} - 20 x^{2} + 8 x + 14$ |
$8$ |
[4,2] |
$2^{24}\cdot 7^{2}\cdot 353$ |
$3$ |
$27.091704826348177$ |
$397.67323269237016$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$2$ |
$5$ |
$563.2648994930739$ |
| 8.6.305462771712.1 |
$x^{8} - 16 x^{6} - 24 x^{5} + 22 x^{4} + 80 x^{3} + 92 x^{2} + 56 x + 14$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 3^{2}\cdot 7\cdot 17^{2}$ |
$4$ |
$27.2658967637$ |
$151.15554902152948$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$2$ |
$6$ |
$927.545247568$ |
