| 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 |
| 8.2.2621440000.2 |
$x^{8} + 2 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}$ |
$2$ |
$15.0424123723$ |
$17.88854381999832$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
trivial |
$2$ |
$4$ |
$33.4431402995$ |
| 8.2.69797412864.2 |
$x^{8} - 8 x^{6} + 10 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{2}\cdot 43^{2}$ |
$3$ |
$22.6714822836$ |
$90.86253353280438$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$221.285965175$ |
| 8.2.69797412864.3 |
$x^{8} + 8 x^{6} + 10 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{2}\cdot 43^{2}$ |
$3$ |
$22.6714822836$ |
$90.86253353280438$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$624.743020038$ |
| 8.0.116530348032.5 |
$x^{8} - 16 x^{6} + 94 x^{4} - 240 x^{2} + 252$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$24.1715711507$ |
$36.66060555964672$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
trivial |
$6$ |
$3$ |
$989.130729175$ |
| 8.0.116530348032.6 |
$x^{8} + 16 x^{6} + 94 x^{4} + 240 x^{2} + 252$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$24.1715711507$ |
$36.66060555964672$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
trivial |
$6$ |
$3$ |
$2153.21165776$ |
| 8.2.119793516544.2 |
$x^{8} + 6 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 13^{4}$ |
$2$ |
$24.2551611404$ |
$28.844410203711913$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
trivial |
$2$ |
$4$ |
$639.195094686$ |
| 8.0.144179200000.2 |
$x^{8} + 8 x^{6} - 34 x^{4} + 160 x^{2} + 220$ |
$8$ |
(0, 4) |
$2^{22}\cdot 5^{5}\cdot 11$ |
$3$ |
$24.8234892208$ |
$88.71842695178528$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$114.993317205$ |
| 8.4.144179200000.3 |
$x^{8} - 8 x^{6} - 34 x^{4} - 160 x^{2} + 220$ |
$8$ |
(4, 2) |
$2^{22}\cdot 5^{5}\cdot 11$ |
$3$ |
$24.8234892208$ |
$88.71842695178528$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$743.050025278$ |
| 8.6.208578543616.3 |
$x^{8} - 8 x^{6} + 8 x^{4} + 16 x^{2} - 4$ |
$8$ |
(6, 1) |
$-\,2^{22}\cdot 223^{2}$ |
$2$ |
$25.996130224$ |
$119.46547618454463$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$929.321271223$ |
| 8.2.208578543616.5 |
$x^{8} + 8 x^{6} + 8 x^{4} - 16 x^{2} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 223^{2}$ |
$2$ |
$25.996130223980877$ |
$119.46547618454463$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$676.4047577258551$ |
| 8.2.212336640000.2 |
$x^{8} + 18 x^{4} - 324$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$26.0542224973$ |
$30.983866769659336$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$679.517708814$ |
| 8.0.249036800000.2 |
$x^{8} + 8 x^{6} - 24 x^{4} + 240 x^{2} + 380$ |
$8$ |
(0, 4) |
$2^{22}\cdot 5^{5}\cdot 19$ |
$3$ |
$26.5786513895$ |
$116.59885635459175$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[10]$ |
$[10]$ |
$2$ |
$3$ |
$46.504351539$ |
| 8.4.249036800000.3 |
$x^{8} - 8 x^{6} - 24 x^{4} - 240 x^{2} + 380$ |
$8$ |
(4, 2) |
$2^{22}\cdot 5^{5}\cdot 19$ |
$3$ |
$26.5786513895$ |
$116.59885635459175$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$734.553092357$ |
| 8.4.412782428160.1 |
$x^{8} - 16 x^{6} + 96 x^{4} - 384 x^{2} + 960$ |
$8$ |
(4, 2) |
$2^{22}\cdot 3^{9}\cdot 5$ |
$3$ |
$28.3116480077$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1853.70753424$ |
| 8.0.412782428160.1 |
$x^{8} + 16 x^{6} + 96 x^{4} + 384 x^{2} + 960$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{9}\cdot 5$ |
$3$ |
$28.3116480077$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$208.556086735$ |
| 8.0.412782428160.4 |
$x^{8} + 24 x^{6} + 174 x^{4} + 512 x^{2} + 540$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{9}\cdot 5$ |
$3$ |
$28.3116480077$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$452.950610441$ |
| 8.4.412782428160.4 |
$x^{8} - 24 x^{6} + 174 x^{4} - 512 x^{2} + 540$ |
$8$ |
(4, 2) |
$2^{22}\cdot 3^{9}\cdot 5$ |
$3$ |
$28.3116480077$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1162.05461352$ |
| 8.2.628176715776.1 |
$x^{8} + 8 x^{6} - 8 x^{4} - 48 x^{2} - 36$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{4}\cdot 43^{2}$ |
$3$ |
$29.8373486685$ |
$90.86253353280438$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$702.813024746$ |
| 8.2.628176715776.3 |
$x^{8} - 8 x^{6} - 8 x^{4} + 48 x^{2} - 36$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{4}\cdot 43^{2}$ |
$3$ |
$29.8373486685$ |
$90.86253353280438$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1175.7662204$ |
| 8.0.1048773132288.12 |
$x^{8} + 120 x^{4} + 4032$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{6}\cdot 7^{3}$ |
$3$ |
$31.8115766437$ |
$78.47918025833762$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$867.247064167$ |
| 8.0.1048773132288.27 |
$x^{8} - 30 x^{4} + 252$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{6}\cdot 7^{3}$ |
$3$ |
$31.8115766437$ |
$78.47918025833762$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$1678.25253935$ |
| 8.2.1173738225664.1 |
$x^{8} - 8 x^{6} + 34 x^{4} - 48 x^{2} - 100$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 23^{4}$ |
$2$ |
$32.2623802889$ |
$64.70063519272051$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1143.16464808$ |
| 8.2.1173738225664.2 |
$x^{8} + 8 x^{6} + 34 x^{4} + 48 x^{2} - 100$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 23^{4}$ |
$2$ |
$32.2623802889$ |
$64.70063519272051$ |
|
|
|
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$2985.98017734$ |
| 8.2.1173738225664.5 |
$x^{8} - 18 x^{4} - 16 x^{2} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 23^{4}$ |
$2$ |
$32.2623802889$ |
$64.70063519272051$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$922.08408025$ |
| 8.2.1173738225664.11 |
$x^{8} - 18 x^{4} + 16 x^{2} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 23^{4}$ |
$2$ |
$32.2623802889$ |
$64.70063519272051$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1882.38307591$ |
| 8.2.1911029760000.7 |
$x^{8} + 12 x^{6} - 24 x^{5} - 108 x^{4} + 96 x^{3} + 280 x^{2} - 432 x + 324$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$34.2892851564$ |
$82.27036014955831$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1075.2892688$ |
| 8.2.2519203840000.15 |
$x^{8} + 38 x^{4} - 3844$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$35.4942426295$ |
$99.59919678390986$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1172.15602044$ |
| 8.2.2519203840000.16 |
$x^{8} + 88 x^{4} - 3844$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$35.4942426295$ |
$99.59919678390986$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1172.15602044$ |
| 8.2.2966551527424.1 |
$x^{8} - 10 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 29^{4}$ |
$2$ |
$36.226926255$ |
$43.08131845707603$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
trivial |
$2$ |
$4$ |
$2003.79537788$ |
| 8.2.3588751360000.1 |
$x^{8} + 8 x^{6} - 138 x^{4} - 1776 x^{2} - 5476$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$37.0994884429$ |
$108.81176406988355$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$680.87230912$ |
| 8.2.3588751360000.4 |
$x^{8} - 8 x^{6} - 138 x^{4} + 1776 x^{2} - 5476$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$37.0994884429$ |
$108.81176406988355$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$1099.94588117$ |
| 8.2.4406640640000.3 |
$x^{8} + 22 x^{4} - 6724$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 41^{2}$ |
$3$ |
$38.0639149603$ |
$114.54256850621083$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[3]$ |
$[6]$ |
$2$ |
$4$ |
$401.861759994$ |
| 8.2.4406640640000.4 |
$x^{8} + 152 x^{4} - 6724$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 41^{2}$ |
$3$ |
$38.0639149603$ |
$114.54256850621083$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[3]$ |
$[6]$ |
$2$ |
$4$ |
$401.861759994$ |
| 8.4.4671947145216.3 |
$x^{8} - 16 x^{6} + 90 x^{4} - 208 x^{2} + 156$ |
$8$ |
(4, 2) |
$2^{22}\cdot 3\cdot 13^{5}$ |
$3$ |
$38.3431015791$ |
$94.86546254332036$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2248.44153801$ |
| 8.0.4671947145216.4 |
$x^{8} + 16 x^{6} + 90 x^{4} + 208 x^{2} + 156$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3\cdot 13^{5}$ |
$3$ |
$38.3431015791$ |
$94.86546254332036$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1217.55149513$ |
| 8.2.6294077440000.2 |
$x^{8} + 98 x^{4} - 9604$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$39.7984822557$ |
$47.32863826479693$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$3527.27206133$ |
| 8.2.7860800978944.2 |
$x^{8} + 24 x^{4} - 4$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 37^{4}$ |
$2$ |
$40.9197856525$ |
$48.662100242385755$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
trivial |
$2$ |
$4$ |
$7451.98389642$ |
| 8.2.7929856000000.1 |
$x^{8} - 190 x^{4} - 12100$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$40.9645475634$ |
$88.71842695178528$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1189.93162134$ |
| 8.2.7929856000000.2 |
$x^{8} - 40 x^{4} - 12100$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$40.9645475634$ |
$88.71842695178528$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$4$ |
$594.965810671$ |
| 8.6.7929856000000.3 |
$x^{8} - 16 x^{6} + 46 x^{4} + 144 x^{2} - 324$ |
$8$ |
(6, 1) |
$-\,2^{22}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$40.9645475634$ |
$88.71842695178528$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2, 2]$ |
$2$ |
$6$ |
$9201.03345184$ |
| 8.2.7929856000000.8 |
$x^{8} + 16 x^{6} + 46 x^{4} - 144 x^{2} - 324$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$40.9645475634$ |
$88.71842695178528$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1423.93825765$ |
| 8.0.9438958190592.1 |
$x^{8} - 36 x^{6} - 8 x^{5} + 366 x^{4} + 112 x^{2} - 1344 x + 1092$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{8}\cdot 7^{3}$ |
$3$ |
$41.8663893318$ |
$124.03806449723977$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$5893.21429701$ |
| 8.2.9703274840064.6 |
$x^{8} + 54 x^{4} - 324$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$42.011171441$ |
$49.95998398718719$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1901.80261372$ |
| 8.0.10121153347584.1 |
$x^{8} - 32 x^{6} + 258 x^{4} - 32 x^{2} + 6076$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{4}\cdot 31^{3}$ |
$3$ |
$42.2331768125$ |
$77.14920608794364$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[3]$ |
$[3]$ |
$6$ |
$3$ |
$2616.54247201$ |
| 8.0.10121153347584.2 |
$x^{8} + 32 x^{6} + 258 x^{4} + 32 x^{2} + 6076$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{4}\cdot 31^{3}$ |
$3$ |
$42.2331768125$ |
$77.14920608794364$ |
|
|
|
$D_{8}$ (as 8T6) |
$[3]$ |
$[3]$ |
$6$ |
$3$ |
$9372.60332776$ |
| 8.4.10319560704000.1 |
$x^{8} - 32 x^{6} + 330 x^{4} - 1200 x^{2} + 1500$ |
$8$ |
(4, 2) |
$2^{22}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$42.3357883426$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$4752.31393767$ |
| 8.0.10319560704000.1 |
$x^{8} + 24 x^{6} - 30 x^{4} + 400 x^{2} + 1500$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$42.3357883426$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1318.33683665$ |
| 8.0.10319560704000.2 |
$x^{8} + 32 x^{6} + 330 x^{4} + 1200 x^{2} + 1500$ |
$8$ |
(0, 4) |
$2^{22}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$42.3357883426$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1889.54009477$ |
| 8.4.10319560704000.2 |
$x^{8} - 24 x^{6} - 30 x^{4} - 400 x^{2} + 1500$ |
$8$ |
(4, 2) |
$2^{22}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$42.3357883426$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$14747.8359216$ |
| 8.2.11075584000000.1 |
$x^{8} - 450 x^{4} - 5200 x^{2} - 16900$ |
$8$ |
(2, 3) |
$-\,2^{22}\cdot 5^{6}\cdot 13^{2}$ |
$3$ |
$42.7115988949$ |
$96.44709838247663$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1488.78875894$ |
