| 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 |
| 8.4.708837376.1 |
$x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{4} - 4 x^{2} + 8 x - 2$ |
$8$ |
[4,2] |
$2^{22}\cdot 13^{2}$ |
$2$ |
$12.7737474703$ |
$24.255161140409015$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$42.9351678954$ |
| 8.2.1438646272.4 |
$x^{8} - 4 x^{7} + 4 x^{6} - 8 x^{5} + 14 x^{4} - 8 x^{3} + 4 x^{2} - 8 x - 2$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 7^{3}$ |
$2$ |
$13.9554631106$ |
$17.798422345016238$ |
|
|
? |
$D_{8}$ (as 8T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$55.5269775606$ |
| 8.0.3057647616.7 |
$x^{8} - 4 x^{7} + 8 x^{6} - 4 x^{5} + 4 x^{4} + 4 x^{3} + 32 x^{2} - 20 x + 25$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}$ |
$2$ |
$15.3346345019$ |
$15.33463450191054$ |
✓ |
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.4.3527409664.3 |
$x^{8} - 4 x^{7} + 4 x^{6} - 2 x^{4} + 8 x^{3} - 12 x^{2} + 8 x - 2$ |
$8$ |
[4,2] |
$2^{22}\cdot 29^{2}$ |
$2$ |
$15.611045429$ |
$36.226926254958926$ |
|
|
✓ |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$96.9158238339$ |
| 8.6.7813988352.1 |
$x^{8} - 8 x^{6} + 14 x^{4} + 8 x^{2} - 23$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 23$ |
$3$ |
$17.2428517772$ |
$55.880081833510175$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$181.328752848$ |
| 8.4.8493465600.3 |
$x^{8} - 4 x^{7} - 4 x^{6} + 12 x^{5} - 28 x^{4} + 12 x^{3} - 4 x^{2} - 4 x + 1$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$17.4235086988$ |
$26.054222497305222$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
$[2]$ |
$2$ |
$5$ |
$141.473799604$ |
| 8.2.10632560640.4 |
$x^{8} + 4 x^{6} + 6 x^{4} - 28 x^{2} - 15$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 5\cdot 13^{2}$ |
$4$ |
$17.9196586899$ |
$93.9398351563814$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$85.6359359861$ |
| 8.4.15003025408.1 |
$x^{8} - 4 x^{7} - 4 x^{6} + 20 x^{5} + 28 x^{4} - 60 x^{3} - 52 x^{2} + 44 x - 7$ |
$8$ |
[4,2] |
$2^{22}\cdot 7^{2}\cdot 73$ |
$3$ |
$18.7077843744$ |
$152.06978717656196$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$222.353888589$ |
| 8.4.15607005184.1 |
$x^{8} - 8 x^{6} + 4 x^{4} + 16 x^{2} + 36$ |
$8$ |
[4,2] |
$2^{22}\cdot 61^{2}$ |
$2$ |
$18.8003072462$ |
$52.54088763765113$ |
|
|
|
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$278.223479659$ |
| 8.4.19969081344.2 |
$x^{8} - 8 x^{6} + 14 x^{4} - 24 x^{2} + 9$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{2}\cdot 23^{2}$ |
$3$ |
$19.3885245437$ |
$55.880081833510175$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$[2]$ |
$2$ |
$5$ |
$278.313000897$ |
| 8.0.23592960000.4 |
$x^{8} - 4 x^{7} + 12 x^{6} - 12 x^{5} + 12 x^{4} + 28 x^{3} - 20 x^{2} - 12 x + 9$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 5^{4}$ |
$3$ |
$19.7969280154$ |
$26.054222497305222$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$93.7211746097$ |
| 8.2.24121442304.7 |
$x^{8} - 4 x^{7} - 12 x^{5} - 12 x^{4} - 28 x^{3} + 8 x^{2} - 28 x - 23$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{4}\cdot 71$ |
$3$ |
$19.8518236709$ |
$98.17983316921564$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$4$ |
$99.9665553623$ |
| 8.2.24456986624.2 |
$x^{8} - 4 x^{7} + 8 x^{6} + 4 x^{5} - 36 x^{4} + 28 x^{3} - 32 x^{2} + 108 x - 79$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 7^{3}\cdot 17$ |
$3$ |
$19.8861343082$ |
$119.36595548495043$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$160.31457416$ |
| 8.4.24800919552.4 |
$x^{8} - 8 x^{6} - 18 x^{4} + 136 x^{2} + 73$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 73$ |
$3$ |
$19.9208778711$ |
$99.55304437891716$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$5$ |
$249.633241771$ |
| 8.0.24868028416.7 |
$x^{8} + 8 x^{6} + 30 x^{4} + 88 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{22}\cdot 7^{2}\cdot 11^{2}$ |
$3$ |
$19.9276079014$ |
$59.030688778696344$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$56.5290889169$ |
| 8.4.36276535296.1 |
$x^{8} - 4 x^{7} + 4 x^{6} - 18 x^{4} - 24 x^{3} + 4 x^{2} + 8 x - 2$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{2}\cdot 31^{2}$ |
$3$ |
$20.8907111967$ |
$64.87449083902186$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$362.972945942$ |
| 8.8.41108373504.1 |
$x^{8} - 4 x^{7} - 8 x^{6} + 32 x^{5} + 18 x^{4} - 56 x^{3} - 20 x^{2} + 16 x - 2$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{4}\cdot 11^{2}$ |
$3$ |
$21.2198000213$ |
$38.644657093393754$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
$[2]$ |
$2$ |
$7$ |
$711.54464646$ |
| 8.4.49832525824.1 |
$x^{8} + 4 x^{6} - 8 x^{5} + 4 x^{4} - 32 x^{3} - 16 x^{2} + 32 x - 8$ |
$8$ |
[4,2] |
$2^{22}\cdot 109^{2}$ |
$2$ |
$21.7364748275$ |
$70.23373053994324$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$525.246169224$ |
| 8.2.51032096768.1 |
$x^{8} + 4 x^{6} - 16 x^{4} - 104 x^{2} - 92$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 23^{3}$ |
$2$ |
$21.8012013814$ |
$32.262380288915416$ |
|
|
|
$D_{8}$ (as 8T6) |
trivial |
$[2]$ |
$2$ |
$4$ |
$382.944923314$ |
| 8.6.56736350208.1 |
$x^{8} - 12 x^{6} + 26 x^{4} + 60 x^{2} - 167$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 167$ |
$3$ |
$22.0918799389$ |
$150.5744727102355$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$606.737083016$ |
| 8.4.57415827456.2 |
$x^{8} - 4 x^{7} + 4 x^{6} - 16 x^{5} + 30 x^{4} - 32 x^{3} + 76 x^{2} + 40 x - 50$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 13^{2}$ |
$3$ |
$22.1247796216$ |
$42.011171440958684$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
$[2]$ |
$2$ |
$5$ |
$412.537999845$ |
| 8.4.57415827456.12 |
$x^{8} - 4 x^{7} + 12 x^{5} - 4 x^{4} - 20 x^{3} - 8 x^{2} + 36 x - 15$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 13^{2}$ |
$3$ |
$22.1247796216$ |
$42.011171440958684$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$344.649029413$ |
| 8.0.76441190400.12 |
$x^{8} + 8 x^{6} + 30 x^{4} + 56 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{2}$ |
$3$ |
$22.9306270129$ |
$34.289285156385596$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$188.3489547$ |
| 8.0.76441190400.16 |
$x^{8} - 4 x^{7} + 20 x^{6} - 28 x^{5} + 52 x^{4} + 28 x^{3} + 20 x^{2} + 4 x + 1$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{2}$ |
$3$ |
$22.9306270129$ |
$34.289285156385596$ |
|
|
? |
$C_2^2 \wr C_2$ (as 8T18) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$80.2752022658$ |
| 8.4.93117743104.5 |
$x^{8} - 4 x^{7} - 4 x^{6} + 16 x^{5} + 30 x^{4} - 48 x^{3} - 4 x^{2} - 72 x + 62$ |
$8$ |
[4,2] |
$2^{22}\cdot 149^{2}$ |
$2$ |
$23.5033114274$ |
$82.11559087892455$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$494.798025226$ |
| 8.2.95693045760.3 |
$x^{8} - 4 x^{7} + 4 x^{6} - 12 x^{5} + 20 x^{4} - 44 x^{3} + 36 x^{2} - 20 x - 15$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{3}\cdot 5\cdot 13^{2}$ |
$4$ |
$23.5835971228$ |
$93.9398351563814$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$499.929118855$ |
| 8.2.116530348032.1 |
$x^{8} - 4 x^{7} - 16 x^{5} + 18 x^{4} + 80 x^{3} + 20 x^{2} - 96 x - 194$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$24.1715711507$ |
$30.827771796137323$ |
|
|
? |
$D_{8}$ (as 8T6) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$162.548874691$ |
| 8.0.119793516544.14 |
$x^{8} - 4 x^{7} + 12 x^{6} - 4 x^{5} + 20 x^{4} + 44 x^{3} + 44 x^{2} + 12 x + 1$ |
$8$ |
[0,4] |
$2^{22}\cdot 13^{4}$ |
$2$ |
$24.2551611404$ |
$24.255161140409015$ |
|
|
? |
$S_4$ (as 8T14) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$3$ |
$65.5363447117$ |
| 8.8.122645643264.1 |
$x^{8} - 4 x^{7} - 16 x^{6} + 36 x^{5} + 68 x^{4} - 60 x^{3} - 88 x^{2} + 20 x + 25$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$24.3266056877$ |
$50.789029699025804$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
$[2]$ |
$2$ |
$7$ |
$1338.38492143$ |
| 8.2.127401984000.5 |
$x^{8} - 8 x^{5} + 18 x^{4} - 80 x^{2} + 120 x - 15$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{5}\cdot 5^{3}$ |
$3$ |
$24.442578796$ |
$51.274440767548086$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$807.558541904$ |
| 8.6.143709437952.2 |
$x^{8} - 4 x^{7} - 4 x^{6} + 8 x^{5} - 50 x^{4} + 16 x^{3} + 284 x^{2} + 232 x + 46$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{6}\cdot 47$ |
$3$ |
$24.81336485$ |
$105.12895756849156$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$456.145667345$ |
| 8.4.149824733184.2 |
$x^{8} - 4 x^{7} + 8 x^{6} + 8 x^{5} - 110 x^{4} + 376 x^{3} - 484 x^{2} + 64 x + 142$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$24.942957063$ |
$40.571629338126115$ |
|
|
? |
$Q_8:C_2$ (as 8T11) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$221.304243895$ |
| 8.4.149824733184.13 |
$x^{8} - 4 x^{7} - 4 x^{6} + 16 x^{5} + 14 x^{4} - 16 x^{3} - 4 x^{2} - 8 x - 2$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$24.942957063$ |
$64.12434941388099$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$877.986319883$ |
| 8.6.156460122112.2 |
$x^{8} + 4 x^{6} - 48 x^{4} + 88 x^{2} - 28$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 7\cdot 73^{2}$ |
$3$ |
$25.0784365539$ |
$152.06978717656196$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1180.07014609$ |
| 8.0.190291378176.3 |
$x^{8} - 4 x^{7} + 16 x^{6} - 8 x^{5} + 18 x^{4} + 96 x^{3} + 52 x^{2} - 32 x + 14$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 71^{2}$ |
$3$ |
$25.6996606611$ |
$98.17983316921564$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$143.473841416$ |
| 8.4.201163014144.1 |
$x^{8} - 8 x^{6} - 50 x^{4} - 24 x^{2} + 9$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{2}\cdot 73^{2}$ |
$3$ |
$25.8787632078$ |
$99.55304437891716$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
$[2]$ |
$2$ |
$5$ |
$990.339548067$ |
| 8.6.203503435776.1 |
$x^{8} - 20 x^{6} + 74 x^{4} + 260 x^{2} - 599$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 599$ |
$3$ |
$25.9162086778$ |
$285.17176699438966$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$931.571997612$ |
| 8.0.212336640000.15 |
$x^{8} - 4 x^{7} + 8 x^{6} + 2 x^{4} + 48 x^{3} - 76 x^{2} - 64 x + 94$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$26.0542224973$ |
$26.054222497305222$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$103.894434917$ |
| 8.0.212336640000.23 |
$x^{8} - 4 x^{7} - 8 x^{6} + 28 x^{5} + 68 x^{4} - 164 x^{3} + 304 x^{2} - 460 x + 505$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$26.0542224973$ |
$26.054222497305222$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$571.947145522$ |
| 8.6.219810889728.2 |
$x^{8} - 4 x^{7} - 12 x^{6} + 36 x^{5} - 12 x^{4} + 44 x^{3} + 548 x^{2} + 452 x + 97$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 647$ |
$3$ |
$26.1671335251$ |
$296.3775173425233$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$891.898835223$ |
| 8.0.247669456896.9 |
$x^{8} + 12 x^{6} + 48 x^{4} - 56 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{10}$ |
$2$ |
$26.5603660728$ |
$50.414421537552215$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$79.0425313849$ |
| 8.0.247669456896.11 |
$x^{8} + 12 x^{6} + 48 x^{4} + 40 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{10}$ |
$2$ |
$26.5603660728$ |
$50.414421537552215$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$161.615115278$ |
| 8.4.251763097600.2 |
$x^{8} - 4 x^{7} - 8 x^{6} + 24 x^{5} + 2 x^{4} - 32 x^{3} + 84 x^{2} - 98$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{2}\cdot 7^{4}$ |
$3$ |
$26.6148491613$ |
$55.04478548664435$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1294.01868912$ |
| 8.6.252425797632.1 |
$x^{8} - 4 x^{7} - 16 x^{6} + 28 x^{5} + 124 x^{4} + 36 x^{3} - 312 x^{2} - 468 x - 207$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 743$ |
$3$ |
$26.6235961656$ |
$317.60514003546626$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1276.92884023$ |
| 8.2.265814016000.4 |
$x^{8} - 4 x^{7} + 12 x^{6} - 4 x^{5} - 12 x^{4} - 20 x^{3} - 4 x^{2} + 12 x - 15$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 5^{3}\cdot 13^{2}$ |
$4$ |
$26.7961397818$ |
$93.9398351563814$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$496.403291298$ |
| 8.4.285720182784.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 142 x^{4} + 456 x^{3} - 868 x^{2} + 944 x - 386$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 29^{2}$ |
$3$ |
$27.0391238424$ |
$62.74687687563977$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
$[2]$ |
$2$ |
$5$ |
$852.716500275$ |
| 8.4.285720182784.6 |
$x^{8} - 40 x^{5} - 28 x^{4} - 32 x^{2} - 16 x + 4$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 29^{2}$ |
$3$ |
$27.0391238424$ |
$62.74687687563977$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$719.191060708$ |
| 8.0.317194240000.2 |
$x^{8} - 4 x^{6} + 42 x^{4} + 244 x^{2} + 361$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$27.3946440308$ |
$49.89003778087012$ |
|
|
|
$D_4\times C_2$ (as 8T9) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$161.176174988$ |
| 8.4.326488817664.8 |
$x^{8} + 4 x^{6} + 16 x^{4} - 72 x^{2} + 36$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$27.4937221181$ |
$64.87449083902186$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$1319.19249096$ |
| 8.6.350270521344.2 |
$x^{8} - 4 x^{7} + 8 x^{5} - 94 x^{4} + 88 x^{3} + 412 x^{2} - 2$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{4}\cdot 1031$ |
$3$ |
$27.7364227829$ |
$374.12992602762944$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1548.27819493$ |
