| 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 |
| 8.0.321272407040.1 |
$x^{8} - 4 x^{7} + 20 x^{6} - 46 x^{5} + 84 x^{4} - 96 x^{3} + 89 x^{2} - 48 x + 16$ |
$8$ |
[0,4] |
$2^{10}\cdot 5\cdot 13^{7}$ |
$3$ |
$27.4384249803$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$231.630834181$ |
| 8.0.321272407040.2 |
$x^{8} - 2 x^{7} + 5 x^{6} + 4 x^{5} - 24 x^{4} + 10 x^{3} + 67 x^{2} - 80 x + 35$ |
$8$ |
[0,4] |
$2^{10}\cdot 5\cdot 13^{7}$ |
$3$ |
$27.4384249803$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$412.262323995$ |
| 8.4.1285089628160.1 |
$x^{8} - 2 x^{7} - 8 x^{6} + 56 x^{5} - 63 x^{4} - 146 x^{3} + 574 x^{2} - 444 x - 108$ |
$8$ |
[4,2] |
$2^{12}\cdot 5\cdot 13^{7}$ |
$3$ |
$32.629970211$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[2, 4]$ |
$2$ |
$5$ |
$1714.23221744$ |
| 8.4.1285089628160.2 |
$x^{8} - 13 x^{6} + 52 x^{4} - 52 x^{3} - 78 x^{2} + 208 x + 104$ |
$8$ |
[4,2] |
$2^{12}\cdot 5\cdot 13^{7}$ |
$3$ |
$32.629970211$ |
$84.38114744244693$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[2, 8]$ |
$2$ |
$5$ |
$3559.39572808$ |
| 8.4.1451059455625.1 |
$x^{8} - 3 x^{7} - 5 x^{6} + 20 x^{5} - 24 x^{4} + 28 x^{3} + 11 x^{2} + 3 x + 9$ |
$8$ |
[4,2] |
$5^{4}\cdot 13^{7}\cdot 37$ |
$3$ |
$33.1291772851$ |
$128.31762048162142$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$3899.68642662$ |
| 8.2.2056143405056.1 |
$x^{8} - 52 x^{4} - 208 x^{2} - 416$ |
$8$ |
[2,3] |
$-\,2^{15}\cdot 13^{7}$ |
$2$ |
$34.6044280199$ |
$63.46480081404899$ |
|
|
|
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$7947.14213439$ |
| 8.2.2056143405056.2 |
$x^{8} - 13 x^{4} - 26 x^{2} - 26$ |
$8$ |
[2,3] |
$-\,2^{15}\cdot 13^{7}$ |
$2$ |
$34.6044280199$ |
$63.46480081404899$ |
|
|
|
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$2492.8901696$ |
| 8.2.2056143405056.3 |
$x^{8} - 2 x^{7} + 5 x^{6} - 22 x^{5} + 2 x^{4} - 42 x^{3} + 93 x^{2} - 2 x + 9$ |
$8$ |
[2,3] |
$-\,2^{15}\cdot 13^{7}$ |
$2$ |
$34.6044280199$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$2506.79375789$ |
| 8.2.2056143405056.4 |
$x^{8} - 2 x^{7} + 5 x^{6} - 22 x^{5} - 24 x^{4} - 42 x^{3} + 41 x^{2} - 2 x + 35$ |
$8$ |
[2,3] |
$-\,2^{15}\cdot 13^{7}$ |
$2$ |
$34.6044280199$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$1669.37627868$ |
| 8.8.4902227890625.1 |
$x^{8} - x^{7} - 28 x^{6} + 7 x^{5} + 265 x^{4} + 123 x^{3} - 808 x^{2} - 909 x - 259$ |
$8$ |
[8,0] |
$5^{7}\cdot 13^{7}$ |
$2$ |
$38.5744006614$ |
$38.57440066138834$ |
|
|
? |
$C_8:C_2$ (as 8T7) |
$[2]$ |
$[4]$ |
$2$ |
$7$ |
$4073.8082525$ |
| 8.0.5140358512640.1 |
$x^{8} - 4 x^{7} + 20 x^{6} - 20 x^{5} + 6 x^{4} - 96 x^{3} + 76 x^{2} + 160 x + 120$ |
$8$ |
[0,4] |
$2^{14}\cdot 5\cdot 13^{7}$ |
$3$ |
$38.8037927373$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$3$ |
$586.709912876$ |
| 8.0.5140358512640.2 |
$x^{8} - 2 x^{7} + 5 x^{6} + 4 x^{5} + 145 x^{4} - 458 x^{3} + 431 x^{2} - 80 x + 178$ |
$8$ |
[0,4] |
$2^{14}\cdot 5\cdot 13^{7}$ |
$3$ |
$38.8037927373$ |
$84.38114744244693$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
$[4, 4]$ |
$[4, 4]$ |
$2$ |
$3$ |
$987.290637943$ |
| 8.2.6863119046875.1 |
$x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} - 150 x^{4} + 307 x^{3} - 353 x^{2} + 199 x - 49$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 7\cdot 13^{7}$ |
$3$ |
$40.2314042436$ |
$83.45972637422375$ |
|
|
|
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$1541.03361117$ |
| 8.2.6863119046875.2 |
$x^{8} - x^{7} - 2 x^{6} + 20 x^{5} + 31 x^{4} - 215 x^{3} + 427 x^{2} - 532 x + 131$ |
$8$ |
[2,3] |
$-\,5^{6}\cdot 7\cdot 13^{7}$ |
$3$ |
$40.2314042436$ |
$83.45972637422375$ |
|
|
|
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$3076.02352398$ |
| 8.0.8031810176000.1 |
$x^{8} - 4 x^{7} - 6 x^{6} + 32 x^{5} - 20 x^{4} - 18 x^{3} + 167 x^{2} - 152 x + 94$ |
$8$ |
[0,4] |
$2^{10}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$41.0300153529$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$3009.77015323$ |
| 8.0.8031810176000.2 |
$x^{8} - 4 x^{7} + 7 x^{6} + 6 x^{5} + 58 x^{4} - 96 x^{3} - 28 x^{2} - 152 x + 328$ |
$8$ |
[0,4] |
$2^{10}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$41.0300153529$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$3956.80664789$ |
| 8.2.8224573620224.1 |
$x^{8} - 52 x^{4} + 208 x^{2} - 416$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[4]$ |
$[2, 4]$ |
$2$ |
$4$ |
$2833.56308854$ |
| 8.2.8224573620224.2 |
$x^{8} - 4 x^{7} - 6 x^{6} - 20 x^{5} + 58 x^{4} + 8 x^{3} - 288 x^{2} + 160 x - 296$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[4]$ |
$[2, 4]$ |
$2$ |
$4$ |
$4112.69118211$ |
| 8.2.8224573620224.3 |
$x^{8} - 4 x^{7} - 6 x^{6} - 20 x^{5} + 110 x^{4} + 372 x^{3} + 570 x^{2} + 628 x - 283$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[4]$ |
$[2, 4]$ |
$2$ |
$4$ |
$1068.79622787$ |
| 8.2.8224573620224.4 |
$x^{8} - 13 x^{4} + 26 x^{2} - 26$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$63.46480081404899$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[4]$ |
$[2, 4]$ |
$2$ |
$4$ |
$3669.00574938$ |
| 8.2.8224573620224.5 |
$x^{8} + 78 x^{4} - 208 x^{2} - 416$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$85.94755853767087$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$6300.36678107$ |
| 8.2.8224573620224.6 |
$x^{8} + 78 x^{4} + 208 x^{2} - 416$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$85.94755853767087$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$8477.27576982$ |
| 8.2.8224573620224.7 |
$x^{8} - 2 x^{7} - 8 x^{6} + 56 x^{5} - 102 x^{4} + 88 x^{3} - 24 x^{2} + 128 x - 56$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$85.94755853767087$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$8822.11592841$ |
| 8.2.8224573620224.8 |
$x^{8} - 2 x^{7} - 8 x^{6} - 22 x^{5} + 93 x^{4} + 88 x^{3} - 76 x^{2} + 24 x - 4$ |
$8$ |
[2,3] |
$-\,2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$85.94755853767087$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$2237.87986793$ |
| 8.4.8224573620224.1 |
$x^{8} - 2 x^{7} - 8 x^{6} + 30 x^{5} + 15 x^{4} - 68 x^{3} + 80 x^{2} + 76 x - 82$ |
$8$ |
[4,2] |
$2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$82.30366402370633$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$14521.6649218$ |
| 8.0.8224573620224.1 |
$x^{8} + 26 x^{6} + 221 x^{4} + 728 x^{2} + 936$ |
$8$ |
[0,4] |
$2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$82.30366402370633$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$1143.013887$ |
| 8.0.8224573620224.2 |
$x^{8} - 2 x^{7} - 8 x^{6} + 4 x^{5} + 28 x^{4} + 36 x^{3} + 80 x^{2} + 24 x + 100$ |
$8$ |
[0,4] |
$2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$82.30366402370633$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$1529.17362315$ |
| 8.4.8224573620224.2 |
$x^{8} - 26 x^{6} + 221 x^{4} - 728 x^{2} + 936$ |
$8$ |
[4,2] |
$2^{17}\cdot 13^{7}$ |
$2$ |
$41.1518320119$ |
$82.30366402370633$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$8670.83961291$ |
| 8.0.9608366665625.1 |
$x^{8} - 4 x^{7} + 20 x^{6} - 46 x^{5} + 201 x^{4} - 330 x^{3} + 921 x^{2} - 763 x + 224$ |
$8$ |
[0,4] |
$5^{5}\cdot 7^{2}\cdot 13^{7}$ |
$3$ |
$41.9595861416$ |
$83.45972637422375$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$3073.88671299$ |
| 8.0.9608366665625.2 |
$x^{8} - 3 x^{7} + 8 x^{6} + 20 x^{5} - 24 x^{4} + 80 x^{3} + 128 x^{2} - 192 x + 256$ |
$8$ |
[0,4] |
$5^{5}\cdot 7^{2}\cdot 13^{7}$ |
$3$ |
$41.9595861416$ |
$83.45972637422375$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$1539.9631065$ |
| 8.2.11294733060000.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 9 x^{5} - 24 x^{4} - 107 x^{3} + 314 x^{2} + 50 x - 4$ |
$8$ |
[2,3] |
$-\,2^{5}\cdot 3^{2}\cdot 5^{4}\cdot 13^{7}$ |
$4$ |
$42.8163356577$ |
$130.207016612642$ |
|
|
|
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$15969.898191$ |
| 8.4.18071572896000.1 |
$x^{8} - 4 x^{7} - 6 x^{6} + 32 x^{5} - 7 x^{4} - 44 x^{3} - 2 x^{2} + 30 x + 3$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{2}\cdot 5^{3}\cdot 13^{7}$ |
$4$ |
$45.4071761561$ |
$82.02528053713955$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$11855.9070966$ |
| 8.4.18071572896000.2 |
$x^{8} - 2 x^{7} - 8 x^{6} + 4 x^{5} - 102 x^{4} - 16 x^{3} + 340 x^{2} - 340 x + 100$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{2}\cdot 5^{3}\cdot 13^{7}$ |
$4$ |
$45.4071761561$ |
$82.02528053713955$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$5181.09899132$ |
| 8.4.18071572896000.3 |
$x^{8} - 2 x^{7} - 8 x^{6} + 82 x^{5} - 141 x^{4} - 328 x^{3} - 128 x^{2} + 128 x + 256$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{2}\cdot 5^{3}\cdot 13^{7}$ |
$4$ |
$45.4071761561$ |
$82.02528053713955$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$15239.4592697$ |
| 8.4.18071572896000.4 |
$x^{8} - 2 x^{7} - 8 x^{6} - 48 x^{5} - 76 x^{4} + 192 x^{3} - 128 x^{2} + 128 x + 256$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{2}\cdot 5^{3}\cdot 13^{7}$ |
$4$ |
$45.4071761561$ |
$82.02528053713955$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$23715.4524944$ |
| 8.0.18832398664625.1 |
$x^{8} - 3 x^{7} + 8 x^{6} - 58 x^{5} + 41 x^{4} + 80 x^{3} + 440 x^{2} - 75 x + 2375$ |
$8$ |
[0,4] |
$5^{3}\cdot 7^{4}\cdot 13^{7}$ |
$3$ |
$45.6418463796$ |
$55.812882868747124$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$917.067876592$ |
| 8.0.18832398664625.2 |
$x^{8} - 2 x^{7} - 21 x^{6} + 17 x^{5} + 106 x^{4} + 75 x^{3} + 795 x^{2} + 2325 x + 2375$ |
$8$ |
[0,4] |
$5^{3}\cdot 7^{4}\cdot 13^{7}$ |
$3$ |
$45.6418463796$ |
$55.812882868747124$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$917.067876592$ |
| 8.0.18832398664625.3 |
$x^{8} - x^{7} - 15 x^{6} + 20 x^{5} + 200 x^{4} - 1008 x^{3} + 2208 x^{2} - 2560 x + 1600$ |
$8$ |
[0,4] |
$5^{3}\cdot 7^{4}\cdot 13^{7}$ |
$3$ |
$45.6418463796$ |
$83.45972637422375$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$3122.0067281$ |
| 8.0.18832398664625.6 |
$x^{8} - 3 x^{7} - 5 x^{6} + 20 x^{5} + 67 x^{4} + 145 x^{3} + 245 x^{2} + 510 x + 620$ |
$8$ |
[0,4] |
$5^{3}\cdot 7^{4}\cdot 13^{7}$ |
$3$ |
$45.6418463796$ |
$83.45972637422375$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$1545.88490357$ |
| 8.2.20079525440000.1 |
$x^{8} - 3 x^{7} - 5 x^{6} + 46 x^{5} - 63 x^{4} - 245 x^{3} + 713 x^{2} - 114 x - 706$ |
$8$ |
[2,3] |
$-\,2^{9}\cdot 5^{4}\cdot 13^{7}$ |
$3$ |
$46.0091468886$ |
$59.66648156085613$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$15102.6295629$ |
| 8.2.20079525440000.2 |
$x^{8} - 13 x^{6} + 65 x^{4} - 91 x^{2} - 26$ |
$8$ |
[2,3] |
$-\,2^{9}\cdot 5^{4}\cdot 13^{7}$ |
$3$ |
$46.0091468886$ |
$59.66648156085613$ |
|
|
|
$Z_8 : Z_8^\times$ (as 8T15) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$15102.6295629$ |
| 8.4.20561434050560.1 |
$x^{8} - 26 x^{4} - 52 x^{3} + 26 x^{2} + 52 x - 26$ |
$8$ |
[4,2] |
$2^{16}\cdot 5\cdot 13^{7}$ |
$3$ |
$46.1457464123$ |
$89.39871157496276$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
$[2]$ |
$[4]$ |
$2$ |
$5$ |
$7145.7360681$ |
| 8.4.20561434050560.2 |
$x^{8} - 4 x^{7} - 6 x^{6} - 20 x^{5} + 6 x^{4} + 424 x^{3} + 1064 x^{2} + 992 x + 328$ |
$8$ |
[4,2] |
$2^{16}\cdot 5\cdot 13^{7}$ |
$3$ |
$46.1457464123$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$5$ |
$2283.04834458$ |
| 8.4.20561434050560.3 |
$x^{8} - 4 x^{7} - 6 x^{6} + 32 x^{5} + 71 x^{4} + 112 x^{3} - 2 x^{2} - 100 x - 10$ |
$8$ |
[4,2] |
$2^{16}\cdot 5\cdot 13^{7}$ |
$3$ |
$46.1457464123$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$5$ |
$2413.91072359$ |
| 8.4.32127240704000.1 |
$x^{8} - 2 x^{7} - 8 x^{6} - 22 x^{5} + 15 x^{4} + 140 x^{3} - 102 x^{2} - 184 x + 178$ |
$8$ |
[4,2] |
$2^{12}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$48.7931861864$ |
$84.38114744244693$ |
|
|
|
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[2, 8]$ |
$2$ |
$5$ |
$9861.85133605$ |
| 8.4.32127240704000.2 |
$x^{8} - 2 x^{7} + 5 x^{6} - 22 x^{5} - 128 x^{4} + 322 x^{3} - 11 x^{2} - 938 x + 61$ |
$8$ |
[4,2] |
$2^{12}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$48.7931861864$ |
$84.38114744244693$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[4]$ |
$[2, 4]$ |
$2$ |
$5$ |
$5881.19025655$ |
| 8.0.32127240704000.4 |
$x^{8} - 2 x^{7} + 5 x^{6} + 30 x^{5} - 37 x^{4} + 192 x^{3} + 600 x^{2} - 2472 x + 1868$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$48.7931861864$ |
$89.22220048178464$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[12]$ |
$[12]$ |
$2$ |
$3$ |
$346.667932632$ |
| 8.0.32127240704000.6 |
$x^{8} - 2 x^{7} - 21 x^{6} + 56 x^{5} + 392 x^{4} - 224 x^{3} - 336 x^{2} + 128 x + 256$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{3}\cdot 13^{7}$ |
$3$ |
$48.7931861864$ |
$89.22220048178464$ |
|
|
|
$C_4\wr C_2$ (as 8T17) |
$[12]$ |
$[12]$ |
$2$ |
$3$ |
$2961.47374169$ |
| 8.2.32898294480896.1 |
$x^{8} - 13 x^{4} - 208 x^{2} - 26$ |
$8$ |
[2,3] |
$-\,2^{19}\cdot 13^{7}$ |
$2$ |
$48.9380514239$ |
$82.30366402370633$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$20158.8192874$ |
| 8.2.32898294480896.2 |
$x^{8} - 117 x^{4} - 104 x^{2} - 26$ |
$8$ |
[2,3] |
$-\,2^{19}\cdot 13^{7}$ |
$2$ |
$48.9380514239$ |
$82.30366402370633$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$15569.1333014$ |
