| 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 |
| 8.2.10582228992.3 |
$x^{8} + 4 x^{6} + 12 x^{4} + 8 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 29^{2}$ |
$3$ |
$17.9090333168$ |
$101.05323856822808$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$98.6244169358$ |
| 8.0.39749419008.5 |
$x^{8} - 20 x^{6} + 126 x^{4} - 128 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 13$ |
$3$ |
$21.1308198831$ |
$89.04370605008683$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$360.353109632$ |
| 8.0.39749419008.9 |
$x^{8} + 8 x^{6} + 30 x^{4} + 56 x^{2} + 52$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 13$ |
$3$ |
$21.1308198831$ |
$89.04370605008683$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$898.457670906$ |
| 8.0.64210599936.8 |
$x^{8} - 12 x^{6} + 60 x^{4} - 120 x^{2} + 84$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 7$ |
$3$ |
$22.436279467$ |
$74.95847250743647$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$715.826667196$ |
| 8.4.102294880256.1 |
$x^{8} - 4 x^{6} + 44 x^{4} - 232 x^{2} + 116$ |
$8$ |
[4,2] |
$2^{22}\cdot 29^{3}$ |
$2$ |
$23.7810889473$ |
$135.3907856917937$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$5$ |
$789.113221614$ |
| 8.0.284361228288.2 |
$x^{8} - 12 x^{6} + 12 x^{4} + 168 x^{2} + 372$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 31$ |
$3$ |
$27.0230147126$ |
$157.7438930763096$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$862.471313551$ |
| 8.2.449474199552.1 |
$x^{8} - 18 x^{4} - 72 x^{2} - 108$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{2}$ |
$3$ |
$28.6146274502$ |
$103.27164477359116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$744.29089701$ |
| 8.2.449474199552.8 |
$x^{8} + 4 x^{6} + 12 x^{4} + 72 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{2}$ |
$3$ |
$28.6146274502$ |
$103.27164477359116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$1290.5983045$ |
| 8.2.720896000000.16 |
$x^{8} + 8 x^{6} - 16 x^{4} - 448 x^{2} - 704$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}\cdot 11$ |
$3$ |
$30.3552683814$ |
$120.14742181497073$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$873.722778712$ |
| 8.2.720896000000.18 |
$x^{8} + 16 x^{6} + 56 x^{4} - 64 x^{2} - 704$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{6}\cdot 11$ |
$3$ |
$30.3552683814$ |
$120.14742181497073$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$991.769434988$ |
| 8.4.1258815488000.4 |
$x^{8} - 8 x^{6} - 2 x^{4} - 200 x^{2} + 500$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{3}\cdot 7^{4}$ |
$3$ |
$32.5458231127$ |
$132.56131594100177$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[3]$ |
$[3]$ |
$2$ |
$5$ |
$1198.82938978$ |
| 8.4.1900544000000.15 |
$x^{8} - 4 x^{6} + 46 x^{4} - 384 x^{2} + 116$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{6}\cdot 29$ |
$3$ |
$34.265710477610526$ |
$195.0819608860828$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2792.5713274761506$ |
| 8.4.1900544000000.20 |
$x^{8} - 8 x^{6} + 24 x^{4} - 512 x^{2} + 1856$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{6}\cdot 29$ |
$3$ |
$34.265710477610526$ |
$195.0819608860828$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1553.891363748466$ |
| 8.0.2763396218880.2 |
$x^{8} + 8 x^{6} + 22 x^{4} + 24 x^{2} + 20$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 5\cdot 11^{4}$ |
$4$ |
$35.9071052652$ |
$139.1658197708139$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[3]$ |
$[3]$ |
$2$ |
$3$ |
$892.034689964$ |
| 8.0.2763396218880.6 |
$x^{8} + 150 x^{4} + 88 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 5\cdot 11^{4}$ |
$4$ |
$35.9071052652$ |
$139.1658197708139$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$2086.38277555$ |
| 8.0.2949120000000.1 |
$x^{8} - 200 x^{4} + 960 x^{2} + 2880$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{2}\cdot 5^{7}$ |
$3$ |
$36.2002488127$ |
$76.72731332300198$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$857.541318921$ |
| 8.4.2949120000000.2 |
$x^{8} - 20 x^{6} + 230 x^{4} - 2160 x^{2} + 180$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{2}\cdot 5^{7}$ |
$3$ |
$36.2002488127$ |
$76.72731332300198$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2436.42736885$ |
| 8.4.3146319396864.6 |
$x^{8} - 20 x^{6} + 174 x^{4} - 336 x^{2} + 84$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$36.4943263128$ |
$167.97923687670303$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$4740.02522637$ |
| 8.0.3146319396864.9 |
$x^{8} + 12 x^{6} + 108 x^{4} + 504 x^{2} + 756$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$36.4943263128$ |
$167.97923687670303$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[10]$ |
$[10]$ |
$2$ |
$3$ |
$233.055313219$ |
| 8.0.3146319396864.20 |
$x^{8} - 36 x^{6} + 462 x^{4} - 2352 x^{2} + 4116$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 7^{3}$ |
$3$ |
$36.4943263128$ |
$74.95847250743647$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$2239.50916496$ |
| 8.6.3234424946688.5 |
$x^{8} - 12 x^{6} + 12 x^{4} + 40 x^{2} - 12$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$36.6205307842$ |
$67.65858543952659$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$4837.81738223$ |
| 8.2.3234424946688.25 |
$x^{8} + 20 x^{6} + 108 x^{4} - 24 x^{2} - 972$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$36.6205307842$ |
$89.04370605008683$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$6981.42523651$ |
| 8.2.3234424946688.34 |
$x^{8} + 8 x^{6} + 14 x^{4} - 8 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$36.6205307842$ |
$67.65858543952659$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1382.69210195$ |
| 8.6.3489136640000.5 |
$x^{8} - 8 x^{6} - 72 x^{4} + 512 x^{2} - 704$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$36.9691739925$ |
$80.34742350667435$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$3785.635385$ |
| 8.2.3489136640000.11 |
$x^{8} - 4 x^{6} - 164 x^{4} - 264 x^{2} - 44$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$36.9691739925$ |
$146.32553684009903$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1569.35876708$ |
| 8.2.3489136640000.21 |
$x^{8} + 16 x^{6} - 8 x^{4} - 576 x^{2} - 704$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$36.9691739925$ |
$80.34742350667435$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$894.637518749$ |
| 8.4.4731699200000.5 |
$x^{8} + 8 x^{6} + 6 x^{4} - 40 x^{2} + 20$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{5}\cdot 19^{2}$ |
$3$ |
$38.4040601318$ |
$157.90464798470384$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$[2]$ |
$2$ |
$5$ |
$5186.78637001$ |
| 8.4.4731699200000.6 |
$x^{8} - 4 x^{6} - 26 x^{4} + 20$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{5}\cdot 19^{2}$ |
$3$ |
$38.4040601318$ |
$157.90464798470384$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2687.31086689$ |
| 8.0.6717651812352.28 |
$x^{8} - 20 x^{6} + 78 x^{4} + 2704 x^{2} + 8788$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$40.123811942$ |
$89.04370605008683$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$[2, 2]$ |
$6$ |
$3$ |
$884.595505971$ |
| 8.0.6717651812352.38 |
$x^{8} + 36 x^{6} + 780 x^{4} + 12168 x^{2} + 79092$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$40.123811942$ |
$89.04370605008683$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$[2, 2]$ |
$6$ |
$3$ |
$2016.71457115$ |
| 8.2.8811708416000.2 |
$x^{8} - 4 x^{6} + 14 x^{4} - 140$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{3}\cdot 7^{5}$ |
$3$ |
$41.5080675385$ |
$183.34390625545254$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$3132.66484538$ |
| 8.2.8811708416000.5 |
$x^{8} + 12 x^{6} - 36 x^{4} - 1000 x^{2} - 3500$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 5^{3}\cdot 7^{5}$ |
$3$ |
$41.5080675385$ |
$183.34390625545254$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1105.96460904$ |
| 8.0.9555148800000.26 |
$x^{8} - 16 x^{6} + 120 x^{4} - 320 x^{2} + 320$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{5}$ |
$3$ |
$41.9304653052$ |
$149.24750426883116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$3$ |
$8317.85980689$ |
| 8.0.9555148800000.29 |
$x^{8} - 20 x^{6} + 150 x^{4} - 400 x^{2} + 500$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{5}$ |
$3$ |
$41.9304653052$ |
$149.24750426883116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$3$ |
$7614.98773555$ |
| 8.0.16056320000000.3 |
$x^{8} - 40 x^{4} + 2240 x^{2} + 15680$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{7}\cdot 7^{2}$ |
$3$ |
$44.7410067115$ |
$117.2029070577501$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1241.78939808$ |
| 8.4.16056320000000.3 |
$x^{8} - 40 x^{6} + 600 x^{4} - 4480 x^{2} + 15680$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{7}\cdot 7^{2}$ |
$3$ |
$44.7410067115$ |
$117.2029070577501$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$[2]$ |
$2$ |
$5$ |
$5464.43196213$ |
| 8.2.22024235778048.23 |
$x^{8} - 4 x^{6} - 234 x^{4} - 5292$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{4}$ |
$3$ |
$46.5438823322$ |
$103.27164477359116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$12993.1116047$ |
| 8.2.22024235778048.41 |
$x^{8} + 12 x^{6} + 204 x^{4} + 56 x^{2} - 588$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3^{7}\cdot 7^{4}$ |
$3$ |
$46.5438823322$ |
$103.27164477359116$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$17802.4747393$ |
| 8.0.24843386880000.1 |
$x^{8} - 100 x^{6} + 3150 x^{4} - 16000 x^{2} + 32500$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{4}\cdot 13$ |
$4$ |
$47.24994967882038$ |
$199.10777969650343$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$14028.42116281527$ |
| 8.0.24870565969920.2 |
$x^{8} - 24 x^{6} + 198 x^{4} - 648 x^{2} + 1620$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 5\cdot 11^{4}$ |
$4$ |
$47.2564081198$ |
$139.1658197708139$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$4268.00595197$ |
| 8.0.24870565969920.3 |
$x^{8} + 4 x^{6} + 124 x^{4} - 24 x^{2} + 1620$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 5\cdot 11^{4}$ |
$4$ |
$47.2564081198$ |
$139.1658197708139$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$8877.05503257$ |
| 8.0.24870565969920.11 |
$x^{8} - 4 x^{6} + 30 x^{4} - 96 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}\cdot 5\cdot 11^{4}$ |
$4$ |
$47.256408119814516$ |
$183.15251889159836$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$6328.701278112316$ |
| 8.6.29109824520192.2 |
$x^{8} - 24 x^{6} + 150 x^{4} - 72 x^{2} - 108$ |
$8$ |
[6,1] |
$-\,2^{22}\cdot 3^{5}\cdot 13^{4}$ |
$3$ |
$48.1953289056$ |
$89.04370605008683$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2, 2, 2]$ |
$2$ |
$6$ |
$24457.8250687$ |
| 8.4.31470387200000.6 |
$x^{8} + 20 x^{6} + 140 x^{4} - 600 x^{2} + 500$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{5}\cdot 7^{4}$ |
$3$ |
$48.6673569254$ |
$132.56131594100177$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$5207.87200316$ |
| 8.0.37152326942720.7 |
$x^{8} + 12 x^{6} + 54 x^{4} - 112 x^{2} + 180$ |
$8$ |
[0,4] |
$2^{22}\cdot 5\cdot 11^{6}$ |
$3$ |
$49.6876265929$ |
$146.32553684009903$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$16989.2403337$ |
| 8.0.37152326942720.12 |
$x^{8} + 8 x^{6} + 46 x^{4} + 120 x^{2} + 500$ |
$8$ |
[0,4] |
$2^{22}\cdot 5\cdot 11^{6}$ |
$3$ |
$49.6876265929$ |
$146.32553684009903$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$46473.0631423$ |
| 8.0.40131624960000.1 |
$x^{8} + 12 x^{6} + 108 x^{4} - 648 x^{2} + 756$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 5^{4}\cdot 7$ |
$4$ |
$50.1690460505$ |
$167.61224001617705$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$7530.01478198$ |
| 8.0.40131624960000.3 |
$x^{8} + 24 x^{6} + 120 x^{4} - 768 x^{2} + 1344$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 5^{4}\cdot 7$ |
$4$ |
$50.1690460505$ |
$167.61224001617705$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$7404.8530668$ |
| 8.0.40131624960000.7 |
$x^{8} - 60 x^{6} + 1500 x^{4} - 15000 x^{2} + 52500$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{7}\cdot 5^{4}\cdot 7$ |
$4$ |
$50.1690460505$ |
$167.61224001617705$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$8524.19200033$ |
| 8.2.60735312887808.17 |
$x^{8} - 20 x^{6} + 46 x^{4} - 32 x^{2} - 12$ |
$8$ |
[2,3] |
$-\,2^{22}\cdot 3\cdot 13^{6}$ |
$3$ |
$52.8360276944$ |
$128.47207886202563$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$10650.1745997$ |
