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 |
8.0.32684089.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 9 x^{5} + 7 x^{4} - 4 x^{3} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$5717^{2}$ |
$1$ |
$8.69544971711$ |
$75.61084578286372$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$4.66178135647$ |
8.0.36445369.1 |
$x^{8} - 2 x^{7} + 3 x^{4} - 2 x^{3} - x + 2$ |
$8$ |
[0,4] |
$6037^{2}$ |
$1$ |
$8.8146544927$ |
$77.69813382572325$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$4.35538852315$ |
8.0.141324544.1 |
$x^{8} - 2 x^{7} + 6 x^{5} - 8 x^{4} + 2 x^{3} + 8 x^{2} - 10 x + 7$ |
$8$ |
[0,4] |
$2^{8}\cdot 743^{2}$ |
$2$ |
$10.4418439638$ |
$61.19220015890557$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$8.66851025275$ |
8.0.277955584.1 |
$x^{8} + 2 x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 2$ |
$8$ |
[0,4] |
$2^{10}\cdot 521^{2}$ |
$2$ |
$11.3631025311$ |
$58.47356465822684$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$19.3521785378$ |
8.4.293471161.1 |
$x^{8} - x^{6} - 6 x^{5} - 6 x^{4} + 3 x^{3} + 9 x^{2} + 7 x + 2$ |
$8$ |
[4,2] |
$37^{2}\cdot 463^{2}$ |
$2$ |
$11.4405177373$ |
$130.88544609695916$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$25.0447497668$ |
8.4.351075169.1 |
$x^{8} - x^{7} + 4 x^{5} - 6 x^{4} + 2 x^{3} + 6 x^{2} - 7 x + 2$ |
$8$ |
[4,2] |
$41^{2}\cdot 457^{2}$ |
$2$ |
$11.699707768$ |
$136.88316185711082$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$28.5295638417$ |
8.0.411602944.1 |
$x^{8} - 2 x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 317^{2}$ |
$2$ |
$11.9346533472$ |
$54.241018826181474$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$24.6814524533$ |
8.0.447407104.1 |
$x^{8} - 2 x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{10}\cdot 661^{2}$ |
$2$ |
$12.0597376299$ |
$65.86298932305145$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$20.5796181117$ |
8.0.600838144.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} + 4 x + 3$ |
$8$ |
[0,4] |
$2^{12}\cdot 383^{2}$ |
$2$ |
$12.5125171859$ |
$93.09296810297933$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$26.7191111935$ |
8.0.600838144.2 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 2 x^{4} - 4 x^{3} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 383^{2}$ |
$2$ |
$12.5125171859$ |
$71.78449158888543$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$16.7425353761$ |
8.0.608559561.1 |
$x^{8} - 3 x^{7} + 3 x^{6} + x^{5} - 5 x^{4} + 3 x^{3} + 4 x^{2} - 7 x + 4$ |
$8$ |
[0,4] |
$3^{4}\cdot 2741^{2}$ |
$2$ |
$12.5325049911$ |
$90.68075870878012$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$9.75289547432$ |
8.0.645160000.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 2 x^{5} + 4 x^{3} - 4 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{6}\cdot 5^{4}\cdot 127^{2}$ |
$3$ |
$12.624332636$ |
$45.6470349996514$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$24.2196664789$ |
8.0.670188544.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 8 x^{5} + 14 x^{4} - 12 x^{3} + 10 x^{2} - 6 x + 2$ |
$8$ |
[0,4] |
$2^{10}\cdot 809^{2}$ |
$2$ |
$12.6845371571$ |
$127.70441679847741$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$35.5414717216$ |
8.0.803835904.1 |
$x^{8} - 4 x^{6} - 6 x^{5} + 10 x^{4} + 8 x^{3} - 4 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 443^{2}$ |
$2$ |
$12.9761520274$ |
$64.1209680568815$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$31.6226101307$ |
8.0.855445504.1 |
$x^{8} - 4 x^{7} + 10 x^{6} - 14 x^{5} + 16 x^{4} - 12 x^{3} + 8 x^{2} - 4 x + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 457^{2}$ |
$2$ |
$13.0774793677$ |
$65.12628529097567$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$30.6378067058$ |
8.0.886133824.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{3} + 4 x^{2} + 8 x + 7$ |
$8$ |
[0,4] |
$2^{6}\cdot 61^{4}$ |
$2$ |
$13.1352219094$ |
$39.538763807281526$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$59.7220674973$ |
8.0.987467776.3 |
$x^{8} - 2 x^{7} + 4 x^{6} - 2 x^{5} + 6 x^{4} - 10 x^{3} + 8 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 491^{2}$ |
$2$ |
$13.3142088931$ |
$66.4005340773643$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$19.2642824169$ |
8.0.1091113024.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + 8 x^{4} - 10 x^{3} + 10 x^{2} - 6 x + 2$ |
$8$ |
[0,4] |
$2^{6}\cdot 4129^{2}$ |
$2$ |
$13.4813603544$ |
$144.25275061524383$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$43.1970353216$ |
8.0.1271350336.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 6 x^{5} + 11 x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1$ |
$8$ |
[0,4] |
$2^{6}\cdot 4457^{2}$ |
$2$ |
$13.7414687727$ |
$188.8279640307547$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$73.28924509930212$ |
8.0.1271350336.2 |
$x^{8} - x^{7} + x^{5} + 5 x^{4} + 8 x^{3} + 9 x^{2} + 5 x + 3$ |
$8$ |
[0,4] |
$2^{6}\cdot 4457^{2}$ |
$2$ |
$13.7414687727$ |
$188.8279640307547$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$26.9069130029748$ |
8.0.1475789056.1 |
$x^{8} - 3 x^{7} + 14 x^{4} - 7 x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 7^{8}$ |
$2$ |
$14.0$ |
$44.50121314235103$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$52.8415257816$ |
8.0.1651609600.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 8 x^{4} + 10 x^{3} - 2 x^{2} - 10 x + 15$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{2}\cdot 127^{2}$ |
$3$ |
$14.1983678884$ |
$76.76885619633542$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$53.5466202698$ |
8.4.1746571264.1 |
$x^{8} - 2 x^{7} - x^{6} + 2 x^{5} - 8 x^{4} + 28 x^{3} - 13 x^{2} - 24 x + 16$ |
$8$ |
[4,2] |
$2^{12}\cdot 653^{2}$ |
$2$ |
$14.2979340265$ |
$121.5553507652958$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$85.5992706429$ |
8.0.1746571264.3 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 7 x^{4} + 4 x^{3} - 8 x + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 653^{2}$ |
$2$ |
$14.2979340265$ |
$72.27724399837061$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$85.9138561285$ |
8.0.1955762176.2 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 6 x^{4} - 4 x^{3} + 8 x^{2} - 8 x + 12$ |
$8$ |
[0,4] |
$2^{12}\cdot 691^{2}$ |
$2$ |
$14.5015527048$ |
$96.42069677742984$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$42.4236949012$ |
8.0.1955762176.4 |
$x^{8} - 2 x^{7} + 3 x^{6} + 2 x^{5} - 7 x^{4} + 10 x^{3} - 8 x + 7$ |
$8$ |
[0,4] |
$2^{12}\cdot 691^{2}$ |
$2$ |
$14.5015527048$ |
$125.04217346798215$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$65.4380353065$ |
8.4.1970649664.1 |
$x^{8} - 3 x^{7} + 2 x^{6} - 4 x^{5} + 4 x^{4} + 4 x^{3} + 4 x - 4$ |
$8$ |
[4,2] |
$2^{6}\cdot 31^{2}\cdot 179^{2}$ |
$3$ |
$14.5153054064$ |
$134.93762841381766$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$119.59294816196319$ |
8.0.2264998464.1 |
$x^{8} - x^{7} + x^{6} - 5 x^{5} + x^{4} - 3 x^{3} + 7 x^{2} + 3 x + 6$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{4}\cdot 661^{2}$ |
$3$ |
$14.7701018125$ |
$80.66535838792625$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$49.9262815604$ |
8.0.2403352576.1 |
$x^{8} - 2 x^{7} + 4 x^{4} - 4 x^{2} - 4 x + 6$ |
$8$ |
[0,4] |
$2^{14}\cdot 383^{2}$ |
$2$ |
$14.879974464$ |
$65.82666902639966$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$25.6513977425$ |
8.4.2601816064.2 |
$x^{8} - 2 x^{7} + 6 x^{5} - 2 x^{4} + 6 x^{3} - 4 x^{2} - 2 x + 1$ |
$8$ |
[4,2] |
$2^{12}\cdot 797^{2}$ |
$2$ |
$15.0282902359$ |
$84.59797881758502$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$110.6151990144815$ |
8.0.2665966689.1 |
$x^{8} - 3 x^{7} + 8 x^{6} - 13 x^{5} + 8 x^{4} - 4 x^{3} - 7 x^{2} + 13 x + 7$ |
$8$ |
[0,4] |
$3^{4}\cdot 5737^{2}$ |
$2$ |
$15.0741155436$ |
$131.190700889964$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$30.7708192485$ |
8.4.2665966689.1 |
$x^{8} - 3 x^{6} - 11 x^{5} + 11 x^{4} - 9 x^{3} + 7 x^{2} + 7 x + 1$ |
$8$ |
[4,2] |
$3^{4}\cdot 5737^{2}$ |
$2$ |
$15.0741155436$ |
$131.190700889964$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$120.862360813$ |
8.0.2680754176.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - 5 x^{4} - 2 x^{3} + 16 x^{2} - 16 x + 8$ |
$8$ |
[0,4] |
$2^{12}\cdot 809^{2}$ |
$2$ |
$15.0845418377$ |
$139.26265401424664$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$58.25606641303309$ |
8.0.3949871104.4 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + 4 x^{4} + 4 x^{3} + 10 x^{2} + 4 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 491^{2}$ |
$2$ |
$15.8333519463$ |
$93.90453584102545$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$151.124343509$ |
8.0.4544917056.1 |
$x^{8} - 2 x^{6} - 4 x^{5} + 12 x^{4} + 24 x^{3} + 42 x^{2} + 36 x + 35$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{2}\cdot 53^{4}$ |
$3$ |
$16.1135319758$ |
$44.26939474722475$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$217.153790443$ |
8.0.4980971776.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 8 x^{5} + 12 x^{4} - 16 x^{3} + 20 x^{2} - 14 x + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 11^{2}\cdot 401^{2}$ |
$3$ |
$16.2991238623$ |
$132.83071933856263$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$24.3914266549$ |
8.4.5903156224.1 |
$x^{8} - x^{7} + 7 x^{5} - 21 x^{3} - 14 x^{2} + 9 x + 5$ |
$8$ |
[4,2] |
$2^{10}\cdot 7^{8}$ |
$2$ |
$16.64889961$ |
$49.950922856015325$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$189.817605265$ |
8.0.6585647104.1 |
$x^{8} - 4 x^{5} - 8 x^{4} + 4 x^{3} + 12 x^{2} + 4 x + 2$ |
$8$ |
[0,4] |
$2^{16}\cdot 317^{2}$ |
$2$ |
$16.8781486258$ |
$76.70838446092021$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$105.615024891$ |
8.0.6986285056.1 |
$x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 20 x^{2} + 16 x + 6$ |
$8$ |
[0,4] |
$2^{14}\cdot 653^{2}$ |
$2$ |
$17.0032048742$ |
$85.95261281565004$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$41.2273874592$ |
8.0.7696201984.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 10 x^{5} + 24 x^{4} - 32 x^{3} + 57 x^{2} - 58 x + 54$ |
$8$ |
[0,4] |
$2^{8}\cdot 5483^{2}$ |
$2$ |
$17.2101460995$ |
$148.09456438370722$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$118.087633018$ |
8.4.7696201984.1 |
$x^{8} - 4 x^{7} + x^{6} + 8 x^{5} - 3 x^{4} - 6 x^{3} - x^{2} + 4 x + 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 5483^{2}$ |
$2$ |
$17.2101460995$ |
$148.09456438370722$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$123.300644995$ |
8.0.7823048704.3 |
$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 8 x^{4} - 16 x^{3} + 20 x^{2} - 44 x + 30$ |
$8$ |
[0,4] |
$2^{14}\cdot 691^{2}$ |
$2$ |
$17.2453496551$ |
$88.41816879351477$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$61.4767365673$ |
8.0.9044770816.1 |
$x^{8} + 2 x^{6} - 4 x^{5} + 20 x^{4} - 8 x^{3} + 2 x^{2} + 16 x + 16$ |
$8$ |
[0,4] |
$2^{14}\cdot 743^{2}$ |
$2$ |
$17.5610183155$ |
$115.51549173293522$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$236.058335779$ |
8.0.9450950656.8 |
$x^{8} - 2 x^{5} + 2 x^{4} + 8 x^{3} + 12 x^{2} - 4 x + 6$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{4}\cdot 31^{2}$ |
$3$ |
$17.6577123184$ |
$72.99659193376111$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$131.963352093$ |
8.0.10322560000.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 14 x^{5} - 2 x^{4} - 22 x^{3} + 24 x^{2} - 6 x + 1$ |
$8$ |
[0,4] |
$2^{10}\cdot 5^{4}\cdot 127^{2}$ |
$3$ |
$17.8535024298$ |
$64.55465597862637$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$44.8586218014$ |
8.0.10437278569.1 |
$x^{8} - 4 x^{7} + 11 x^{6} - 17 x^{5} + 17 x^{4} - 8 x^{3} + 5 x^{2} - 10 x + 9$ |
$8$ |
[0,4] |
$19^{4}\cdot 283^{2}$ |
$2$ |
$17.8781842754$ |
$73.32803011127464$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$54.260850192$ |
8.0.10723016704.2 |
$x^{8} - 2 x^{7} + 7 x^{6} - 12 x^{5} + 23 x^{4} - 26 x^{3} + 25 x^{2} - 12 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 809^{2}$ |
$2$ |
$17.9386444799$ |
$170.46494509614888$ |
|
|
✓ |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$252.95288051016774$ |
8.0.10723016704.3 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} + 4 x^{4} - 28 x^{3} + 32 x^{2} - 12 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 809^{2}$ |
$2$ |
$17.9386444799$ |
$170.46494509614888$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$249.8040079356163$ |
8.0.12861374464.1 |
$x^{8} - 4 x^{6} - 4 x^{5} - 4 x^{4} + 8 x^{3} + 40 x^{2} + 40 x + 12$ |
$8$ |
[0,4] |
$2^{16}\cdot 443^{2}$ |
$2$ |
$18.3510501846$ |
$90.68074265853382$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$122.926631324$ |
8.0.13687128064.4 |
$x^{8} - 4 x^{5} - 2 x^{4} - 4 x^{3} + 8 x^{2} + 12 x + 7$ |
$8$ |
[0,4] |
$2^{16}\cdot 457^{2}$ |
$2$ |
$18.4943486834$ |
$92.10247592547722$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$3$ |
$179.561418902$ |