| 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 |
Unit signature rank |
Max $p$ |
| 8.2.110215168.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} - 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 7\cdot 31^{2}$ |
$3$ |
$10.1223225218$ |
$49.548710823589474$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$10.3253728377$ |
$1$ |
$31$ |
| 8.2.199344128.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 4 x^{4} + 6 x^{3} + 6 x^{2} - 2 x - 3$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{3}$ |
$2$ |
$10.9006006907$ |
$35.32631762433002$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$21.8065546771$ |
$1$ |
$23$ |
| 8.2.221626368.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 6 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{4}\cdot 167$ |
$3$ |
$11.0459399694$ |
$75.28723635511776$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$19.0453050111$ |
$1$ |
$167$ |
| 8.2.268681216.1 |
$x^{8} - 2 x^{7} + 4 x^{2} - 4 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 31$ |
$3$ |
$11.3150027319$ |
$89.8146656163465$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$26.1830206102$ |
$1$ |
$31$ |
| 8.2.338018304.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 10 x^{5} + 16 x^{4} - 14 x^{3} + 2 x^{2} + 6 x - 3$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3\cdot 13\cdot 23^{2}$ |
$4$ |
$11.6444110387$ |
$100.73925016392235$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$23.1113421005$ |
$1$ |
$23$ |
| 8.4.355352576.1 |
$x^{8} - 4 x^{6} - 8 x^{5} + 10 x^{4} + 8 x^{3} - 4 x^{2} + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 23^{2}\cdot 41$ |
$3$ |
$11.7174317749$ |
$103.29001459261505$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$25.2687845117$ |
$3$ |
$41$ |
| 8.2.407355392.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 16 x^{5} - 8 x^{4} - 8 x^{3} + 4 x^{2} + 4 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 47$ |
$3$ |
$11.9191883774$ |
$110.58986792379547$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$19.8383576617$ |
$1$ |
$47$ |
| 8.2.488095744.2 |
$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 8 x^{4} - 12 x^{3} - 12 x^{2} + 16 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 31^{3}$ |
$2$ |
$12.1916680007$ |
$44.189975704393966$ |
|
|
? |
$Q_8:S_4$ (as 8T40) |
trivial |
$[2]$ |
$2$ |
$4$ |
$23.7743707251$ |
$1$ |
$31$ |
| 8.0.494026752.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 6 x^{5} + 8 x^{4} - 6 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{14}\cdot 3\cdot 19\cdot 23^{2}$ |
$4$ |
$12.2100884046$ |
$121.78781483452694$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$9.75833574485$ |
$0$ |
$23$ |
| 8.2.571981824.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} - 6 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{4}\cdot 431$ |
$3$ |
$12.4357727887$ |
$120.94885319500675$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$24.2526327122$ |
$1$ |
$431$ |
| 8.4.632700928.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} - 6 x^{3} - 2 x^{2} + 2 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 23^{2}\cdot 73$ |
$3$ |
$12.5935975027$ |
$137.8249490106759$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$36.2726578272$ |
$3$ |
$73$ |
| 8.0.668745728.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{14}\cdot 7^{4}\cdot 17$ |
$3$ |
$12.681120448$ |
$50.74878469362679$ |
|
|
✓ |
$C_2\wr A_4$ (as 8T38) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$18.9776036637$ |
$0$ |
$17$ |
| 8.2.684703744.1 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 8 x^{3} - 12 x^{2} + 8 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 79$ |
$3$ |
$12.7185569166$ |
$143.37715418662523$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$25.3428754645$ |
$1$ |
$79$ |
| 8.4.702038016.2 |
$x^{8} - 2 x^{7} + 4 x^{6} - 16 x^{4} + 4 x^{3} + 12 x^{2} - 2$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 23^{2}$ |
$3$ |
$12.7583666508$ |
$27.940040916755088$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$48.2532110622$ |
$3$ |
$23$ |
| 8.2.754040832.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 4 x^{5} + 8 x^{4} + 4 x^{3} - 4 x^{2} - 4 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3\cdot 23^{2}\cdot 29$ |
$4$ |
$12.8728396049$ |
$150.46172505480757$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$37.0927109312$ |
$1$ |
$29$ |
| 8.0.771375104.1 |
$x^{8} - 2 x^{7} + 4 x^{6} - 8 x^{5} + 12 x^{4} - 12 x^{3} + 12 x^{2} - 4 x + 6$ |
$8$ |
(0, 4) |
$2^{14}\cdot 23^{2}\cdot 89$ |
$3$ |
$12.9094637468$ |
$152.18134346043146$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$18.4414753764$ |
$0$ |
$89$ |
| 8.4.861290496.1 |
$x^{8} - 2 x^{7} + 4 x^{3} - 4 x^{2} + 4 x - 2$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 11\cdot 59$ |
$4$ |
$13.0886154128$ |
$148.41762175538096$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$5$ |
$44.7855859829$ |
$3$ |
$59$ |
| 8.2.865976320.1 |
$x^{8} - 2 x^{7} + 8 x^{5} - 16 x^{4} + 20 x^{3} - 16 x^{2} + 8 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 5\cdot 11\cdot 31^{2}$ |
$4$ |
$13.0974953236$ |
$138.887987208286$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$35.1066431721$ |
$1$ |
$31$ |
| 8.0.967458816.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 8 x^{4} + 2 x^{3} - 2 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{14}\cdot 3^{10}$ |
$2$ |
$13.2801830364$ |
$17.477703781463642$ |
|
|
✓ |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$21.4899921701$ |
$0$ |
$3$ |
| 8.2.1017888768.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 10 x^{5} + 16 x^{4} - 18 x^{3} + 14 x^{2} - 10 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{4}\cdot 13\cdot 59$ |
$4$ |
$13.3648023451$ |
$161.34696543834946$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$47.1403689751$ |
$1$ |
$59$ |
| 8.4.1082146816.2 |
$x^{8} - 2 x^{7} - 6 x^{6} + 14 x^{5} + 4 x^{4} - 14 x^{3} - 6 x^{2} + 6 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 257^{2}$ |
$2$ |
$13.4674624477$ |
$53.92238017965345$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$60.5758054556$ |
$3$ |
$257$ |
| 8.0.1082146816.2 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{14}\cdot 257^{2}$ |
$2$ |
$13.4674624477$ |
$53.92238017965345$ |
|
|
✓ |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$26.6366524886$ |
$0$ |
$257$ |
| 8.2.1100726272.1 |
$x^{8} - 2 x^{7} - 2 x^{6} - 2 x^{5} + 4 x^{4} + 14 x^{3} + 14 x^{2} + 10 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 127$ |
$3$ |
$13.4961506233$ |
$181.7892805572828$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$37.4311157345$ |
$1$ |
$127$ |
| 8.4.1116094464.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 6 x^{5} - 16 x^{4} + 6 x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 29^{2}$ |
$3$ |
$13.5195619212$ |
$31.373438437819885$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$54.5512576952$ |
$3$ |
$29$ |
| 8.4.1118060544.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 10 x^{5} - 20 x^{4} + 26 x^{3} - 34 x^{2} + 18 x - 3$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3\cdot 23^{2}\cdot 43$ |
$4$ |
$13.5225365885$ |
$183.215100678104$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$61.2847713236$ |
$3$ |
$43$ |
| 8.0.1149386752.3 |
$x^{8} - 2 x^{7} + 6 x^{6} - 2 x^{5} + 4 x^{4} + 6 x^{3} + 2 x^{2} + 2 x + 5$ |
$8$ |
(0, 4) |
$2^{14}\cdot 31^{2}\cdot 73$ |
$3$ |
$13.5693259053$ |
$160.00913203065164$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$20.405285427$ |
$0$ |
$73$ |
| 8.0.1187397632.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 18 x^{5} + 24 x^{4} - 34 x^{3} + 42 x^{2} - 22 x + 9$ |
$8$ |
(0, 4) |
$2^{14}\cdot 23^{2}\cdot 137$ |
$3$ |
$13.624623889$ |
$188.81073984363542$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$21.276372553$ |
$0$ |
$137$ |
| 8.4.1275346944.1 |
$x^{8} - 2 x^{7} + 4 x^{5} + 8 x^{4} - 4 x^{3} - 20 x^{2} - 12 x - 2$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$13.746861059$ |
$32.43724541951093$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$88.5691792187$ |
$3$ |
$31$ |
| 8.4.1275346944.2 |
$x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{3} - 2 x^{2} + 2 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$13.746861059$ |
$32.43724541951093$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$53.5813233866$ |
$3$ |
$31$ |
| 8.4.1275346944.3 |
$x^{8} - 2 x^{7} - 2 x^{6} + 14 x^{5} - 12 x^{4} - 14 x^{3} + 34 x^{2} - 10 x - 11$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 31^{2}$ |
$3$ |
$13.746861059$ |
$32.43724541951093$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
$[2]$ |
$2$ |
$5$ |
$54.3294214763$ |
$3$ |
$31$ |
| 8.0.1298153472.1 |
$x^{8} - 2 x^{7} - 8 x^{5} + 12 x^{4} + 20 x^{2} - 12 x + 14$ |
$8$ |
(0, 4) |
$2^{14}\cdot 3\cdot 7^{4}\cdot 11$ |
$4$ |
$13.7773520155$ |
$70.70630718186776$ |
|
|
? |
$C_2\wr A_4$ (as 8T38) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$26.8461655737$ |
$0$ |
$11$ |
| 8.2.1308737536.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} + 12 x^{4} - 6 x^{3} - 18 x^{2} - 10 x + 1$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 151$ |
$3$ |
$13.7913433184$ |
$198.2233831236216$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$66.5044093768$ |
$1$ |
$151$ |
| 8.2.1378074624.2 |
$x^{8} - 2 x^{7} + 4 x^{6} + 4 x^{5} - 4 x^{4} + 16 x^{3} + 4 x^{2} + 12 x + 6$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3\cdot 23^{2}\cdot 53$ |
$4$ |
$13.8806272536$ |
$203.40656818497104$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$52.835343321$ |
$1$ |
$53$ |
| 8.2.1495777280.1 |
$x^{8} - 2 x^{7} - 4 x^{5} - 4 x^{3} + 4 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 5\cdot 19\cdot 31^{2}$ |
$4$ |
$14.0235628918$ |
$182.5345762575138$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$53.3984908099$ |
$1$ |
$31$ |
| 8.4.1498300416.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 8 x^{4} - 16 x^{3} - 4 x^{2} + 12 x - 2$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 1129$ |
$3$ |
$14.0265176492$ |
$195.75375012004594$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$5$ |
$74.3432131625$ |
$3$ |
$1129$ |
| 8.4.1527267328.1 |
$x^{8} - 2 x^{7} - 6 x^{6} + 6 x^{5} + 4 x^{4} - 18 x^{3} - 6 x^{2} + 10 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 31^{2}\cdot 97$ |
$3$ |
$14.0601315042$ |
$184.44598520013162$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$73.0225431892$ |
$3$ |
$97$ |
| 8.4.1562001408.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} - 4 x^{4} - 2 x^{3} + 6 x^{2} - 6 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{4}\cdot 11\cdot 107$ |
$4$ |
$14.0997099143$ |
$199.87172063579976$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$5$ |
$77.8471802368$ |
$3$ |
$107$ |
| 8.2.1621737472.2 |
$x^{8} - 2 x^{7} + 8 x^{6} - 20 x^{5} + 32 x^{4} - 48 x^{3} + 32 x^{2} + 8 x - 10$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 31^{2}\cdot 103$ |
$3$ |
$14.1660108129$ |
$190.06491321982168$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$54.7472286241$ |
$1$ |
$103$ |
| 8.0.1672757248.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 6 x^{5} + 12 x^{4} - 14 x^{3} + 14 x^{2} - 14 x + 13$ |
$8$ |
(0, 4) |
$2^{14}\cdot 23^{2}\cdot 193$ |
$3$ |
$14.2209665549$ |
$224.10165556504342$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$27.6097574613$ |
$0$ |
$193$ |
| 8.2.1676132352.1 |
$x^{8} - 2 x^{7} + 4 x^{5} - 4 x^{4} - 4 x^{3} + 4 x^{2} - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{5}\cdot 421$ |
$3$ |
$14.2245500788$ |
$157.32019692678125$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$59.6354015098$ |
$1$ |
$421$ |
| 8.4.1779187712.1 |
$x^{8} - 2 x^{7} - 4 x^{6} + 8 x^{5} + 4 x^{4} - 12 x^{3} + 12 x - 2$ |
$8$ |
(4, 2) |
$2^{14}\cdot 31^{2}\cdot 113$ |
$3$ |
$14.331040433$ |
$199.0776754735287$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$86.1743354752$ |
$3$ |
$113$ |
| 8.4.1859272704.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 2 x^{5} - 4 x^{4} + 14 x^{3} - 2 x^{2} - 6 x + 1$ |
$8$ |
(4, 2) |
$2^{14}\cdot 3^{5}\cdot 467$ |
$3$ |
$14.4101295983$ |
$165.69212726353012$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$5$ |
$90.3751061922$ |
$3$ |
$467$ |
| 8.0.1905147904.1 |
$x^{8} - 2 x^{7} + 6 x^{6} + 2 x^{5} + 8 x^{4} + 2 x^{3} + 6 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{14}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$14.4541010691$ |
$62.11259613116975$ |
|
|
? |
$C_2^3:S_4$ (as 8T39) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$16.5213826187$ |
$0$ |
$31$ |
| 8.2.1932771328.1 |
$x^{8} - 2 x^{7} + 6 x^{6} - 14 x^{5} + 16 x^{4} - 22 x^{3} + 18 x^{2} - 2 x - 3$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 223$ |
$3$ |
$14.4801332809$ |
$240.89003900388417$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$83.0807447485$ |
$1$ |
$223$ |
| 8.2.1932771328.4 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 14 x^{3} - 38 x^{2} + 42 x - 19$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 23^{2}\cdot 223$ |
$3$ |
$14.4801332809$ |
$240.89003900388417$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$47.893824423$ |
$1$ |
$223$ |
| 8.6.2005254144.1 |
$x^{8} - 2 x^{7} - 6 x^{6} + 10 x^{5} + 12 x^{4} - 14 x^{3} - 10 x^{2} + 6 x + 1$ |
$8$ |
(6, 1) |
$-\,2^{14}\cdot 3^{4}\cdot 1511$ |
$3$ |
$14.5469242657$ |
$226.46200702523572$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$6$ |
$92.81864751$ |
$5$ |
$1511$ |
| 8.2.2005254144.2 |
$x^{8} - 2 x^{7} - 4 x^{6} + 12 x^{5} - 4 x^{4} - 4 x^{2} + 4 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{4}\cdot 1511$ |
$3$ |
$14.5469242657$ |
$226.46200702523572$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$87.7551910968$ |
$1$ |
$1511$ |
| 8.2.2005254144.3 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{3} - 8 x^{2} + 8 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 3^{4}\cdot 1511$ |
$3$ |
$14.5469242657$ |
$226.46200702523572$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
$[2]$ |
$2$ |
$4$ |
$49.432464755$ |
$1$ |
$1511$ |
| 8.0.2108178432.1 |
$x^{8} - 2 x^{7} - 8 x^{5} + 20 x^{4} - 4 x^{3} + 8 x^{2} - 36 x + 22$ |
$8$ |
(0, 4) |
$2^{14}\cdot 3^{2}\cdot 17\cdot 29^{2}$ |
$4$ |
$14.6382250825$ |
$129.35600051794452$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$19.9002997912$ |
$0$ |
$29$ |
| 8.2.2140782592.2 |
$x^{8} - 2 x^{7} + 4 x^{6} + 8 x^{5} - 28 x^{4} + 48 x^{3} - 32 x^{2} + 12 x - 2$ |
$8$ |
(2, 3) |
$-\,2^{14}\cdot 13\cdot 19\cdot 23^{2}$ |
$4$ |
$14.6663339834$ |
$253.52155329031183$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$4$ |
$86.3524209379$ |
$1$ |
$23$ |
