| 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 $p$ |
| 8.0.10784768.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 2633$ |
$2$ |
$7.57009536994$ |
$145.13442045221387$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$1.48066499263$ |
$0$ |
$2633$ |
| 8.0.14258176.2 |
$x^{8} - 2 x^{7} + x^{6} + x^{4} + x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 59^{2}$ |
$2$ |
$7.83895184211$ |
$21.72556098240043$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
trivial |
$2$ |
$3$ |
$2.14010881952$ |
$0$ |
$59$ |
| 8.0.18911232.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 12 x^{5} + 17 x^{4} - 12 x^{3} + 5 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{5}\cdot 19$ |
$3$ |
$8.12063476098$ |
$28.103650443517264$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$6.13315917971$ |
$0$ |
$19$ |
| 8.0.20123648.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 17^{3}$ |
$2$ |
$8.18395700311$ |
$23.679999262753405$ |
|
|
? |
$C_4\wr C_2$ (as 8T17) |
trivial |
trivial |
$2$ |
$3$ |
$1.81338098584$ |
$0$ |
$17$ |
| 8.0.32182272.2 |
$x^{8} - 2 x^{7} + 3 x^{6} + 4 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 97$ |
$3$ |
$8.67864827177$ |
$48.249352327259274$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$10.6790810115$ |
$0$ |
$97$ |
| 8.0.39063552.1 |
$x^{8} + 2 x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 11\cdot 17^{2}$ |
$4$ |
$8.89142698184$ |
$66.9925368977769$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$5.01199318449$ |
$0$ |
$17$ |
| 8.0.40931328.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 2 x^{3} + 2 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 3331$ |
$3$ |
$8.94348904642$ |
$282.7437001950707$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$3.30880467249$ |
$0$ |
$3331$ |
| 8.0.42799104.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 8 x^{4} - 4 x^{3} - 5 x^{2} + 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{5}\cdot 43$ |
$3$ |
$8.99351233489$ |
$42.27855760797761$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$15.6809550844$ |
$0$ |
$43$ |
| 8.0.56070144.3 |
$x^{8} + 8 x^{4} - 24 x^{2} + 16$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 13^{2}$ |
$3$ |
$9.30232393605$ |
$17.663521732655695$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
trivial |
$6$ |
$3$ |
$8.33817267848$ |
$0$ |
$13$ |
| 8.0.62263296.1 |
$x^{8} - 2 x^{7} + x^{6} + 3 x^{4} - 4 x^{3} - x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{3}\cdot 563$ |
$3$ |
$9.42494909829$ |
$241.79129136919119$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$5.39102364575$ |
$0$ |
$563$ |
| 8.0.64000000.1 |
$x^{8} - 2 x^{6} + 4 x^{4} - 8 x^{2} + 16$ |
$8$ |
(0, 4) |
$2^{12}\cdot 5^{6}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
trivial |
$10$ |
$3$ |
$18.013034165$ |
$0$ |
$5$ |
| 8.0.73699328.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{3} + 2 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 19\cdot 947$ |
$3$ |
$9.62571371742$ |
$379.3995255663876$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$4.15555324926$ |
$0$ |
$947$ |
| 8.0.75829248.1 |
$x^{8} - 2 x^{7} + x^{6} - x^{4} + x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{2}\cdot 11^{2}\cdot 17$ |
$4$ |
$9.66005487851$ |
$66.9925368977769$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$6.02440295549$ |
$0$ |
$17$ |
| 8.0.80613376.1 |
$x^{8} - 2 x^{5} + 4 x^{3} + 3 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 19681$ |
$2$ |
$9.73421397727$ |
$396.79717740931574$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$6.2065139528$ |
$0$ |
$19681$ |
| 8.0.82120704.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 11 x^{4} - 12 x^{3} + 11 x^{2} - 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 41\cdot 163$ |
$4$ |
$9.75678158455$ |
$400.48970024209115$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$6.23160113776$ |
$0$ |
$163$ |
| 8.0.83038208.1 |
$x^{8} - 2 x^{7} + x^{6} - 4 x^{5} + 5 x^{4} + 3 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 11\cdot 19\cdot 97$ |
$4$ |
$9.77034155143$ |
$402.72074692024495$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$4.83207796746$ |
$0$ |
$97$ |
| 8.0.101912576.1 |
$x^{8} - 2 x^{6} + x^{4} - 4 x^{3} + 4 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 139\cdot 179$ |
$3$ |
$10.0237095149$ |
$446.1479575208207$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$9.02134845986$ |
$0$ |
$179$ |
| 8.0.109416448.1 |
$x^{8} - 2 x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{3} - x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 26713$ |
$2$ |
$10.1131238656$ |
$462.28129964340974$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$3.80402093255$ |
$0$ |
$26713$ |
| 8.0.113938432.1 |
$x^{8} - 2 x^{5} - 2 x^{4} + 3 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 27817$ |
$2$ |
$10.1644475646$ |
$471.7372149830878$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$7.57209496263$ |
$0$ |
$27817$ |
| 8.0.116822016.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 2 x^{3} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{2}\cdot 3169$ |
$3$ |
$10.1962526239$ |
$275.78252301405905$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$4.05622585169$ |
$0$ |
$3169$ |
| 8.0.119443456.1 |
$x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 2 x^{4} - 2 x^{3} + 4 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 11^{2}\cdot 241$ |
$3$ |
$10.2245757101$ |
$217.17773771911808$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.15200928286$ |
$0$ |
$241$ |
| 8.0.119771136.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 7 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$10.228077759$ |
$28.103650443517264$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
trivial |
trivial |
$2$ |
$3$ |
$8.1166878033$ |
$0$ |
$19$ |
| 8.0.131272704.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 6 x^{4} - 2 x^{3} + 4 x^{2} - 4 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{3}\cdot 1187$ |
$3$ |
$10.3459840344$ |
$351.084629792807$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$10.2960563385$ |
$0$ |
$1187$ |
| 8.0.133042176.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 6 x^{4} - 6 x^{3} + 4 x^{2} - 4 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 401$ |
$3$ |
$10.363314246$ |
$245.06362467562292$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.8008672037$ |
$0$ |
$401$ |
| 8.0.135696384.2 |
$x^{8} - 2 x^{7} + 7 x^{6} - 8 x^{5} + 11 x^{4} - 12 x^{3} + 7 x^{2} - 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 409$ |
$3$ |
$10.388935127$ |
$99.07572861200669$ |
|
|
✓ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$24.5352227264$ |
$0$ |
$409$ |
| 8.0.143659008.2 |
$x^{8} - 4 x^{7} + 12 x^{6} - 22 x^{5} + 32 x^{4} - 32 x^{3} + 31 x^{2} - 18 x + 19$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 433$ |
$3$ |
$10.4632501396$ |
$101.94115949899727$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$14.224263349$ |
$0$ |
$433$ |
| 8.0.146313216.6 |
$x^{8} - 10 x^{6} + 36 x^{4} - 40 x^{2} + 16$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$10.4872215901$ |
$17.058268835716344$ |
|
|
? |
$D_4\times C_2$ (as 8T9) |
trivial |
trivial |
$6$ |
$3$ |
$24.0529722782$ |
$0$ |
$7$ |
| 8.0.151621632.1 |
$x^{8} - 2 x^{7} - 3 x^{6} + 13 x^{4} - 3 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 457$ |
$3$ |
$10.5340444322$ |
$104.72821969268837$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$25.7568314736$ |
$0$ |
$457$ |
| 8.0.152702976.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 11 x^{4} - 8 x^{3} + 5 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 17^{2}\cdot 43$ |
$4$ |
$10.5434061748$ |
$132.4537655183876$ |
|
|
✓ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$7.20820764383$ |
$0$ |
$43$ |
| 8.0.156700672.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 5 x^{4} - 4 x^{3} + 5 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 67\cdot 571$ |
$3$ |
$10.5775200535$ |
$553.2232822287941$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$9.19900378005$ |
$0$ |
$571$ |
| 8.0.162172928.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + x^{4} + x^{2} - 6 x + 9$ |
$8$ |
(0, 4) |
$2^{12}\cdot 17^{2}\cdot 137$ |
$3$ |
$10.6230027703$ |
$136.49908424601244$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$10.043698927$ |
$0$ |
$137$ |
| 8.0.162238464.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 14 x^{4} - 16 x^{3} + 13 x^{2} - 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{5}\cdot 163$ |
$3$ |
$10.6235392856$ |
$82.3151429520076$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$33.9219694587$ |
$0$ |
$163$ |
| 8.0.163975168.1 |
$x^{8} - 4 x^{5} + 5 x^{4} - 4 x^{3} + 4 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 7^{2}\cdot 19\cdot 43$ |
$4$ |
$10.6376882967$ |
$213.89717155680202$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$7.13098804089$ |
$0$ |
$43$ |
| 8.0.168431616.1 |
$x^{8} - 4 x^{5} - 3 x^{4} + 4 x^{3} + 4 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{3}\cdot 1523$ |
$3$ |
$10.6734040903$ |
$397.68243471597935$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$9.23645889778$ |
$0$ |
$1523$ |
| 8.0.170037248.1 |
$x^{8} - 4 x^{7} + 10 x^{6} - 14 x^{5} + 16 x^{4} - 12 x^{3} + 7 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 41513$ |
$2$ |
$10.6860698447$ |
$576.2846518865482$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$6.23898709232$ |
$0$ |
$41513$ |
| 8.0.173903872.1 |
$x^{8} - 2 x^{7} + x^{6} - x^{4} + 3 x^{2} - 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 42457$ |
$2$ |
$10.7161468521$ |
$582.8001372683435$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$7.43768225436$ |
$0$ |
$42457$ |
| 8.0.185438208.1 |
$x^{8} - 2 x^{5} + x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 15091$ |
$3$ |
$10.8025156142$ |
$601.8172480080643$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$10.2540540221$ |
$0$ |
$15091$ |
| 8.0.190451712.1 |
$x^{8} - 2 x^{7} + x^{6} - 4 x^{5} + 5 x^{4} + 4 x^{3} - 5 x^{2} - 2 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 11\cdot 1409$ |
$4$ |
$10.8385980342$ |
$609.8983521866575$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$12.9046494932$ |
$0$ |
$1409$ |
| 8.0.199856128.1 |
$x^{8} - 2 x^{7} + 7 x^{6} - 8 x^{5} + 12 x^{4} - 6 x^{3} + 4 x^{2} + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 59\cdot 827$ |
$3$ |
$10.9040964334$ |
$624.7751595574204$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.54709855805$ |
$0$ |
$827$ |
| 8.0.202346496.1 |
$x^{8} + 2 x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 5 x^{2} - 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{2}\cdot 11\cdot 499$ |
$4$ |
$10.9209887826$ |
$362.9545426082996$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$13.6338712845$ |
$0$ |
$499$ |
| 8.0.202870784.1 |
$x^{8} - 2 x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{3} + 5 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 49529$ |
$2$ |
$10.9245218703$ |
$629.4696180118624$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.39044766968$ |
$0$ |
$49529$ |
| 8.0.209522688.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 8 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 17^{2}\cdot 59$ |
$4$ |
$10.968667765$ |
$155.15153882575578$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$14.1620419372$ |
$0$ |
$59$ |
| 8.0.214798336.5 |
$x^{8} + 8 x^{4} + 8 x^{2} + 16$ |
$8$ |
(0, 4) |
$2^{12}\cdot 229^{2}$ |
$2$ |
$11.0028163487$ |
$42.80186911806539$ |
|
|
? |
$S_4\times C_2$ (as 8T24) |
trivial |
trivial |
$2$ |
$3$ |
$10.7477801893$ |
$0$ |
$229$ |
| 8.0.215912448.1 |
$x^{8} - 2 x^{7} - x^{6} + 8 x^{5} - 7 x^{4} - 4 x^{3} + 13 x^{2} - 10 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{2}\cdot 5857$ |
$3$ |
$11.0099338635$ |
$374.9239922971055$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.32930764785$ |
$0$ |
$5857$ |
| 8.0.217976832.2 |
$x^{8} - 2 x^{7} + 9 x^{6} - 20 x^{5} + 28 x^{4} - 30 x^{3} + 24 x^{2} - 12 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{6}\cdot 73$ |
$3$ |
$11.0230376822$ |
$55.086777132635675$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$29.4223722539$ |
$0$ |
$73$ |
| 8.0.222728192.1 |
$x^{8} - 2 x^{7} - x^{6} + 10 x^{4} - 6 x^{3} - 8 x^{2} + 4 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 54377$ |
$2$ |
$11.0527894996$ |
$659.557427370809$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$13.9942723771$ |
$0$ |
$54377$ |
| 8.0.223285248.2 |
$x^{8} - 4 x^{7} + 2 x^{6} + 2 x^{5} + 8 x^{4} - 4 x^{3} + x^{2} - 6 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3^{4}\cdot 673$ |
$3$ |
$11.0562411821$ |
$127.09051892253804$ |
|
|
|
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
trivial |
trivial |
$6$ |
$3$ |
$53.4677238188$ |
$0$ |
$673$ |
| 8.0.226791424.1 |
$x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 6 x^{3} + 8 x^{2} - 4 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 17\cdot 3257$ |
$3$ |
$11.0777951131$ |
$665.5463920719577$ |
|
|
✓ |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$5.33843539481$ |
$0$ |
$3257$ |
| 8.0.228462592.1 |
$x^{8} - 2 x^{7} + x^{6} + x^{4} + 4 x^{3} + x^{2} + 2 x + 3$ |
$8$ |
(0, 4) |
$2^{12}\cdot 17^{2}\cdot 193$ |
$3$ |
$11.0879660488$ |
$162.01234520862909$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$3$ |
$10.9606990579$ |
$0$ |
$193$ |
| 8.0.231739392.1 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} - x^{4} + 5 x^{2} + 2 x + 1$ |
$8$ |
(0, 4) |
$2^{12}\cdot 3\cdot 18859$ |
$3$ |
$11.1077215153$ |
$672.7674189495208$ |
|
|
? |
$S_4\wr C_2$ (as 8T47) |
trivial |
trivial |
$2$ |
$3$ |
$8.21422779351$ |
$0$ |
$18859$ |
