| 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 |
| 8.0.67108864.2 |
$x^{8} + 4 x^{4} - 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{26}$ |
$1$ |
$9.51365692002$ |
$14.050017282986396$ |
|
|
✓ |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$13.2231905688$ |
| 8.0.268435456.1 |
$x^{8} - 4 x^{6} + 10 x^{4} + 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{28}$ |
$1$ |
$11.313708499$ |
$14.050017282986396$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$21.1807989421$ |
| 8.0.342102016.6 |
$x^{8} - 2 x^{7} + 12 x^{5} - 2 x^{4} - 16 x^{3} + 24 x^{2} + 48 x + 20$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{4}$ |
$2$ |
$11.6619037897$ |
$23.679999262753405$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$11.0055627957$ |
| 8.0.534534400.2 |
$x^{8} - 2 x^{7} - 3 x^{6} + 14 x^{5} - x^{4} - 22 x^{3} + 10 x^{2} + 12 x + 20$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{2}\cdot 17^{4}$ |
$3$ |
$12.3309619442$ |
$37.44136633070439$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$17.5503091851$ |
| 8.0.534534400.3 |
$x^{8} - 2 x^{7} + 5 x^{6} - 8 x^{5} + 20 x^{4} - 36 x^{3} + 65 x^{2} - 66 x + 41$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{2}\cdot 17^{4}$ |
$3$ |
$12.3309619442$ |
$37.44136633070439$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$16.4873901267$ |
| 8.0.655360000.3 |
$x^{8} - 4 x^{7} + 12 x^{6} - 20 x^{5} + 22 x^{4} - 16 x^{3} + 8 x^{2} + 2$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{4}$ |
$2$ |
$12.6491106407$ |
$18.914832180063517$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$62.1183097555$ |
| 8.0.655360000.4 |
$x^{8} - 4 x^{6} - 4 x^{5} + 24 x^{4} - 40 x^{3} + 40 x^{2} - 20 x + 5$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{4}$ |
$2$ |
$12.6491106407$ |
$18.914832180063517$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$46.063440043$ |
| 8.0.829440000.2 |
$x^{8} - 2 x^{7} + 2 x^{5} + 8 x^{4} + 2 x^{3} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$13.0271112487$ |
$19.480074928505935$ |
|
|
✓ |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$35.7750629354$ |
| 8.0.829440000.3 |
$x^{8} - 2 x^{7} + 10 x^{6} - 20 x^{5} + 30 x^{4} - 52 x^{3} + 64 x^{2} - 40 x + 10$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$13.0271112487$ |
$19.480074928505935$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$30.2786214211$ |
| 8.0.1366263369.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 18 x^{4} - 9 x^{3} + 47 x^{2} + 54 x + 13$ |
$8$ |
[0,4] |
$3^{6}\cdot 37^{4}$ |
$2$ |
$13.8657001136$ |
$34.197332740531884$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$41.476887411$ |
| 8.0.1368408064.2 |
$x^{8} - x^{7} + 7 x^{6} - 8 x^{5} + 11 x^{4} + 5 x^{3} + 11 x^{2} - 2 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 17^{4}$ |
$2$ |
$13.8684189612$ |
$27.736837922354518$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$56.0168760267$ |
| 8.0.1368408064.3 |
$x^{8} + x^{6} + 2 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{14}\cdot 17^{4}$ |
$2$ |
$13.8684189612$ |
$27.736837922354518$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$146.707653129$ |
| 8.0.1677721600.2 |
$x^{8} - 8 x^{6} + 12 x^{4} + 20 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 5^{2}$ |
$2$ |
$14.2262352803$ |
$31.416793729804482$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$75.0232672451$ |
| 8.0.1677721600.3 |
$x^{8} - 4 x^{6} + 12 x^{4} + 40 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 5^{2}$ |
$2$ |
$14.2262352803$ |
$31.416793729804482$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$72.1052877958$ |
| 8.0.1766100625.2 |
$x^{8} - 2 x^{7} + 12 x^{6} - 13 x^{5} + 24 x^{4} - 13 x^{3} + 12 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 41^{4}$ |
$2$ |
$14.3178210633$ |
$21.410136276713814$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$83.3183166589$ |
| 8.0.2304000000.1 |
$x^{8} - 2 x^{7} - 2 x^{5} + 4 x^{4} + 2 x^{3} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$14.8016560898$ |
$19.480074928505935$ |
|
|
✓ |
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$19.959184944$ |
| 8.0.2304000000.2 |
$x^{8} - 2 x^{7} + 2 x^{6} - 14 x^{4} + 28 x^{2} + 24 x + 6$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{2}\cdot 5^{6}$ |
$3$ |
$14.8016560898$ |
$19.480074928505935$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$23.5823516394$ |
| 8.0.2385443281.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 2 x^{5} - 9 x^{4} + 2 x^{3} + 5 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$13^{4}\cdot 17^{4}$ |
$2$ |
$14.8660687473$ |
$30.186194580660594$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$38.2639392965$ |
| 8.0.2415919104.3 |
$x^{8} - 8 x^{5} + 36 x^{4} - 64 x^{3} + 64 x^{2} - 32 x + 6$ |
$8$ |
[0,4] |
$2^{28}\cdot 3^{2}$ |
$2$ |
$14.8896777456$ |
$24.33534378135327$ |
|
|
✓ |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$74.7621102798$ |
| 8.0.2415919104.4 |
$x^{8} - 8 x^{6} - 8 x^{5} + 24 x^{4} + 64 x^{3} + 56 x^{2} + 16 x + 2$ |
$8$ |
[0,4] |
$2^{28}\cdot 3^{2}$ |
$2$ |
$14.8896777456$ |
$24.33534378135327$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$64.2462187806$ |
| 8.0.2621440000.3 |
$x^{8} - 8 x^{6} + 30 x^{4} - 40 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{4}$ |
$2$ |
$15.0424123723$ |
$24.529502540692157$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$92.8340447505$ |
| 8.0.2621440000.13 |
$x^{8} - 4 x^{6} + 10 x^{4} + 20 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{4}$ |
$2$ |
$15.0424123723$ |
$24.529502540692157$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$131.354817675$ |
| 8.0.3186376704.5 |
$x^{8} - 3 x^{6} + 8 x^{4} - 6 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$15.4138858981$ |
$30.827771796137323$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$50.228691141$ |
| 8.0.3186376704.6 |
$x^{8} - 2 x^{6} + 2 x^{4} + 20 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$15.4138858981$ |
$30.827771796137323$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$117.994234012$ |
| 8.0.3613452544.1 |
$x^{8} - 2 x^{7} - x^{6} - 34 x^{3} + 11 x^{2} + 188 x + 157$ |
$8$ |
[0,4] |
$2^{8}\cdot 13^{2}\cdot 17^{4}$ |
$3$ |
$15.6581444217$ |
$60.37238916132119$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$44.1173611467$ |
| 8.0.3613452544.2 |
$x^{8} - 5 x^{6} - 11 x^{4} - 48 x^{3} + 36 x^{2} + 240 x + 212$ |
$8$ |
[0,4] |
$2^{8}\cdot 13^{2}\cdot 17^{4}$ |
$3$ |
$15.6581444217$ |
$60.37238916132119$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$44.1429509142$ |
| 8.0.3991080625.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 12 x^{5} + 19 x^{4} - 18 x^{3} + 27 x^{2} - 7 x + 7$ |
$8$ |
[0,4] |
$5^{4}\cdot 7^{2}\cdot 19^{4}$ |
$3$ |
$15.853907233$ |
$38.561447133599124$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$21.7487431742$ |
| 8.0.3991080625.2 |
$x^{8} - x^{7} + 5 x^{6} - 3 x^{5} + 20 x^{4} + 5 x^{3} + 45 x^{2} + 15 x + 25$ |
$8$ |
[0,4] |
$5^{4}\cdot 7^{2}\cdot 19^{4}$ |
$3$ |
$15.853907233$ |
$38.561447133599124$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$27.5585815662$ |
| 8.0.4569760000.7 |
$x^{8} - 2 x^{7} + 3 x^{6} - 8 x^{5} + 28 x^{4} - 42 x^{3} + 11 x^{2} + 20 x + 5$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$16.1245154966$ |
$45.78413496570207$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$52.0946915903$ |
| 8.0.4569760000.8 |
$x^{8} - 2 x^{7} + x^{6} + 12 x^{5} - 7 x^{4} - 20 x^{3} + 20 x^{2} + 40 x + 20$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$16.1245154966$ |
$45.78413496570207$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$80.6142380077$ |
| 8.0.5435817984.8 |
$x^{8} - 4 x^{6} + 20 x^{4} - 8 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}$ |
$2$ |
$16.4781371513$ |
$24.33534378135327$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$76.4628919919$ |
| 8.0.5435817984.9 |
$x^{8} - 4 x^{4} - 12 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}$ |
$2$ |
$16.4781371513$ |
$24.33534378135327$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$88.9784219508$ |
| 8.0.5435817984.10 |
$x^{8} + 36 x^{4} - 108 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{26}\cdot 3^{4}$ |
$2$ |
$16.4781371513$ |
$24.33534378135327$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$64.5578477059$ |
| 8.0.5473632256.7 |
$x^{8} - x^{6} - 2 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{4}$ |
$2$ |
$16.4924225025$ |
$32.984845004941285$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$170.938544508$ |
| 8.0.5473632256.8 |
$x^{8} - 8 x^{6} + 34 x^{4} - 72 x^{2} + 64$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{4}$ |
$2$ |
$16.4924225025$ |
$32.984845004941285$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$170.609444956$ |
| 8.0.5473632256.9 |
$x^{8} - 8 x^{6} + 51 x^{4} - 136 x^{2} + 289$ |
$8$ |
[0,4] |
$2^{16}\cdot 17^{4}$ |
$2$ |
$16.4924225025$ |
$33.48857611437076$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$4$ |
$3$ |
$45.5644963366$ |
| 8.0.7269949696.1 |
$x^{8} - 2 x^{7} + x^{6} + 12 x^{5} - 7 x^{4} - 12 x^{3} + 52 x^{2} + 24 x + 4$ |
$8$ |
[0,4] |
$2^{8}\cdot 73^{4}$ |
$2$ |
$17.0880074906$ |
$49.94846437712294$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$133.797677094$ |
| 8.0.7438545009.1 |
$x^{8} - 6 x^{6} - 12 x^{5} + 23 x^{4} + 78 x^{3} + 3 x^{2} - 411 x + 367$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 37^{4}$ |
$3$ |
$17.1370474566$ |
$68.74813805509002$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$52.4212437466$ |
| 8.0.7438545009.2 |
$x^{8} - 3 x^{7} - 5 x^{6} + 27 x^{5} - 23 x^{4} - 6 x^{3} + 84 x^{2} - 360 x + 432$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{2}\cdot 37^{4}$ |
$3$ |
$17.1370474566$ |
$68.74813805509002$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$198.395438613$ |
| 8.0.8653650625.1 |
$x^{8} + 9 x^{6} - 18 x^{5} + 14 x^{4} - 20 x^{3} + 30 x^{2} - 20 x + 5$ |
$8$ |
[0,4] |
$5^{4}\cdot 61^{4}$ |
$2$ |
$17.4642491966$ |
$26.115143751039085$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$2$ |
$3$ |
$111.97909024$ |
| 8.0.9475854336.13 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 24 x^{4} - 56 x^{3} - 17 x^{2} + 46 x + 19$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$17.6635217327$ |
$33.54000593239012$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$90.6500778691$ |
| 8.0.9475854336.14 |
$x^{8} - 4 x^{7} + 8 x^{6} - 7 x^{4} - 12 x^{3} + 50 x^{2} + 80 x + 28$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$17.6635217327$ |
$33.54000593239012$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$126.444530989$ |
| 8.0.9855525625.1 |
$x^{8} - 2 x^{7} + 3 x^{6} - 7 x^{5} + 8 x^{4} - 7 x^{3} + 51 x^{2} - 5 x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 11^{2}\cdot 19^{4}$ |
$3$ |
$17.7504747847$ |
$48.339332189090904$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$35.0485217432$ |
| 8.0.9855525625.2 |
$x^{8} - x^{7} + 4 x^{6} - 10 x^{5} + 19 x^{4} - 30 x^{3} + 60 x^{2} - 40 x + 80$ |
$8$ |
[0,4] |
$5^{4}\cdot 11^{2}\cdot 19^{4}$ |
$3$ |
$17.7504747847$ |
$48.339332189090904$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$2$ |
$3$ |
$29.9420194007$ |
| 8.0.10093618089.2 |
$x^{8} - x^{7} - 6 x^{6} + 20 x^{5} - 32 x^{4} - 51 x^{3} + 228 x^{2} - 240 x + 129$ |
$8$ |
[0,4] |
$3^{6}\cdot 61^{4}$ |
$2$ |
$17.8035192528$ |
$49.755181783405924$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[2]$ |
$6$ |
$3$ |
$131.269561521$ |
| 8.0.11051265625.2 |
$x^{8} - x^{7} + 8 x^{6} - 5 x^{5} + 21 x^{4} + 5 x^{3} + 12 x^{2} + 3 x + 1$ |
$8$ |
[0,4] |
$5^{6}\cdot 29^{4}$ |
$2$ |
$18.0063837774$ |
$41.78553833475025$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$20.525602563$ |
| 8.0.11051265625.3 |
$x^{8} - 2 x^{7} - 2 x^{6} - 4 x^{5} + 40 x^{4} - 14 x^{3} - 37 x^{2} - 142 x + 236$ |
$8$ |
[0,4] |
$5^{6}\cdot 29^{4}$ |
$2$ |
$18.0063837774$ |
$41.78553833475025$ |
|
|
|
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$26.2355904197$ |
| 8.0.11209515625.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 5 x^{5} - 4 x^{4} + 10 x^{3} - 7 x^{2} - 14 x + 16$ |
$8$ |
[0,4] |
$5^{6}\cdot 7^{2}\cdot 11^{4}$ |
$3$ |
$18.0384142338$ |
$29.34086180290925$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$73.1797759177$ |
| 8.0.11209515625.2 |
$x^{8} - 4 x^{7} + 14 x^{5} - x^{4} - 26 x^{3} - 5 x^{2} + 21 x + 26$ |
$8$ |
[0,4] |
$5^{6}\cdot 7^{2}\cdot 11^{4}$ |
$3$ |
$18.0384142338$ |
$29.34086180290925$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
$[4]$ |
$2$ |
$3$ |
$53.9336554629$ |
| 8.0.11341398016.3 |
$x^{8} - 12 x^{6} + 28 x^{4} + 104 x^{2} + 169$ |
$8$ |
[0,4] |
$2^{26}\cdot 13^{2}$ |
$2$ |
$18.0648069148$ |
$50.658057734962696$ |
|
|
? |
$C_2^3 : C_4 $ (as 8T19) |
trivial |
$4$ |
$3$ |
$206.862391313$ |
