| 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 |
| 8.0.3276800000.1 |
$x^{8} + 2 x^{6} + x^{4} + 10 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}$ |
$2$ |
$15.467895946$ |
$26.74961219905688$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
trivial |
$2$ |
$3$ |
$44.8092227915$ |
| 8.2.7208960000.3 |
$x^{8} - 4 x^{6} - 2 x^{4} + 12 x^{2} - 11$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 11$ |
$3$ |
$17.0700218481$ |
$59.329587896765304$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$4$ |
$77.9057059157$ |
| 8.2.12451840000.4 |
$x^{8} - 18 x^{4} + 40 x^{2} - 19$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 19$ |
$3$ |
$18.2769696829$ |
$77.9743547584717$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$4$ |
$49.8587617388$ |
| 8.2.20639121408.4 |
$x^{8} + 2 x^{6} - 3 x^{4} - 6 x^{2} - 3$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{9}$ |
$2$ |
$19.4686752433$ |
$41.569219381653056$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$237.607680445$ |
| 8.2.20639121408.6 |
$x^{8} + 6 x^{6} + 9 x^{4} + 2 x^{2} - 3$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{9}$ |
$2$ |
$19.4686752433$ |
$41.569219381653056$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$4$ |
$356.236062906$ |
| 8.0.34398535680.3 |
$x^{8} + 10 x^{6} + 33 x^{4} + 38 x^{2} + 5$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{8}\cdot 5$ |
$3$ |
$20.7523600825$ |
$77.39923391345346$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
$[3]$ |
$[3]$ |
$2$ |
$3$ |
$78.6395613566$ |
| 8.2.38666240000.2 |
$x^{8} - 6 x^{6} + x^{4} - 26 x^{2} - 59$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 59$ |
$3$ |
$21.0579695222$ |
$137.40451229854133$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$4$ |
$292.690658586$ |
| 8.4.39976960000.2 |
$x^{8} - 14 x^{6} + 61 x^{4} - 134 x^{2} + 61$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{4}\cdot 61$ |
$3$ |
$21.1459022704$ |
$139.71399357258383$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$5$ |
$408.1647324$ |
| 8.4.39976960000.3 |
$x^{8} - 10 x^{6} + 37 x^{4} - 70 x^{2} + 61$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{4}\cdot 61$ |
$3$ |
$21.1459022704$ |
$139.71399357258383$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$5$ |
$226.870166322$ |
| 8.0.54103375872.2 |
$x^{8} + 14 x^{6} + 45 x^{4} - 46 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{2}\cdot 13$ |
$4$ |
$21.9610472104$ |
$132.18169313486644$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$1658.05161842$ |
| 8.0.54103375872.4 |
$x^{8} - 6 x^{6} + 5 x^{4} + 18 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{2}\cdot 13$ |
$4$ |
$21.9610472104$ |
$132.18169313486644$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$385.983143793$ |
| 8.0.87397761024.6 |
$x^{8} - 18 x^{6} + 93 x^{4} - 126 x^{2} + 189$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{5}\cdot 7^{3}$ |
$3$ |
$23.3177981417$ |
$78.47918025833762$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$467.821911784$ |
| 8.0.87397761024.7 |
$x^{8} + 6 x^{6} - 15 x^{4} - 90 x^{2} + 189$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{5}\cdot 7^{3}$ |
$3$ |
$23.3177981417$ |
$48.24807027615272$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$1581.17983925$ |
| 8.0.87397761024.11 |
$x^{8} + 8 x^{6} - 8 x^{4} - 96 x^{2} + 336$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{5}\cdot 7^{3}$ |
$3$ |
$23.3177981417$ |
$48.24807027615272$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$639.117303607$ |
| 8.2.89845137408.3 |
$x^{8} - 4 x^{6} + 14 x^{4} - 20 x^{2} - 27$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3\cdot 13^{4}$ |
$3$ |
$23.3984356184$ |
$49.95998398718719$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$4$ |
$340.610795452$ |
| 8.2.101580800000.1 |
$x^{8} - 6 x^{6} + 49 x^{4} - 250 x^{2} - 155$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{5}\cdot 31$ |
$3$ |
$23.760274494625612$ |
$148.9355375214321$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$150.90430257848288$ |
| 8.4.149741895680.2 |
$x^{8} - 6 x^{6} + x^{4} + 6 x^{2} + 5$ |
$8$ |
[4,2] |
$2^{20}\cdot 5\cdot 13^{4}$ |
$3$ |
$24.9412327881$ |
$98.90173052539754$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$5$ |
$552.981588745$ |
| 8.6.156433907712.2 |
$x^{8} - 10 x^{6} + 21 x^{4} + 10 x^{2} - 3$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 3\cdot 223^{2}$ |
$3$ |
$25.0779112887$ |
$206.920274502041$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$1049.68594494$ |
| 8.2.180224000000.3 |
$x^{8} - 10 x^{6} + 25 x^{4} + 50 x^{2} - 275$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{6}\cdot 11$ |
$3$ |
$25.525636366$ |
$88.71842695178528$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$206.977317682$ |
| 8.4.265420800000.1 |
$x^{8} - 6 x^{6} + 9 x^{4} - 270 x^{2} + 405$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{4}\cdot 5^{5}$ |
$3$ |
$26.7911816646$ |
$46.331687411530766$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
$[2]$ |
$2$ |
$5$ |
$708.013241096$ |
| 8.4.309586821120.2 |
$x^{8} - 18 x^{4} - 24 x^{2} + 45$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{10}\cdot 5$ |
$3$ |
$27.3116418119$ |
$92.951600308978$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2, 2]$ |
$2$ |
$5$ |
$1306.83432109$ |
| 8.2.311296000000.8 |
$x^{8} - 10 x^{6} - 35 x^{4} + 550 x^{2} - 475$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{6}\cdot 19$ |
$3$ |
$27.3304443397$ |
$116.59885635459175$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$313.579167415$ |
| 8.0.389328928768.3 |
$x^{8} - 2 x^{6} + x^{4} + 26 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{20}\cdot 13^{5}$ |
$2$ |
$28.1053879461$ |
$54.770600336184366$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
trivial |
trivial |
$2$ |
$3$ |
$793.003095523$ |
| 8.0.389328928768.4 |
$x^{8} + 2 x^{6} + 13 x^{4} + 26 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{20}\cdot 13^{5}$ |
$2$ |
$28.1053879461$ |
$67.82286225883439$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$3$ |
$360.117406671$ |
| 8.0.389328928768.6 |
$x^{8} + 6 x^{6} + 25 x^{4} + 34 x^{2} + 13$ |
$8$ |
[0,4] |
$2^{20}\cdot 13^{5}$ |
$2$ |
$28.1053879461$ |
$67.82286225883439$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[3]$ |
$[3]$ |
$2$ |
$3$ |
$146.762404236$ |
| 8.4.396492800000.2 |
$x^{8} - 14 x^{6} + 109 x^{4} - 550 x^{2} + 605$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$28.1695178177$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$336.049448398$ |
| 8.0.396492800000.4 |
$x^{8} + 16 x^{6} + 94 x^{4} + 440 x^{2} + 605$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$28.1695178177$ |
$88.71842695178528$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$59.9958306252$ |
| 8.0.553779200000.2 |
$x^{8} + 6 x^{6} - 171 x^{4} + 650 x^{2} + 845$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 13^{2}$ |
$3$ |
$29.3708881865$ |
$96.44709838247663$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$188.689132285$ |
| 8.0.553779200000.3 |
$x^{8} + 22 x^{6} + 181 x^{4} + 650 x^{2} + 845$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 13^{2}$ |
$3$ |
$29.3708881865$ |
$96.44709838247663$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$194.054878417$ |
| 8.6.573590994944.1 |
$x^{8} - 12 x^{6} + 20 x^{4} + 80 x^{2} - 176$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 11\cdot 223^{2}$ |
$3$ |
$29.5002224314$ |
$396.2221599052734$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$2601.06865037$ |
| 8.6.573590994944.4 |
$x^{8} - 6 x^{6} - 3 x^{4} + 46 x^{2} - 11$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 11\cdot 223^{2}$ |
$3$ |
$29.5002224314$ |
$396.2221599052734$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$2569.35085403$ |
| 8.2.583925760000.3 |
$x^{8} + 12 x^{6} + 20 x^{4} + 144 x^{2} - 176$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 5^{4}\cdot 11$ |
$4$ |
$29.5661451272$ |
$102.76186062932103$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$527.66456841$ |
| 8.2.583925760000.6 |
$x^{8} + 12 x^{6} - 18 x^{4} - 324 x^{2} - 891$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 5^{4}\cdot 11$ |
$4$ |
$29.5661451272$ |
$102.76186062932103$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$836.792170066$ |
| 8.2.583925760000.11 |
$x^{8} - 2 x^{6} + 5 x^{4} - 34 x^{2} - 11$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 5^{4}\cdot 11$ |
$4$ |
$29.5661451272$ |
$102.76186062932103$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$534.419455005$ |
| 8.8.677880266752.1 |
$x^{8} - 18 x^{6} + 57 x^{4} - 50 x^{2} + 13$ |
$8$ |
[8,0] |
$2^{20}\cdot 13\cdot 223^{2}$ |
$3$ |
$30.1227157722$ |
$430.7389000310977$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$7$ |
$4081.82804294$ |
| 8.2.808606236672.10 |
$x^{8} - 8 x^{6} + 6 x^{4} + 144 x^{2} - 27$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{3}\cdot 13^{4}$ |
$3$ |
$30.7940730611$ |
$49.95998398718719$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1191.03403396$ |
| 8.0.859963392000.4 |
$x^{8} + 2 x^{6} + 45 x^{4} + 250 x^{2} + 125$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{8}\cdot 5^{3}$ |
$3$ |
$31.0320163568$ |
$77.39923391345346$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
trivial |
$2$ |
$3$ |
$793.643482738$ |
| 8.4.868502994944.2 |
$x^{8} + 14 x^{6} + 21 x^{4} - 274 x^{2} + 261$ |
$8$ |
[4,2] |
$2^{20}\cdot 13^{4}\cdot 29$ |
$3$ |
$31.070369283871262$ |
$155.3319027115808$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$5$ |
$1309.564163091945$ |
| 8.4.868502994944.3 |
$x^{8} - 14 x^{6} + 73 x^{4} - 194 x^{2} + 261$ |
$8$ |
[4,2] |
$2^{20}\cdot 13^{4}\cdot 29$ |
$3$ |
$31.070369283871262$ |
$155.3319027115808$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$2$ |
$5$ |
$2802.8538417503732$ |
| 8.2.872284160000.1 |
$x^{8} + 12 x^{6} + 22 x^{4} - 484 x^{2} - 1331$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 11^{3}$ |
$3$ |
$31.0872458852$ |
$59.329587896765304$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$893.285491818$ |
| 8.0.946995200000.2 |
$x^{8} + 18 x^{6} + 121 x^{4} + 510 x^{2} + 1445$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 17^{2}$ |
$3$ |
$31.4082306974$ |
$110.29147654102222$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$338.41645259$ |
| 8.0.946995200000.3 |
$x^{8} + 34 x^{6} + 369 x^{4} + 1530 x^{2} + 1445$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 17^{2}$ |
$3$ |
$31.4082306974$ |
$110.29147654102222$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$193.265379293$ |
| 8.2.966656000000.1 |
$x^{8} - 10 x^{6} + 85 x^{4} - 550 x^{2} - 1475$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{6}\cdot 59$ |
$3$ |
$31.489009059953656$ |
$205.46766999992002$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$302.50075961452904$ |
| 8.6.990748082176.1 |
$x^{8} + 2 x^{6} - 63 x^{4} + 202 x^{2} - 171$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 19\cdot 223^{2}$ |
$3$ |
$31.586056293$ |
$520.7379379303951$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$3223.64404143$ |
| 8.4.999424000000.9 |
$x^{8} - 30 x^{6} + 385 x^{4} - 2150 x^{2} + 1525$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{6}\cdot 61$ |
$3$ |
$31.620499187798174$ |
$208.92115000831268$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$740.3955646346337$ |
| 8.4.999424000000.11 |
$x^{8} - 20 x^{6} + 190 x^{4} - 900 x^{2} + 1525$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{6}\cdot 61$ |
$3$ |
$31.620499187798174$ |
$208.92115000831268$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$612.3774044800797$ |
| 8.2.1008599040000.1 |
$x^{8} - 162 x^{4} - 1080 x^{2} - 1539$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 5^{4}\cdot 19$ |
$4$ |
$31.6566400991$ |
$135.05554412907307$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1584.89637476$ |
| 8.4.1182924800000.1 |
$x^{8} - 18 x^{6} + 201 x^{4} - 1330 x^{2} + 1805$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{5}\cdot 19^{2}$ |
$3$ |
$32.293836496$ |
$116.59885635459175$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$1004.80694569$ |
| 8.0.1182924800000.6 |
$x^{8} + 22 x^{6} + 161 x^{4} + 950 x^{2} + 1805$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 19^{2}$ |
$3$ |
$32.293836496$ |
$116.59885635459175$ |
|
|
? |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$333.427634572$ |
| 8.0.1679412953088.6 |
$x^{8} - 10 x^{6} + 57 x^{4} - 286 x^{2} + 637$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{6}\cdot 13^{3}$ |
$3$ |
$33.7399696283$ |
$124.84996997998198$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$[4]$ |
$6$ |
$3$ |
$2137.5612008$ |
