| 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 |
| 8.2.655360000.2 |
$x^{8} - 2 x^{6} - 3 x^{4} - 6 x^{2} - 1$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}$ |
$2$ |
$12.6491106407$ |
$20.371270394561137$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$2$ |
$4$ |
$24.3691119794$ |
| 8.0.29132587008.1 |
$x^{8} - 8 x^{6} + 32 x^{4} - 28 x^{2} + 7$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$20.3257875317$ |
$67.9074259225896$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$6$ |
$3$ |
$241.680907066$ |
| 8.0.29132587008.11 |
$x^{8} + 10 x^{6} + 31 x^{4} + 42 x^{2} + 63$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$20.3257875317$ |
$67.9074259225896$ |
|
|
|
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$6$ |
$3$ |
$1234.03553345$ |
| 8.2.29948379136.7 |
$x^{8} - 4 x^{6} + 8 x^{2} - 9$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 13^{4}$ |
$2$ |
$20.3960780544$ |
$32.84768651624708$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$2$ |
$4$ |
$120.15634248$ |
| 8.0.36044800000.1 |
$x^{8} + 8 x^{6} + 16 x^{4} + 20 x^{2} + 55$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 11$ |
$3$ |
$20.8739830999$ |
$101.03153630618483$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$28.7336793351$ |
| 8.4.36044800000.2 |
$x^{8} - 6 x^{6} + 19 x^{4} - 50 x^{2} + 55$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{5}\cdot 11$ |
$3$ |
$20.8739830999$ |
$101.03153630618483$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$222.196444205$ |
| 8.4.46530560000.2 |
$x^{8} - 6 x^{6} - 19 x^{4} - 66 x^{2} + 71$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{4}\cdot 71$ |
$3$ |
$21.550992954152623$ |
$171.6513754144456$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$396.7772938841415$ |
| 8.2.52144635904.2 |
$x^{8} + 4 x^{6} - 8 x^{4} - 8 x^{2} - 1$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 223^{2}$ |
$2$ |
$21.860052715814263$ |
$136.04592652475563$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$179.1994650807335$ |
| 8.6.52144635904.3 |
$x^{8} - 2 x^{6} - 5 x^{4} + 10 x^{2} - 1$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 223^{2}$ |
$2$ |
$21.8600527158$ |
$136.04592652475563$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$6$ |
$750.097510111$ |
| 8.2.53084160000.4 |
$x^{8} + 6 x^{6} - 27 x^{4} + 162 x^{2} - 81$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$21.9089023002$ |
$35.28407533810358$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$169.813322687$ |
| 8.2.58327040000.3 |
$x^{8} - 4 x^{6} + 16 x^{4} - 24 x^{2} - 89$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 89$ |
$3$ |
$22.16836901764578$ |
$192.18218053831305$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$330.62443820118955$ |
| 8.0.62259200000.1 |
$x^{8} + 6 x^{6} - 11 x^{4} - 30 x^{2} + 95$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{5}\cdot 19$ |
$3$ |
$22.3498926757$ |
$132.78145244223714$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$68.4453615059$ |
| 8.4.62259200000.2 |
$x^{8} - 12 x^{6} + 56 x^{4} - 120 x^{2} + 95$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{5}\cdot 19$ |
$3$ |
$22.3498926757$ |
$132.78145244223714$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$453.757092911$ |
| 8.4.103195607040.2 |
$x^{8} - 10 x^{6} + 33 x^{4} - 42 x^{2} + 15$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{9}\cdot 5$ |
$3$ |
$23.8071633196$ |
$105.85222601431074$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1047.59935763$ |
| 8.4.103195607040.3 |
$x^{8} - 6 x^{6} + 15 x^{4} - 22 x^{2} + 15$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{9}\cdot 5$ |
$3$ |
$23.8071633196$ |
$105.85222601431074$ |
|
|
✓ |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1088.08951777$ |
| 8.0.103195607040.7 |
$x^{8} + 8 x^{6} + 24 x^{4} + 156 x^{2} + 15$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{9}\cdot 5$ |
$3$ |
$23.8071633196$ |
$105.85222601431074$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$253.585184156$ |
| 8.0.103195607040.12 |
$x^{8} + 12 x^{6} + 60 x^{4} + 176 x^{2} + 240$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{9}\cdot 5$ |
$3$ |
$23.8071633196$ |
$105.85222601431074$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$191.791411924$ |
| 8.4.114688000000.1 |
$x^{8} - 8 x^{6} - 8 x^{5} + 10 x^{4} + 24 x^{3} - 32 x - 12$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{6}\cdot 7$ |
$3$ |
$24.1234682832$ |
$153.42553140168474$ |
|
|
? |
$S_8$ (as 8T50) |
trivial |
trivial |
$2$ |
$5$ |
$930.650366561$ |
| 8.0.162310127616.3 |
$x^{8} + 2 x^{6} - 5 x^{4} + 6 x^{2} + 39$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{5}\cdot 7^{2}\cdot 13$ |
$4$ |
$25.193772444633453$ |
$198.10468593061537$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$753.8306933848534$ |
| 8.0.162310127616.7 |
$x^{8} - 4 x^{6} - 20 x^{4} - 48 x^{2} + 624$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{5}\cdot 7^{2}\cdot 13$ |
$4$ |
$25.193772444633453$ |
$198.10468593061537$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
trivial |
$6$ |
$3$ |
$1392.3168962338611$ |
| 8.0.262193283072.16 |
$x^{8} - 12 x^{6} + 24 x^{4} + 72 x^{2} + 63$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{6}\cdot 7^{3}$ |
$3$ |
$26.7502407632$ |
$54.94435407942486$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$883.049832992$ |
| 8.0.262193283072.19 |
$x^{8} - 24 x^{6} + 192 x^{4} - 540 x^{2} + 567$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{6}\cdot 7^{3}$ |
$3$ |
$26.7502407632$ |
$54.94435407942486$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$1082.66520497$ |
| 8.2.477757440000.24 |
$x^{8} + 6 x^{6} - 33 x^{4} + 54 x^{2} - 9$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$28.8337369696$ |
$46.43645462353605$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$726.139109237$ |
| 8.2.477757440000.25 |
$x^{8} + 12 x^{6} + 48 x^{4} + 72 x^{2} - 9$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$28.8337369696$ |
$46.43645462353605$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$583.564126338$ |
| 8.4.507904000000.5 |
$x^{8} - 20 x^{6} + 160 x^{4} - 600 x^{2} + 775$ |
$8$ |
[4,2] |
$2^{20}\cdot 5^{6}\cdot 31$ |
$3$ |
$29.05512205330948$ |
$169.6060974407857$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2, 2]$ |
$2$ |
$5$ |
$1124.907631081904$ |
| 8.0.507904000000.9 |
$x^{8} + 10 x^{6} - 35 x^{4} - 50 x^{2} + 775$ |
$8$ |
[0,4] |
$2^{20}\cdot 5^{6}\cdot 31$ |
$3$ |
$29.05512205330948$ |
$169.6060974407857$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$83.61859519607$ |
| 8.2.629800960000.9 |
$x^{8} - 2 x^{6} - 23 x^{4} - 1426 x^{2} - 961$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$29.8469813893$ |
$113.42243332841178$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$359.859599185$ |
| 8.2.629800960000.10 |
$x^{8} - 24 x^{6} + 168 x^{4} - 868 x^{2} - 961$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$29.8469813893$ |
$113.42243332841178$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$475.934997387$ |
| 8.4.688812720128.2 |
$x^{8} - 18 x^{6} + 123 x^{4} - 326 x^{2} + 207$ |
$8$ |
[4,2] |
$2^{20}\cdot 13^{4}\cdot 23$ |
$3$ |
$30.1830167559$ |
$157.5319704625119$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2414.37482167$ |
| 8.0.688812720128.5 |
$x^{8} + 12 x^{6} + 48 x^{4} + 72 x^{2} + 23$ |
$8$ |
[0,4] |
$2^{20}\cdot 13^{4}\cdot 23$ |
$3$ |
$30.1830167559$ |
$157.5319704625119$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[4]$ |
$[4]$ |
$2$ |
$3$ |
$239.930053903$ |
| 8.2.741637881856.6 |
$x^{8} - 2 x^{6} - 23 x^{4} - 34 x^{2} - 1$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 29^{4}$ |
$2$ |
$30.4630924235$ |
$49.06051582925188$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$2$ |
$4$ |
$941.668897853$ |
| 8.6.886458810368.3 |
$x^{8} - 6 x^{6} - 33 x^{4} + 74 x^{2} - 17$ |
$8$ |
[6,1] |
$-\,2^{20}\cdot 17\cdot 223^{2}$ |
$3$ |
$31.1499475758$ |
$560.9317249965869$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
trivial |
$[2, 2]$ |
$2$ |
$6$ |
$1724.56598742$ |
| 8.2.897187840000.1 |
$x^{8} + 8 x^{6} - 16 x^{4} - 1628 x^{2} - 1369$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$31.1968268394$ |
$123.91360025060992$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[4]$ |
$2$ |
$4$ |
$218.183040545$ |
| 8.2.897187840000.3 |
$x^{8} + 26 x^{6} + 201 x^{4} + 666 x^{2} - 1369$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 37^{2}$ |
$3$ |
$31.1968268394$ |
$123.91360025060992$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$601.024614874$ |
| 8.2.1101660160000.2 |
$x^{8} - 26 x^{6} + 273 x^{4} - 1722 x^{2} - 1681$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 41^{2}$ |
$3$ |
$32.0078096406$ |
$130.43977521071264$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$665.537746274$ |
| 8.2.1101660160000.4 |
$x^{8} + 8 x^{6} - 88 x^{4} + 1804 x^{2} - 1681$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 41^{2}$ |
$3$ |
$32.0078096406$ |
$130.43977521071264$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1304.84169761$ |
| 8.4.1167986786304.1 |
$x^{8} - 12 x^{6} + 88 x^{4} - 312 x^{2} + 351$ |
$8$ |
[4,2] |
$2^{20}\cdot 3\cdot 13^{5}$ |
$3$ |
$32.2425766676$ |
$108.03171057526986$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2158.79716554$ |
| 8.0.1167986786304.10 |
$x^{8} + 18 x^{6} + 81 x^{4} + 130 x^{2} + 39$ |
$8$ |
[0,4] |
$2^{20}\cdot 3\cdot 13^{5}$ |
$3$ |
$32.2425766676$ |
$108.03171057526986$ |
|
|
? |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$160.174489019$ |
| 8.0.1427496763392.12 |
$x^{8} + 14 x^{6} + 217 x^{4} + 1470 x^{2} + 3087$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{5}$ |
$3$ |
$33.0614495971$ |
$67.9074259225896$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2, 2]$ |
$[2, 2]$ |
$6$ |
$3$ |
$533.575399316$ |
| 8.0.1427496763392.25 |
$x^{8} + 28 x^{6} + 224 x^{4} + 392 x^{2} + 343$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 7^{5}$ |
$3$ |
$33.0614495971$ |
$67.9074259225896$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$6$ |
$3$ |
$1219.35544792$ |
| 8.2.1573519360000.9 |
$x^{8} + 14 x^{6} - 147 x^{4} + 2058 x^{2} - 2401$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$33.4664010614$ |
$53.89731535446141$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$4$ |
$1582.38889725$ |
| 8.2.1965200244736.3 |
$x^{8} - 6 x^{6} - 29 x^{4} - 34 x^{2} - 9$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 37^{4}$ |
$2$ |
$34.4093010682$ |
$55.41584669941975$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
trivial |
$2$ |
$4$ |
$1855.21472273$ |
| 8.2.1982464000000.1 |
$x^{8} - 10 x^{6} - 125 x^{4} - 2750 x^{2} - 3025$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$34.4469411985$ |
$101.03153630618483$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$4$ |
$371.732386357$ |
| 8.2.1982464000000.2 |
$x^{8} - 30 x^{6} + 375 x^{4} - 2750 x^{2} - 3025$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{6}\cdot 11^{2}$ |
$3$ |
$34.4469411985$ |
$101.03153630618483$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$470.30491588$ |
| 8.2.2425818710016.15 |
$x^{8} + 12 x^{6} - 216 x^{2} - 729$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$35.3270434653$ |
$56.893861957235075$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$1020.86603627$ |
| 8.2.2438594560000.3 |
$x^{8} + 6 x^{6} - 97 x^{4} - 1098 x^{2} - 3721$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 61^{2}$ |
$3$ |
$35.3502467904$ |
$159.10470799692794$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$884.218098183$ |
| 8.2.2438594560000.5 |
$x^{8} + 18 x^{6} + 97 x^{4} - 366 x^{2} - 3721$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 5^{4}\cdot 61^{2}$ |
$3$ |
$35.3502467904$ |
$159.10470799692794$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[4]$ |
$[4]$ |
$2$ |
$4$ |
$385.721794593$ |
| 8.0.2530288336896.1 |
$x^{8} - 20 x^{6} + 244 x^{4} - 1392 x^{2} + 4464$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 31^{3}$ |
$3$ |
$35.5137269864$ |
$87.85663907345199$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[3]$ |
$[3]$ |
$6$ |
$3$ |
$2462.35642381$ |
| 8.0.2530288336896.20 |
$x^{8} + 10 x^{6} + 61 x^{4} + 174 x^{2} + 279$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{4}\cdot 31^{3}$ |
$3$ |
$35.5137269864$ |
$87.85663907345199$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[3]$ |
$[3]$ |
$6$ |
$3$ |
$2778.79809681$ |
| 8.0.2579890176000.2 |
$x^{8} + 12 x^{6} - 200 x^{2} + 375$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{9}\cdot 5^{3}$ |
$3$ |
$35.6000126542$ |
$105.85222601431074$ |
|
|
? |
$C_2 \wr S_4$ (as 8T44) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$542.786775943$ |
