| 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 |
| 8.0.20912329.1 |
$x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{4} - x^{3} + 3 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$17^{2}\cdot 269^{2}$ |
$2$ |
$8.22337888284$ |
$275.5079493491839$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$1.7716238366$ |
| 8.0.34904464.1 |
$x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$2^{4}\cdot 7^{2}\cdot 211^{2}$ |
$3$ |
$8.76718400641$ |
$291.15348432675637$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$4.07876117756$ |
| 8.0.76877824.2 |
$x^{8} - 2 x^{5} - 3 x^{4} + 2 x^{2} + 2 x + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 137^{2}$ |
$2$ |
$9.676652276782349$ |
$130.11902033846712$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$10.162535029744886$ |
| 8.4.144889369.1 |
$x^{8} - 2 x^{7} + 3 x^{5} - 5 x^{4} + 2 x^{3} + 2 x^{2} - x + 1$ |
$8$ |
[4,2] |
$12037^{2}$ |
$1$ |
$10.4744098948$ |
$109.71326264403953$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$11.7944241661$ |
| 8.4.164326761.1 |
$x^{8} - x^{7} - 2 x^{6} + x^{5} - 3 x^{4} + 6 x^{2} + 3 x - 1$ |
$8$ |
[4,2] |
$3^{2}\cdot 4273^{2}$ |
$2$ |
$10.6405367714$ |
$456.0886057209614$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$16.2649451455$ |
| 8.4.229583104.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{3} - 2 x^{2} + 4 x - 3$ |
$8$ |
[4,2] |
$2^{8}\cdot 947^{2}$ |
$2$ |
$11.0947492278$ |
$272.7585121832274$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$15.6010778815589$ |
| 8.4.405780736.1 |
$x^{8} - 2 x^{7} - 5 x^{6} + 10 x^{5} + 6 x^{4} - 14 x^{3} + 2 x^{2} + 2 x - 1$ |
$8$ |
[4,2] |
$2^{8}\cdot 1259^{2}$ |
$2$ |
$11.9134193242$ |
$329.7834169990931$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$19.054750792278618$ |
| 8.4.797497600.1 |
$x^{8} - 4 x^{6} - 4 x^{5} + 8 x^{4} + 8 x^{3} - 2 x^{2} - 10 x + 2$ |
$8$ |
[4,2] |
$2^{8}\cdot 5^{2}\cdot 353^{2}$ |
$3$ |
$12.9633179511$ |
$90.50145560316005$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$39.81410124055594$ |
| 8.0.2916000000.11 |
$x^{8} - 2 x^{7} + 6 x^{6} - 12 x^{5} + 30 x^{4} - 38 x^{3} + 36 x^{2} - 18 x + 6$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$15.2439824446$ |
$102.75927104246999$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$107.44581306$ |
| 8.0.10000000000.1 |
$x^{8} - 3 x^{7} - 2 x^{6} + 9 x^{5} + 10 x^{4} - 27 x^{3} - 4 x^{2} + 19 x + 7$ |
$8$ |
[0,4] |
$2^{10}\cdot 5^{10}$ |
$2$ |
$17.7827941004$ |
$73.07682410398822$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$161.074155309$ |
| 8.8.46664208361.1 |
$x^{8} - 2 x^{7} - 11 x^{6} + 6 x^{5} + 30 x^{4} - 2 x^{3} - 22 x^{2} + x + 3$ |
$8$ |
[8,0] |
$17^{2}\cdot 97^{2}\cdot 131^{2}$ |
$3$ |
$21.558720784$ |
$996.264368545655$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$7$ |
$1069.35479695$ |
| 8.4.82944000000.3 |
$x^{8} - 8 x^{6} - 8 x^{5} - 28 x^{3} - 60 x^{2} - 36 x - 6$ |
$8$ |
[4,2] |
$2^{16}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$23.1658437058$ |
$118.65618559619952$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$1136.121459$ |
| 8.8.137172455424.1 |
$x^{8} - 2 x^{7} - 10 x^{6} + 16 x^{5} + 32 x^{4} - 36 x^{3} - 32 x^{2} + 24 x + 4$ |
$8$ |
[8,0] |
$2^{12}\cdot 3^{4}\cdot 643^{2}$ |
$3$ |
$24.6693873452$ |
$965.9021839833975$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$7$ |
$2098.03295535$ |
| 8.0.186624000000.6 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + 20 x^{4} + 4 x^{3} + 22 x^{2} + 40 x + 14$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$25.6372203838$ |
$141.7004270627813$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$1590.41162767$ |
| 8.4.440301256704.1 |
$x^{8} - 4 x^{6} - 8 x^{5} + 8 x^{3} + 8 x^{2} - 2$ |
$8$ |
[4,2] |
$2^{26}\cdot 3^{8}$ |
$2$ |
$28.5409707601$ |
$76.38466425389826$ |
|
|
✓ |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$2278.8486767$ |
| 8.0.576650390625.1 |
$x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 15 x^{4} - 21 x^{3} + 6 x^{2} + 3 x + 3$ |
$8$ |
[0,4] |
$3^{10}\cdot 5^{10}$ |
$2$ |
$29.519845069$ |
$160.52793591098725$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$789.661358398$ |
| 8.0.640000000000.1 |
$x^{8} - 4 x^{7} + 12 x^{6} - 12 x^{5} + 10 x^{4} + 60 x^{3} + 60 x^{2} + 20 x + 5$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{10}$ |
$2$ |
$29.9069756244$ |
$72.02913619280338$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$496.981919166$ |
| 8.0.656100000000.1 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + 5 x^{4} - 8 x^{3} + 36 x^{2} + 27$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$30.0$ |
$287.35685581795485$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$2569.8882381$ |
| 8.0.1476225000000.1 |
$x^{8} - x^{7} + x^{6} - x^{5} + 10 x^{4} - 10 x^{3} + 10 x^{2} - 10 x + 10$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{10}\cdot 5^{8}$ |
$3$ |
$33.200457591$ |
$247.35229842035835$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$2579.17689465$ |
| 8.4.1679616000000.1 |
$x^{8} - 2 x^{7} - 4 x^{6} - 12 x^{5} + 120 x^{3} + 270$ |
$8$ |
[4,2] |
$2^{14}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$33.7404795114$ |
$204.81758600676352$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$8163.65905957$ |
| 8.0.1679616000000.16 |
$x^{8} - 2 x^{7} + 11 x^{6} - 12 x^{5} - 12 x^{3} + 14 x^{2} + 8 x + 4$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$33.7404795114$ |
$359.0219950523538$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$7623.23716978$ |
| 8.0.3572100000000.1 |
$x^{8} - 4 x^{7} + 22 x^{6} - 32 x^{5} + 125 x^{4} - 86 x^{3} + 364 x^{2} - 112 x + 532$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2}$ |
$4$ |
$37.0779275107$ |
$340.82211738448854$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$8155.38632987$ |
| 8.4.5143824000000.1 |
$x^{8} - 3 x^{7} + 15 x^{6} - 15 x^{5} - 45 x^{4} + 81 x^{3} - 153 x^{2} - 135 x + 270$ |
$8$ |
[4,2] |
$2^{10}\cdot 3^{8}\cdot 5^{6}\cdot 7^{2}$ |
$4$ |
$38.8070618285$ |
$376.7795468312192$ |
|
|
|
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$42594.0261345$ |
| 8.4.5308416000000.54 |
$x^{8} - 4 x^{6} - 8 x^{5} - 60 x^{4} + 128 x^{3} + 160 x^{2} - 192 x + 56$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$38.960149857$ |
$143.15919477176385$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$12157.8127318$ |
| 8.0.5904900000000.1 |
$x^{8} - 8 x^{6} - 2 x^{5} + 30 x^{4} + 10 x^{3} - 50 x^{2} - 30 x + 55$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{10}\cdot 5^{8}$ |
$3$ |
$39.4822203886$ |
$279.0216036308045$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$2683.86166284$ |
| 8.4.6718464000000.6 |
$x^{8} - 4 x^{7} + 10 x^{6} - 12 x^{5} + 15 x^{4} + 48 x^{3} - 82 x^{2} - 20 x - 1$ |
$8$ |
[4,2] |
$2^{16}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$40.1244182986$ |
$129.11803760167285$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$5$ |
$4747.51307212$ |
| 8.0.6718464000000.16 |
$x^{8} - 4 x^{7} + 10 x^{6} - 15 x^{4} - 24 x^{3} + 86 x^{2} - 80 x + 35$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$40.1244182986$ |
$206.7210676368938$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$7495.7957377$ |
| 8.0.10497600000000.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 6 x^{5} + 24 x^{3} + 32 x^{2} - 88 x + 194$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$42.4264068712$ |
$159.38638506255012$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$5892.97099314$ |
| 8.4.10497600000000.1 |
$x^{8} - 32 x^{5} + 96 x^{3} - 320 x^{2} + 48$ |
$8$ |
[4,2] |
$2^{12}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$42.4264068712$ |
$319.5156069265828$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$17295.2036427$ |
| 8.0.10497600000000.2 |
$x^{8} - 4 x^{7} + 22 x^{6} - 52 x^{5} + 145 x^{4} - 112 x^{3} + 208 x^{2} - 184 x + 244$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$42.4264068712$ |
$147.97829087117032$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$12511.9906741$ |
| 8.4.11943936000000.14 |
$x^{8} - 4 x^{7} + 4 x^{6} + 10 x^{4} - 40 x^{2} + 20$ |
$8$ |
[4,2] |
$2^{20}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$43.1164934356$ |
$210.21250207008706$ |
|
|
? |
$A_8$ (as 8T49) |
$[2, 2]$ |
$2$ |
$5$ |
$2925.7003899$ |
| 8.0.15850845241344.1 |
$x^{8} - 8 x^{5} - 12 x^{4} + 40 x^{2} + 48 x + 18$ |
$8$ |
[0,4] |
$2^{28}\cdot 3^{10}$ |
$2$ |
$44.6690332369$ |
$138.57327225362695$ |
|
|
? |
$A_8$ (as 8T49) |
$[4]$ |
$2$ |
$3$ |
$1219.55072005$ |
| 8.4.16402500000000.1 |
$x^{8} - 2 x^{7} + 56 x^{5} - 70 x^{4} + 42 x^{3} - 89 x^{2} + 40 x - 3$ |
$8$ |
[4,2] |
$2^{8}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$44.8604634366$ |
$335.7033490039568$ |
|
|
|
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$26855.0139903$ |
| 8.0.26214400000000.1 |
$x^{8} - 8 x^{3} + 10$ |
$8$ |
[0,4] |
$2^{26}\cdot 5^{8}$ |
$2$ |
$47.5682846001$ |
$103.54650600993837$ |
|
|
✓ |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$2904.860668$ |
| 8.4.40960000000000.1 |
$x^{8} - 4 x^{7} - 8 x^{6} + 28 x^{5} - 40 x^{4} + 60 x^{3} - 40 x^{2} + 20 x + 5$ |
$8$ |
[4,2] |
$2^{22}\cdot 5^{10}$ |
$2$ |
$50.2973371873$ |
$119.40135217728802$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$29330.6475034$ |
| 8.0.41990400000000.1 |
$x^{8} - 2 x^{7} + 23 x^{6} + 4 x^{5} + 145 x^{4} + 158 x^{3} + 579 x^{2} + 444 x + 762$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$50.4537849152$ |
$752.9429563224276$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$37670.855183$ |
| 8.0.63734036889600.1 |
$x^{8} + 24 x^{6} - 20 x^{5} + 192 x^{4} - 336 x^{3} + 672 x^{2} - 1404 x + 1539$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{8}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}$ |
$5$ |
$53.1552822336$ |
$923.2559817143889$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$8544.53240835$ |
| 8.0.65610000000000.1 |
$x^{8} - 4 x^{7} + 7 x^{6} + 8 x^{5} - 5 x^{4} + 122 x^{3} + 57 x^{2} - 126 x + 66$ |
$8$ |
[0,4] |
$2^{10}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$53.3483823012$ |
$466.5821068046912$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$59867.4307599$ |
| 8.0.68797071360000.2 |
$x^{8} - 48 x^{3} + 360$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{8}\cdot 5^{4}$ |
$3$ |
$53.66563146$ |
$154.49240061856077$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$13454.0135384$ |
| 8.0.74649600000000.1 |
$x^{8} + 10 x^{6} - 44 x^{5} + 90 x^{4} - 128 x^{3} + 210 x^{2} - 180 x + 57$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{6}\cdot 5^{8}$ |
$3$ |
$54.2161202166$ |
$662.074399556565$ |
|
|
? |
$A_8$ (as 8T49) |
$[4]$ |
$2$ |
$3$ |
$19474.4488776$ |
| 8.4.113820562243584.1 |
$x^{8} - x^{7} + 8 x^{6} - 76 x^{5} - 38 x^{4} + 766 x^{3} - 824 x^{2} - 496 x + 704$ |
$8$ |
[4,2] |
$2^{14}\cdot 3^{10}\cdot 7^{6}$ |
$3$ |
$57.1514943986$ |
$339.55969201699526$ |
|
|
|
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$5$ |
$95724.1713129$ |
| 8.4.115201238777856.1 |
$x^{8} - 22 x^{6} + 77 x^{4} - 176 x^{3} + 308 x^{2} + 880 x - 1452$ |
$8$ |
[4,2] |
$2^{14}\cdot 3^{4}\cdot 7^{2}\cdot 11^{6}$ |
$4$ |
$57.2376959926$ |
$298.21476867113756$ |
|
|
|
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$191109.07128$ |
| 8.0.298598400000000.1 |
$x^{8} - 4 x^{7} + 32 x^{6} - 52 x^{5} + 40 x^{4} + 40 x^{3} + 80 x^{2} + 40 x + 10$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{6}\cdot 5^{8}$ |
$3$ |
$64.4741959094$ |
$125.29338713344646$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$10086.8109446$ |
| 8.4.429981696000000.5 |
$x^{8} - 24 x^{6} - 72 x^{5} + 90 x^{4} + 480 x^{3} + 440 x^{2} - 1320 x - 135$ |
$8$ |
[4,2] |
$2^{22}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$67.4809590228$ |
$257.20767053892934$ |
|
|
|
$A_8$ (as 8T49) |
trivial |
$2$ |
$5$ |
$224847.13879$ |
| 8.0.1184787066781696.7 |
$x^{8} - 4 x^{7} + 4802$ |
$8$ |
[0,4] |
$2^{22}\cdot 7^{10}$ |
$2$ |
$76.5958143926$ |
$144.37803864980123$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$26813.0725261$ |
| 8.0.1547476985184256.7 |
$x^{8} - 128 x + 224$ |
$8$ |
[0,4] |
$2^{28}\cdot 7^{8}$ |
$2$ |
$79.1959594929$ |
$156.31070344097333$ |
|
|
? |
$A_8$ (as 8T49) |
$[8]$ |
$2$ |
$3$ |
$3357.27406536$ |
| 8.4.1719926784000000.21 |
$x^{8} - 32 x^{5} + 240 x^{3} - 320 x^{2} + 120$ |
$8$ |
[4,2] |
$2^{24}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$80.2488365972$ |
$489.6693764131204$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$5$ |
$153176.299992$ |
| 8.0.2687385600000000.1 |
$x^{8} - 32 x^{5} + 400 x^{2} + 900$ |
$8$ |
[0,4] |
$2^{20}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$84.8528137424$ |
$921.6424935927497$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$81899.7415499$ |
| 8.0.4199040000000000.1 |
$x^{8} - 20 x^{5} + 120 x^{4} + 288 x^{3} + 1440 x^{2} + 45$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$89.7209268733$ |
$417.73629839961626$ |
|
|
? |
$A_8$ (as 8T49) |
$[2]$ |
$2$ |
$3$ |
$49377.13749$ |
| 8.0.4592206902398976.1 |
$x^{8} - 4 x^{7} + 21 x^{6} + 98 x^{5} + 294 x^{4} + 448 x^{3} + 1680 x^{2} + 1588 x + 494$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{12}$ |
$3$ |
$90.7303697777$ |
$341.06709656564954$ |
|
|
? |
$A_8$ (as 8T49) |
trivial |
$2$ |
$3$ |
$509162.682147$ |
