| 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 |
| 8.0.12230590464.1 |
$x^{8} + 12 x^{6} + 36 x^{4} + 36 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.12230590464.1 |
$x^{8} - 12 x^{6} + 36 x^{4} - 36 x^{2} + 9$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}$ |
$2$ |
$18.2360564556$ |
$18.23605645563822$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$356.934254411$ |
| 8.8.1340095640625.1 |
$x^{8} - x^{7} - 34 x^{6} + 29 x^{5} + 361 x^{4} - 305 x^{3} - 1090 x^{2} + 1345 x - 395$ |
$8$ |
[8,0] |
$3^{6}\cdot 5^{6}\cdot 7^{6}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$1621.61298869$ |
| 8.0.1340095640625.1 |
$x^{8} - 3 x^{7} + 22 x^{6} - 60 x^{5} + 201 x^{4} - 450 x^{3} + 1528 x^{2} - 3069 x + 4561$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{6}\cdot 7^{6}$ |
$3$ |
$32.8013693377$ |
$32.801369337662685$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2, 2]$ |
$2$ |
$3$ |
$53.1582098182$ |
| 8.0.7644119040000.1 |
$x^{8} + 60 x^{6} + 900 x^{4} + 4500 x^{2} + 5625$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.7644119040000.1 |
$x^{8} - 60 x^{6} + 900 x^{4} - 4500 x^{2} + 5625$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$40.7770618763$ |
$40.77706187633094$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$4900.6997022$ |
| 8.8.9294114390625.1 |
$x^{8} - x^{7} - 47 x^{6} + 40 x^{5} + 581 x^{4} - 220 x^{3} - 2038 x^{2} - 932 x - 109$ |
$8$ |
[8,0] |
$5^{6}\cdot 29^{6}$ |
$2$ |
$41.7855383348$ |
$41.78553833475025$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$3903.0092275$ |
| 8.0.29365647704064.1 |
$x^{8} + 84 x^{6} + 1764 x^{4} + 12348 x^{2} + 21609$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$48.2480702762$ |
$48.24807027615272$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 10, 10]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.29365647704064.1 |
$x^{8} - 84 x^{6} + 1764 x^{4} - 12348 x^{2} + 21609$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$48.2480702762$ |
$48.24807027615272$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$6040.95115845$ |
| 8.0.29721861554176.1 |
$x^{8} + 44 x^{6} + 308 x^{4} + 484 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{24}\cdot 11^{6}$ |
$2$ |
$48.3208428363$ |
$48.32084283629789$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[3, 6]$ |
$2$ |
$3$ |
$126.131828435$ |
| 8.8.29721861554176.1 |
$x^{8} - 44 x^{6} + 308 x^{4} - 484 x^{2} + 121$ |
$8$ |
[8,0] |
$2^{24}\cdot 11^{6}$ |
$2$ |
$48.3208428363$ |
$48.32084283629789$ |
|
✓ |
|
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$43308.6570657$ |
| 8.0.47775744000000.1 |
$x^{8} + 60 x^{6} + 810 x^{4} + 1800 x^{2} + 900$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$51.2744407675$ |
$51.274440767548086$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$54.5213185364$ |
| 8.0.47775744000000.2 |
$x^{8} + 60 x^{6} + 1170 x^{4} + 9000 x^{2} + 22500$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$51.2744407675$ |
$51.274440767548086$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$54.5213185364$ |
| 8.8.47775744000000.2 |
$x^{8} - 60 x^{6} + 810 x^{4} - 1800 x^{2} + 900$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$51.2744407675$ |
$51.274440767548086$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$7185.91630418$ |
| 8.8.47775744000000.3 |
$x^{8} - 60 x^{6} + 1170 x^{4} - 9000 x^{2} + 22500$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{6}\cdot 5^{6}$ |
$3$ |
$51.2744407675$ |
$51.274440767548086$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$15790.3322286$ |
| 8.8.74220378765625.1 |
$x^{8} - 3 x^{7} - 63 x^{6} + 90 x^{5} + 1311 x^{4} - 20 x^{3} - 7702 x^{2} - 5524 x - 1009$ |
$8$ |
[8,0] |
$5^{6}\cdot 41^{6}$ |
$2$ |
$54.1770552722$ |
$54.17705527224281$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$7481.34415348$ |
| 8.0.101240302206976.2 |
$x^{8} + 68 x^{6} + 986 x^{4} + 4624 x^{2} + 4624$ |
$8$ |
[0,4] |
$2^{22}\cdot 17^{6}$ |
$2$ |
$56.3208472131$ |
$56.32084721305108$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$125.49277292$ |
| 8.8.101240302206976.2 |
$x^{8} - 68 x^{6} + 986 x^{4} - 4624 x^{2} + 4624$ |
$8$ |
[8,0] |
$2^{22}\cdot 17^{6}$ |
$2$ |
$56.3208472131$ |
$56.32084721305108$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$20695.2249192$ |
| 8.8.116507435287321.1 |
$x^{8} - 3 x^{7} - 67 x^{6} - 16 x^{5} + 863 x^{4} + 1276 x^{3} + 392 x^{2} - 54 x + 1$ |
$8$ |
[8,0] |
$13^{6}\cdot 17^{6}$ |
$2$ |
$57.3184193184$ |
$57.318419318377835$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$7915.1159478$ |
| 8.0.151939915084881.1 |
$x^{8} - x^{7} + 50 x^{6} + 71 x^{5} + 529 x^{4} + 2173 x^{3} + 842 x^{2} + 5545 x + 17623$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{6}\cdot 11^{6}$ |
$3$ |
$59.2528146123$ |
$59.252814612259755$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$104.827448547$ |
| 8.8.151939915084881.1 |
$x^{8} - 3 x^{7} - 62 x^{6} + 66 x^{5} + 1125 x^{4} + 264 x^{3} - 4982 x^{2} - 4245 x + 823$ |
$8$ |
[8,0] |
$3^{6}\cdot 7^{6}\cdot 11^{6}$ |
$3$ |
$59.2528146123$ |
$59.252814612259755$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$17804.5169355$ |
| 8.0.179068074983424.1 |
$x^{8} + 132 x^{6} + 4356 x^{4} + 47916 x^{2} + 131769$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 11^{4}$ |
$3$ |
$60.4821569191$ |
$60.48215691909035$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 14, 14]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.179068074983424.2 |
$x^{8} - 132 x^{6} + 4356 x^{4} - 47916 x^{2} + 131769$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 11^{4}$ |
$3$ |
$60.4821569191$ |
$60.48215691909035$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2]$ |
$2$ |
$7$ |
$8119.67595047$ |
| 8.0.343064484000000.1 |
$x^{8} + 105 x^{6} + 3780 x^{4} + 55125 x^{2} + 275625$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}$ |
$4$ |
$65.6027386753$ |
$65.60273867532537$ |
✓ |
✓ |
|
$Q_8$ (as 8T5) |
$[2, 2, 2, 6, 6]$ |
$2$ |
$3$ |
$53.1582098182$ |
| 8.8.343064484000000.1 |
$x^{8} - 105 x^{6} + 3465 x^{4} - 44100 x^{2} + 176400$ |
$8$ |
[8,0] |
$2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6}$ |
$4$ |
$65.6027386753$ |
$65.60273867532537$ |
|
✓ |
|
$Q_8$ (as 8T5) |
$[2, 2]$ |
$2$ |
$7$ |
$13005.5748428$ |
| 8.0.349317894242304.1 |
$x^{8} + 156 x^{6} + 6084 x^{4} + 79092 x^{2} + 257049$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 13^{4}$ |
$3$ |
$65.7510366131$ |
$65.75103661305971$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 14, 14]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.349317894242304.3 |
$x^{8} - 156 x^{6} + 6084 x^{4} - 79092 x^{2} + 257049$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 13^{4}$ |
$3$ |
$65.7510366131$ |
$65.75103661305971$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$39169.5612478$ |
| 8.0.359729184374784.1 |
$x^{8} + 84 x^{6} + 1890 x^{4} + 10584 x^{2} + 1764$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$65.9928613513$ |
$65.99286135128618$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$97.698846762$ |
| 8.0.359729184374784.2 |
$x^{8} + 84 x^{6} + 2394 x^{4} + 24696 x^{2} + 44100$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$65.9928613513$ |
$65.99286135128618$ |
✓ |
✓ |
|
$Q_8$ (as 8T5) |
$[2, 14, 14]$ |
$2$ |
$3$ |
$97.698846762$ |
| 8.8.359729184374784.2 |
$x^{8} - 84 x^{6} + 1890 x^{4} - 10584 x^{2} + 1764$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$65.9928613513$ |
$65.99286135128618$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$32924.8756983$ |
| 8.8.359729184374784.3 |
$x^{8} - 84 x^{6} + 2394 x^{4} - 24696 x^{2} + 44100$ |
$8$ |
[8,0] |
$2^{22}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$65.9928613513$ |
$65.99286135128618$ |
|
✓ |
|
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$199628.854108$ |
| 8.0.752823265640625.1 |
$x^{8} - x^{7} + 98 x^{6} - 105 x^{5} + 3191 x^{4} + 1665 x^{3} + 44072 x^{2} + 47933 x + 328171$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 29^{6}$ |
$3$ |
$72.3746754174$ |
$72.37467541740445$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2, 4, 4, 4]$ |
$2$ |
$3$ |
$40.3281811419$ |
| 8.0.789298907447296.1 |
$x^{8} + 76 x^{6} + 1748 x^{4} + 12996 x^{2} + 29241$ |
$8$ |
[0,4] |
$2^{24}\cdot 19^{6}$ |
$2$ |
$72.8039910674$ |
$72.80399106742335$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[7, 14]$ |
$2$ |
$3$ |
$176.888572156$ |
| 8.8.789298907447296.1 |
$x^{8} - 76 x^{6} + 1748 x^{4} - 12996 x^{2} + 29241$ |
$8$ |
[8,0] |
$2^{24}\cdot 19^{6}$ |
$2$ |
$72.8039910674$ |
$72.80399106742335$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
trivial |
$2$ |
$7$ |
$138230.921404$ |
| 8.0.805005849390625.1 |
$x^{8} - 3 x^{7} + 57 x^{6} + 135 x^{5} + 306 x^{4} + 5365 x^{3} + 23383 x^{2} + 40951 x + 75421$ |
$8$ |
[0,4] |
$5^{6}\cdot 61^{6}$ |
$2$ |
$72.9835324231$ |
$72.98353242310733$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$194.255649708$ |
| 8.0.1021511146143744.1 |
$x^{8} + 204 x^{6} + 10404 x^{4} + 176868 x^{2} + 751689$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 17^{4}$ |
$3$ |
$75.1891869613$ |
$75.1891869613232$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 22, 22]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.1021511146143744.3 |
$x^{8} - 204 x^{6} + 10404 x^{4} - 176868 x^{2} + 751689$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 17^{4}$ |
$3$ |
$75.1891869613$ |
$75.1891869613232$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2]$ |
$2$ |
$7$ |
$21588.1959162$ |
| 8.0.1438916737499136.1 |
$x^{8} + 84 x^{6} + 1260 x^{4} + 5292 x^{2} + 441$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$78.4791802583$ |
$78.47918025833762$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 12]$ |
$2$ |
$3$ |
$116.658894546$ |
| 8.8.1438916737499136.1 |
$x^{8} - 84 x^{6} + 2268 x^{4} - 19404 x^{2} + 441$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$78.4791802583$ |
$78.47918025833762$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$102678.701141$ |
| 8.0.1438916737499136.2 |
$x^{8} + 84 x^{6} + 2268 x^{4} + 19404 x^{2} + 441$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$78.4791802583$ |
$78.47918025833762$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 10, 20]$ |
$2$ |
$3$ |
$116.658894546$ |
| 8.8.1438916737499136.2 |
$x^{8} - 84 x^{6} + 1260 x^{4} - 5292 x^{2} + 441$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 7^{6}$ |
$3$ |
$78.4791802583$ |
$78.47918025833762$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$118750.668157$ |
| 8.0.1593902779858944.1 |
$x^{8} + 228 x^{6} + 12996 x^{4} + 246924 x^{2} + 1172889$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{6}\cdot 19^{4}$ |
$3$ |
$79.4891272188$ |
$79.48912721882952$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 22, 22]$ |
$2$ |
$3$ |
$21.2871886415$ |
| 8.8.1593902779858944.2 |
$x^{8} - 228 x^{6} + 12996 x^{4} - 246924 x^{2} + 1172889$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{6}\cdot 19^{4}$ |
$3$ |
$79.4891272188$ |
$79.48912721882952$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2]$ |
$2$ |
$7$ |
$25804.5112489$ |
| 8.0.1686221298140625.1 |
$x^{8} - 3 x^{7} + 64 x^{6} - 192 x^{5} + 1836 x^{4} - 4635 x^{3} + 39520 x^{2} - 110850 x + 565795$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{6}\cdot 23^{6}$ |
$3$ |
$80.050550212$ |
$80.05055021202112$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$235.623843305$ |
| 8.8.1686221298140625.1 |
$x^{8} - x^{7} - 112 x^{6} + 95 x^{5} + 2881 x^{4} + 835 x^{3} - 16858 x^{2} - 25817 x - 10769$ |
$8$ |
[8,0] |
$3^{6}\cdot 5^{6}\cdot 23^{6}$ |
$3$ |
$80.050550212$ |
$80.05055021202112$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$112143.767488$ |
| 8.0.2070185663499849.1 |
$x^{8} - x^{7} + 65 x^{6} - 439 x^{5} + 1876 x^{4} - 12191 x^{3} + 60887 x^{2} - 124718 x + 121291$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{6}\cdot 17^{6}$ |
$3$ |
$82.1298750461$ |
$82.12987504608633$ |
✓ |
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 6, 6]$ |
$2$ |
$3$ |
$154.472027483$ |
| 8.8.2070185663499849.1 |
$x^{8} - 3 x^{7} - 110 x^{6} + 153 x^{5} + 3789 x^{4} + 1989 x^{3} - 44000 x^{2} - 97899 x - 46703$ |
$8$ |
[8,0] |
$3^{6}\cdot 7^{6}\cdot 17^{6}$ |
$3$ |
$82.1298750461$ |
$82.12987504608633$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2]$ |
$2$ |
$7$ |
$36250.7464952$ |
| 8.0.2379293284000000.1 |
$x^{8} + 145 x^{6} + 6380 x^{4} + 105125 x^{2} + 525625$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 29^{6}$ |
$3$ |
$83.5710766695$ |
$83.5710766695005$ |
✓ |
✓ |
|
$Q_8$ (as 8T5) |
$[2, 2, 2, 6, 12]$ |
$2$ |
$3$ |
$40.3281811419$ |
| 8.0.2407470785888256.1 |
$x^{8} + 132 x^{6} + 2772 x^{4} + 13068 x^{2} + 9801$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}\cdot 11^{6}$ |
$3$ |
$83.694154857$ |
$83.69415485701856$ |
✓ |
✓ |
|
$Q_8$ (as 8T5) |
$[2, 18, 18]$ |
$2$ |
$3$ |
$126.131828435$ |
| 8.8.2407470785888256.1 |
$x^{8} - 132 x^{6} + 2772 x^{4} - 13068 x^{2} + 9801$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{4}\cdot 11^{6}$ |
$3$ |
$83.694154857$ |
$83.69415485701856$ |
|
✓ |
? |
$Q_8$ (as 8T5) |
$[2, 2]$ |
$2$ |
$7$ |
$33511.7621402$ |
