| 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 |
| 8.0.1265625.1 |
$x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}$ |
$2$ |
$5.79146092644$ |
$5.791460926441346$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$30$ |
$3$ |
$4.6618207773$ |
| 8.0.4000000.1 |
$x^{8} - x^{6} + x^{4} - x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}$ |
$2$ |
$6.68740304976$ |
$6.68740304976422$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$20$ |
$3$ |
$7.41124225589$ |
| 8.0.16777216.1 |
$x^{8} + 1$ |
$8$ |
[0,4] |
$2^{24}$ |
$1$ |
$8.0$ |
$8.0$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$16$ |
$3$ |
$19.534360053$ |
| 8.0.37515625.1 |
$x^{8} - x^{7} - x^{6} + 3 x^{5} - x^{4} + 6 x^{3} - 4 x^{2} - 8 x + 16$ |
$8$ |
[0,4] |
$5^{6}\cdot 7^{4}$ |
$2$ |
$8.84660269327$ |
$8.846602693265513$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$10$ |
$3$ |
$13.4644594003$ |
| 8.0.64000000.1 |
$x^{8} - 2 x^{6} + 4 x^{4} - 8 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{6}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$10$ |
$3$ |
$18.013034165$ |
| 8.0.64000000.2 |
$x^{8} + 2 x^{6} + 4 x^{4} + 8 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{6}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$10$ |
$3$ |
$12.3400472787$ |
| 8.0.228765625.1 |
$x^{8} - x^{7} - 2 x^{6} + 5 x^{5} + x^{4} + 15 x^{3} - 18 x^{2} - 27 x + 81$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{4}$ |
$2$ |
$11.089803369$ |
$11.08980336897316$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$10$ |
$3$ |
$21.1778234548$ |
| 8.0.324000000.1 |
$x^{8} + 9 x^{6} + 26 x^{4} + 24 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$11.582921852882691$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$4$ |
$3$ |
$9.32364155459$ |
| 8.8.324000000.1 |
$x^{8} - 7 x^{6} + 14 x^{4} - 8 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$11.582921852882691$ |
|
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$24.3884064258$ |
| 8.0.324000000.2 |
$x^{8} + 5 x^{6} + 20 x^{4} + 25 x^{2} + 25$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$11.582921852882691$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$6$ |
$3$ |
$14.8224845118$ |
| 8.0.324000000.3 |
$x^{8} + 3 x^{6} + 9 x^{4} + 27 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$11.5829218529$ |
$11.582921852882691$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$10$ |
$3$ |
$20.9227801969$ |
| 8.0.339738624.1 |
$x^{8} - 4 x^{6} + 14 x^{4} - 8 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
trivial |
$6$ |
$3$ |
$44.7013091231$ |
| 8.0.339738624.2 |
$x^{8} + 4 x^{6} + 14 x^{4} + 8 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$6$ |
$3$ |
$19.534360053$ |
| 8.0.390971529.1 |
$x^{8} - x^{7} - x^{6} - 10 x^{5} + 5 x^{4} + 14 x^{3} + 10 x^{2} + 12 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{6}$ |
$2$ |
$11.8581828179$ |
$11.858182817915045$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$6$ |
$3$ |
$37.7892910903$ |
| 8.0.446265625.1 |
$x^{8} - x^{7} + 4 x^{6} - 7 x^{5} + 19 x^{4} + 21 x^{3} + 36 x^{2} + 27 x + 81$ |
$8$ |
[0,4] |
$5^{6}\cdot 13^{4}$ |
$2$ |
$12.0558872978$ |
$12.055887297809578$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$10$ |
$3$ |
$25.5406213931$ |
| 8.0.1024000000.1 |
$x^{8} + 8 x^{6} + 19 x^{4} + 12 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$13.37480609952844$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$7.41124225589$ |
| 8.8.1024000000.1 |
$x^{8} - 8 x^{6} + 19 x^{4} - 12 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$13.37480609952844$ |
|
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$55.5791824785$ |
| 8.0.1024000000.2 |
$x^{8} + 15 x^{4} + 25$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$13.37480609952844$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$4$ |
$3$ |
$18.013034165$ |
| 8.0.1235663104.1 |
$x^{8} - 3 x^{6} + 18 x^{4} + 4 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 13^{6}$ |
$2$ |
$13.692650084$ |
$13.692650084046091$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
trivial |
$4$ |
$3$ |
$35.7224800402$ |
| 8.0.1305015625.1 |
$x^{8} - x^{7} + 5 x^{6} - 9 x^{5} + 29 x^{4} + 36 x^{3} + 80 x^{2} + 64 x + 256$ |
$8$ |
[0,4] |
$5^{6}\cdot 17^{4}$ |
$2$ |
$13.7864345676$ |
$13.786434567627778$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$10$ |
$3$ |
$35.6323756756$ |
| 8.8.1358954496.1 |
$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{24}\cdot 3^{4}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
|
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$93.4711768963$ |
| 8.0.1358954496.3 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
✓ |
✓ |
✓ |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$10.6435943208$ |
| 8.0.1358954496.4 |
$x^{8} + 81$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$8$ |
$3$ |
$44.7013091231$ |
| 8.0.1955143089.1 |
$x^{8} - x^{7} + 7 x^{6} + 4 x^{5} + 36 x^{4} - 4 x^{3} + 7 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 17^{6}$ |
$2$ |
$14.5009788258$ |
$14.500978825806921$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[5]$ |
$6$ |
$3$ |
$27.6959098582$ |
| 8.0.2036265625.1 |
$x^{8} - x^{7} - 4 x^{6} + 9 x^{5} + 11 x^{4} + 45 x^{3} - 100 x^{2} - 125 x + 625$ |
$8$ |
[0,4] |
$5^{6}\cdot 19^{4}$ |
$2$ |
$14.5748570443$ |
$14.574857044323968$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[4]$ |
$10$ |
$3$ |
$39.4015337086$ |
| 8.0.2621440000.1 |
$x^{8} + 12 x^{6} + 30 x^{4} + 24 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{22}\cdot 5^{4}$ |
$2$ |
$15.0424123723$ |
$15.042412372345574$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$3$ |
$12.3400472787$ |
| 8.8.2621440000.1 |
$x^{8} - 12 x^{6} + 30 x^{4} - 24 x^{2} + 4$ |
$8$ |
[8,0] |
$2^{22}\cdot 5^{4}$ |
$2$ |
$15.0424123723$ |
$15.042412372345574$ |
|
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$95.3043068345$ |
| 8.0.3016755625.1 |
$x^{8} - x^{7} + 5 x^{6} + 18 x^{5} + 37 x^{4} + 20 x^{3} + 2 x^{2} - 12 x + 9$ |
$8$ |
[0,4] |
$5^{4}\cdot 13^{6}$ |
$2$ |
$15.30884819$ |
$15.308848190022635$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$3$ |
$25.5406213931$ |
| 8.0.3038765625.1 |
$x^{8} - x^{7} + 10 x^{6} - 9 x^{5} + 79 x^{4} - 59 x^{3} + 180 x^{2} + 99 x + 121$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$15.3227653391$ |
$15.322765339111537$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$6$ |
$3$ |
$26.9289188006$ |
| 8.8.3038765625.1 |
$x^{8} - x^{7} - 14 x^{6} + 9 x^{5} + 61 x^{4} - 5 x^{3} - 90 x^{2} - 45 x - 5$ |
$8$ |
[8,0] |
$3^{4}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$15.3227653391$ |
$15.322765339111537$ |
|
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$112.572494501$ |
| 8.0.3038765625.2 |
$x^{8} - 2 x^{7} - 2 x^{5} + 29 x^{4} + 2 x^{3} + 55 x^{2} + 27 x + 151$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$15.3227653391$ |
$15.322765339111537$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$9.32364155459$ |
| 8.0.3038765625.3 |
$x^{8} - x^{7} + 6 x^{6} - 11 x^{5} + 41 x^{4} + 55 x^{3} + 150 x^{2} + 125 x + 625$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$15.3227653391$ |
$15.322765339111537$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$10$ |
$3$ |
$53.1582098182$ |
| 8.0.4372515625.1 |
$x^{8} - x^{7} - 5 x^{6} + 11 x^{5} + 19 x^{4} + 66 x^{3} - 180 x^{2} - 216 x + 1296$ |
$8$ |
[0,4] |
$5^{6}\cdot 23^{4}$ |
$2$ |
$16.0358291776$ |
$16.03582917757843$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[3]$ |
$10$ |
$3$ |
$39.3022218671$ |
| 8.0.5184000000.1 |
$x^{8} + 14 x^{6} + 56 x^{4} + 64 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[4]$ |
$2$ |
$3$ |
$9.32364155459$ |
| 8.8.5184000000.1 |
$x^{8} - 2 x^{7} - 15 x^{6} + 28 x^{5} + 44 x^{4} - 58 x^{3} - 20 x^{2} + 12 x + 1$ |
$8$ |
[8,0] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
|
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$130.424947215$ |
| 8.0.5184000000.2 |
$x^{8} - 2 x^{7} + x^{6} + 4 x^{5} + 24 x^{4} - 58 x^{3} + 124 x^{2} - 124 x + 241$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$9.32364155459$ |
| 8.8.5184000000.2 |
$x^{8} - 14 x^{6} + 56 x^{4} - 64 x^{2} + 16$ |
$8$ |
[8,0] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
|
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$154.463632753$ |
| 8.0.5184000000.3 |
$x^{8} - 10 x^{6} + 80 x^{4} - 200 x^{2} + 400$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2, 2]$ |
$6$ |
$3$ |
$33.6001200213$ |
| 8.0.5184000000.4 |
$x^{8} + 10 x^{6} + 80 x^{4} + 200 x^{2} + 400$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$6$ |
$3$ |
$36.02606833$ |
| 8.0.5184000000.5 |
$x^{8} - 6 x^{6} + 36 x^{4} - 216 x^{2} + 1296$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[4]$ |
$10$ |
$3$ |
$67.2002400426$ |
| 8.0.5184000000.6 |
$x^{8} + 6 x^{6} + 36 x^{4} + 216 x^{2} + 1296$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$10$ |
$3$ |
$54.5213185364$ |
| 8.0.6179217664.1 |
$x^{8} + 13 x^{6} + 40 x^{4} + 13 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{6}$ |
$2$ |
$16.7442880572$ |
$16.74428805718538$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[4]$ |
$4$ |
$3$ |
$27.6959098582$ |
| 8.0.9604000000.1 |
$x^{8} + 19 x^{6} + 121 x^{4} + 279 x^{2} + 121$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$17.6932053865$ |
$17.693205386531027$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$4$ |
$3$ |
$26.9289188006$ |
| 8.8.9604000000.1 |
$x^{8} - 12 x^{6} + 34 x^{4} - 23 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{8}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$17.6932053865$ |
$17.693205386531027$ |
|
✓ |
? |
$C_4\times C_2$ (as 8T2) |
trivial |
$2$ |
$7$ |
$177.829981289$ |
| 8.0.9604000000.2 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + 29 x^{4} - 66 x^{3} + 36 x^{2} - 2 x + 281$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$17.6932053865$ |
$17.693205386531027$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$14.8224845118$ |
| 8.0.9604000000.3 |
$x^{8} + 7 x^{6} + 49 x^{4} + 343 x^{2} + 2401$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$17.6932053865$ |
$17.693205386531027$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$10$ |
$3$ |
$52.8211197622$ |
| 8.0.10070523904.1 |
$x^{8} - 4 x^{7} + 22 x^{6} - 52 x^{5} + 113 x^{4} - 144 x^{3} + 120 x^{2} - 56 x + 14$ |
$8$ |
[0,4] |
$2^{22}\cdot 7^{4}$ |
$2$ |
$17.798422345$ |
$17.798422345016238$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$93.7356023859$ |
| 8.0.10070523904.2 |
$x^{8} + 12 x^{6} + 66 x^{4} + 96 x^{2} + 64$ |
$8$ |
[0,4] |
$2^{22}\cdot 7^{4}$ |
$2$ |
$17.798422345$ |
$17.798422345016238$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[4]$ |
$2$ |
$3$ |
$19.534360053$ |
| 8.0.10485760000.1 |
$x^{8} - 8 x^{6} + 20 x^{4} - 16 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 5^{4}$ |
$2$ |
$17.88854382$ |
$17.88854381999832$ |
✓ |
✓ |
|
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$78.6242549932$ |
| 8.0.10485760000.2 |
$x^{8} + 8 x^{6} + 20 x^{4} + 16 x^{2} + 49$ |
$8$ |
[0,4] |
$2^{24}\cdot 5^{4}$ |
$2$ |
$17.88854382$ |
$17.88854381999832$ |
✓ |
✓ |
? |
$C_4\times C_2$ (as 8T2) |
$[2]$ |
$2$ |
$3$ |
$19.534360053$ |
