| 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 |
| 8.0.1750329.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{4}$ |
$2$ |
$6.03100878452$ |
$6.03100878451909$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$1.1656993933$ |
| 8.0.2313441.1 |
$x^{8} - x^{7} + 2 x^{6} + 3 x^{5} - x^{4} + 3 x^{3} + 2 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{4}$ |
$2$ |
$6.2449979984$ |
$6.244997998398398$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$1.41187738145$ |
| 8.0.2560000.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}$ |
$2$ |
$6.32455532034$ |
$6.324555320336759$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$1.0839823354$ |
| 8.0.2985984.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 7 x^{4} - 10 x^{3} + 8 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{6}$ |
$2$ |
$6.44741959094$ |
$6.4474195909412515$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$12$ |
$3$ |
$3.64163813098$ |
| 8.0.4194304.1 |
$x^{8} + 6 x^{4} + 1$ |
$8$ |
[0,4] |
$2^{22}$ |
$1$ |
$6.72717132203$ |
$6.727171322029716$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$8$ |
$3$ |
$4.11870999032$ |
| 8.0.9150625.1 |
$x^{8} - 3 x^{7} + 9 x^{6} - 13 x^{5} + 18 x^{4} - 11 x^{3} + 11 x^{2} - 4 x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 11^{4}$ |
$2$ |
$7.4161984871$ |
$7.416198487095663$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$1.13294889772$ |
| 8.0.9834496.2 |
$x^{8} + 4 x^{6} + x^{4} - 6 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{4}$ |
$2$ |
$7.48331477355$ |
$7.483314773547883$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$1.41251218667$ |
| 8.0.16777216.2 |
$x^{8} - 4 x^{6} + 8 x^{4} - 4 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{24}$ |
$1$ |
$8.0$ |
$8.0$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$8$ |
$3$ |
$10.5675272107$ |
| 8.0.21381376.2 |
$x^{8} + 5 x^{6} + 4 x^{4} + 5 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 17^{4}$ |
$2$ |
$8.24621125124$ |
$8.246211251235321$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$4.5001159868$ |
| 8.0.30118144.2 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - x^{4} + 4 x^{3} + 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 7^{6}$ |
$2$ |
$8.60703414132$ |
$8.607034141317701$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$6.11392463052$ |
| 8.0.40960000.2 |
$x^{8} + 3 x^{4} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{4}$ |
$2$ |
$8.94427191$ |
$8.94427190999916$ |
|
✓ |
✓ |
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$8.3114696565$ |
| 8.0.47775744.1 |
$x^{8} + 3 x^{4} + 9$ |
$8$ |
[0,4] |
$2^{16}\cdot 3^{6}$ |
$2$ |
$9.11802822782$ |
$9.11802822781911$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$12$ |
$3$ |
$20.8957982344$ |
| 8.0.64000000.3 |
$x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 11 x^{4} - 10 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{6}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$4$ |
$3$ |
$5.03238945812$ |
| 8.0.81450625.1 |
$x^{8} - x^{7} + 8 x^{6} + 7 x^{5} + 19 x^{4} + 7 x^{3} + 8 x^{2} - x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 19^{4}$ |
$2$ |
$9.74679434481$ |
$9.746794344808963$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$2.76676434196$ |
| 8.0.95004009.1 |
$x^{8} - 3 x^{7} + x^{6} + 6 x^{5} + 6 x^{4} + 6 x^{3} + x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 19^{4}$ |
$2$ |
$9.93614090235$ |
$9.93614090235369$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$22.0487159216$ |
| 8.0.116985856.1 |
$x^{8} - 4 x^{7} + 8 x^{6} - 6 x^{5} + 7 x^{4} - 10 x^{3} + 2 x^{2} - 6 x + 9$ |
$8$ |
[0,4] |
$2^{12}\cdot 13^{4}$ |
$2$ |
$10.1980390272$ |
$10.198039027185569$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$4$ |
$3$ |
$10.9289876348$ |
| 8.0.143496441.1 |
$x^{8} - x^{7} + 2 x^{6} - 3 x^{5} - x^{4} + 6 x^{3} + 8 x^{2} + 8 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 11^{6}$ |
$2$ |
$10.4617693571$ |
$10.46176935712732$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$29.5003847252$ |
| 8.0.151807041.1 |
$x^{8} - 5 x^{6} + 28 x^{4} + 15 x^{2} + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 37^{4}$ |
$2$ |
$10.5356537529$ |
$10.535653752852738$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$21.2686658839$ |
| 8.0.157351936.3 |
$x^{8} + 2 x^{6} + 10 x^{4} + 2 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{16}\cdot 7^{4}$ |
$2$ |
$10.5830052443$ |
$10.583005244258363$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$8.97767398312$ |
| 8.0.207360000.5 |
$x^{8} - 2 x^{7} + 2 x^{6} - 6 x^{5} + 14 x^{4} - 30 x^{3} + 50 x^{2} - 50 x + 25$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$10.9544511501$ |
$10.954451150103322$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$4$ |
$3$ |
$11.5813939574$ |
| 8.0.228765625.2 |
$x^{8} - x^{6} + 16 x^{4} - x^{2} + 1$ |
$8$ |
[0,4] |
$5^{6}\cdot 11^{4}$ |
$2$ |
$11.089803369$ |
$11.08980336897316$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$7.35870441282$ |
| 8.0.339738624.3 |
$x^{8} - 4 x^{7} + 4 x^{6} - 4 x^{5} + 12 x^{4} + 4 x^{3} + 4 x^{2} + 4 x + 1$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$8.58619336777$ |
| 8.0.339738624.6 |
$x^{8} - 4 x^{7} + 8 x^{6} - 4 x^{5} - 4 x^{4} - 4 x^{3} + 16 x^{2} - 12 x + 9$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$18.5753876419$ |
| 8.0.339738624.8 |
$x^{8} - 4 x^{7} + 8 x^{5} + 14 x^{4} - 32 x^{3} + 28 x^{2} - 48 x + 34$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$8$ |
$3$ |
$29.9370957064$ |
| 8.0.339738624.9 |
$x^{8} - 4 x^{6} + 10 x^{4} - 24 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$30.1437202202$ |
| 8.0.339738624.10 |
$x^{8} + 4 x^{6} + 10 x^{4} + 24 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{22}\cdot 3^{4}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$6$ |
$3$ |
$78.9985555157$ |
| 8.0.342102016.2 |
$x^{8} - 2 x^{7} + 3 x^{6} + 20 x^{5} + 3 x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 8$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{4}$ |
$2$ |
$11.6619037897$ |
$11.661903789690601$ |
✓ |
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$62.7463864602$ |
| 8.0.342102016.4 |
$x^{8} - 2 x^{7} + x^{6} - 10 x^{5} + 50 x^{4} - 74 x^{3} + 59 x^{2} - 30 x + 9$ |
$8$ |
[0,4] |
$2^{12}\cdot 17^{4}$ |
$2$ |
$11.6619037897$ |
$11.661903789690601$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$11.666039167$ |
| 8.0.390971529.2 |
$x^{8} - 9 x^{6} + 32 x^{4} - 9 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 13^{6}$ |
$2$ |
$11.8581828179$ |
$11.858182817915045$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$27.3084770575$ |
| 8.8.442050625.1 |
$x^{8} - 2 x^{7} - 12 x^{6} + 26 x^{5} + 17 x^{4} - 36 x^{3} - 5 x^{2} + 11 x - 1$ |
$8$ |
[8,0] |
$5^{4}\cdot 29^{4}$ |
$2$ |
$12.0415945788$ |
$12.041594578792296$ |
|
✓ |
? |
$D_4$ (as 8T4) |
trivial |
$2$ |
$7$ |
$29.6385151004$ |
| 8.0.448084224.6 |
$x^{8} - 3 x^{6} + 12 x^{4} + 9 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 7^{4}$ |
$3$ |
$12.062017569$ |
$12.06201756903818$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$25.2649174316$ |
| 8.0.481890304.3 |
$x^{8} - 2 x^{7} - 3 x^{6} + 8 x^{5} + x^{4} - 2 x^{3} + 23 x^{2} - 12 x + 2$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{6}$ |
$2$ |
$12.1721844145$ |
$12.172184414459759$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$77.3449401793$ |
| 8.0.577200625.1 |
$x^{8} - 5 x^{6} + 32 x^{4} - 45 x^{2} + 81$ |
$8$ |
[0,4] |
$5^{4}\cdot 31^{4}$ |
$2$ |
$12.449899598$ |
$12.449899597988733$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[3]$ |
$2$ |
$3$ |
$6.26135590995$ |
| 8.0.592240896.5 |
$x^{8} + x^{6} + 4 x^{4} - 3 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$12.4899959968$ |
$12.489995996796797$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$63.3899064382$ |
| 8.0.673246809.1 |
$x^{8} - 3 x^{7} - 2 x^{6} + 15 x^{5} + 27 x^{4} + 15 x^{3} - 2 x^{2} - 3 x + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 31^{4}$ |
$2$ |
$12.6917581565$ |
$12.691758156532355$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[3]$ |
$6$ |
$3$ |
$19.6943302296$ |
| 8.0.723394816.1 |
$x^{8} + 13 x^{6} + 40 x^{4} + 52 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{8}\cdot 41^{4}$ |
$2$ |
$12.8062484749$ |
$12.806248474865697$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$4$ |
$3$ |
$97.9223809114$ |
| 8.0.741200625.3 |
$x^{8} - 3 x^{7} + 4 x^{6} - 14 x^{5} + 29 x^{4} - 28 x^{3} + 36 x^{2} - 55 x + 55$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 11^{4}$ |
$3$ |
$12.8452325787$ |
$12.84523257866513$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$11.609777874$ |
| 8.0.796594176.7 |
$x^{8} - 2 x^{7} + 8 x^{6} + 12 x^{5} + 11 x^{4} + 12 x^{3} + 8 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$32.324670943$ |
| 8.0.796594176.12 |
$x^{8} - 2 x^{7} + 5 x^{6} - 4 x^{5} + x^{4} - 18 x^{3} + 15 x^{2} + 18$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$2$ |
$3$ |
$55.2311084368$ |
| 8.0.796594176.14 |
$x^{8} - 2 x^{7} + 4 x^{6} + 12 x^{5} - 21 x^{4} + 36 x^{3} + 36 x^{2} - 54 x + 81$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$12.96148139681572$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$63.8564851446$ |
| 8.0.1024000000.6 |
$x^{8} + 4 x^{6} + 16 x^{4} - 56 x^{2} + 36$ |
$8$ |
[0,4] |
$2^{16}\cdot 5^{6}$ |
$2$ |
$13.3748060995$ |
$13.37480609952844$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$4$ |
$3$ |
$24.6646630038$ |
| 8.0.1093955625.1 |
$x^{8} - 5 x^{6} - 18 x^{4} + 100 x^{2} + 1$ |
$8$ |
[0,4] |
$3^{6}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$13.4857456151$ |
$13.485745615083065$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$28.9625337109$ |
| 8.0.1121513121.2 |
$x^{8} + 7 x^{6} + 52 x^{4} - 21 x^{2} + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 61^{4}$ |
$2$ |
$13.5277492585$ |
$13.527749258468683$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$6$ |
$3$ |
$65.524825026$ |
| 8.0.1146228736.5 |
$x^{8} - 6 x^{6} - 4 x^{5} + 43 x^{4} + 104 x^{3} + 86 x^{2} + 24 x + 36$ |
$8$ |
[0,4] |
$2^{12}\cdot 23^{4}$ |
$2$ |
$13.5646599663$ |
$13.564659966250536$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[3]$ |
$2$ |
$3$ |
$7.19956921879$ |
| 8.0.1358954496.9 |
$x^{8} - 12 x^{6} + 72 x^{4} - 108 x^{2} + 81$ |
$8$ |
[0,4] |
$2^{24}\cdot 3^{4}$ |
$2$ |
$13.8564064606$ |
$13.856406460551018$ |
|
✓ |
? |
$D_4$ (as 8T4) |
$[2]$ |
$8$ |
$3$ |
$62.7365525512$ |
| 8.0.1445900625.2 |
$x^{8} - x^{7} + x^{6} + 16 x^{5} - 7 x^{4} - 2 x^{3} + 64 x^{2} + 8 x + 1$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$13.9642400438$ |
$13.96424004376894$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[4]$ |
$6$ |
$3$ |
$42.1126760756$ |
| 8.0.1698181681.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 6 x^{5} + 16 x^{4} - 70 x^{3} + 49 x^{2} - 98 x + 196$ |
$8$ |
[0,4] |
$7^{4}\cdot 29^{4}$ |
$2$ |
$14.2478068488$ |
$14.247806848775006$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$32.694948397$ |
| 8.0.1722499009.1 |
$x^{8} + x^{6} - 11 x^{4} + 4 x^{2} + 16$ |
$8$ |
[0,4] |
$7^{6}\cdot 11^{4}$ |
$2$ |
$14.2731514023$ |
$14.273151402264794$ |
|
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$39.9791630368$ |
| 8.0.1731891456.3 |
$x^{8} + 3 x^{6} + 11 x^{4} + 45 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{4}\cdot 17^{4}$ |
$3$ |
$14.2828568571$ |
$14.2828568570857$ |
|
✓ |
|
$D_4$ (as 8T4) |
$[2]$ |
$4$ |
$3$ |
$175.04615365$ |
| 8.0.1766100625.1 |
$x^{8} + 15 x^{6} + 48 x^{4} + 15 x^{2} + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 41^{4}$ |
$2$ |
$14.3178210633$ |
$14.317821063276353$ |
✓ |
✓ |
|
$D_4$ (as 8T4) |
trivial |
$2$ |
$3$ |
$60.2132974531$ |
