| 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 |
| 8.0.17850625.1 |
$x^{8} - x^{7} + 3 x^{6} - x^{5} + 3 x^{4} + x^{3} + 3 x^{2} + x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 13^{4}$ |
$2$ |
$8.0622577483$ |
$12.362716315674692$ |
|
|
✓ |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$1.8314637705$ |
| 8.0.39337984.2 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{4} - 8 x^{3} + 12 x^{2} - 8 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 7^{4}$ |
$2$ |
$8.89921117251$ |
$12.308388215503062$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$9.87310860784$ |
| 8.0.68574961.1 |
$x^{8} - x^{7} + x^{6} - x^{5} - x^{4} + x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 13^{4}$ |
$2$ |
$9.53939201417$ |
$13.193814370085985$ |
|
|
✓ |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$6.25889635732$ |
| 8.0.107495424.1 |
$x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 4 x^{4} - 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{8}$ |
$2$ |
$10.090756983$ |
$14.553389922872519$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$18.7814327095$ |
| 8.0.236421376.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 16 x^{4} + 2 x^{3} + x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 31^{4}$ |
$2$ |
$11.1355287257$ |
$19.736544806437948$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$4$ |
$3$ |
$11.897056192$ |
| 8.0.241864704.1 |
$x^{8} - 4 x^{7} + 4 x^{6} + 2 x^{5} + x^{4} - 10 x^{3} + 4 x^{2} + 2 x + 7$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{10}$ |
$2$ |
$11.1672583092$ |
$14.696938456699069$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$6$ |
$3$ |
$44.585463933$ |
| 8.0.312900721.1 |
$x^{8} - x^{7} + 4 x^{6} + 6 x^{4} + 4 x^{2} + x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 19^{4}$ |
$2$ |
$11.5325625947$ |
$18.838721275076466$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$11.9301806104$ |
| 8.0.467943424.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 10 x^{5} + 4 x^{4} - 10 x^{3} - 2 x^{2} + 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 13^{4}$ |
$2$ |
$12.1275805702$ |
$18.59650768627035$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$34.4320572782$ |
| 8.0.481890304.5 |
$x^{8} - 2 x^{7} + 2 x^{6} - 8 x^{5} + 18 x^{4} - 16 x^{3} + 8 x^{2} + 8$ |
$8$ |
[0,4] |
$2^{12}\cdot 7^{6}$ |
$2$ |
$12.1721844145$ |
$14.315066180821045$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$33.5359316489$ |
| 8.0.547981281.1 |
$x^{8} - x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{8}\cdot 17^{4}$ |
$2$ |
$12.3693168769$ |
$17.839641950637386$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$35.4938400054$ |
| 8.0.629407744.3 |
$x^{8} + 2 x^{6} + 10 x^{4} - 4 x^{3} + 10 x^{2} - 4 x + 3$ |
$8$ |
[0,4] |
$2^{18}\cdot 7^{4}$ |
$2$ |
$12.5853851346$ |
$17.406689545317608$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$33.9076141972$ |
| 8.0.629407744.4 |
$x^{8} + 2 x^{6} - 4 x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 8 x + 7$ |
$8$ |
[0,4] |
$2^{18}\cdot 7^{4}$ |
$2$ |
$12.5853851346$ |
$17.406689545317608$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$24.8329714658$ |
| 8.0.796594176.15 |
$x^{8} - 2 x^{7} + 2 x^{6} - 4 x^{5} + 2 x^{4} + 8 x^{3} - 4 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$12.9614813968$ |
$17.926863604818365$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$6$ |
$3$ |
$73.2514248176$ |
| 8.0.855036081.1 |
$x^{8} - x^{7} + 5 x^{6} + x^{5} + 11 x^{4} - x^{3} + 5 x^{2} + x + 1$ |
$8$ |
[0,4] |
$3^{8}\cdot 19^{4}$ |
$2$ |
$13.0766968306$ |
$18.859860385004858$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$12.4411009149$ |
| 8.0.875213056.3 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} - 9 x^{4} + 4 x^{3} + 18 x^{2} - 30 x + 25$ |
$8$ |
[0,4] |
$2^{8}\cdot 43^{4}$ |
$2$ |
$13.1148770486$ |
$24.54759593904292$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$49.0174297738$ |
| 8.0.967458816.1 |
$x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} + 8 x^{4} + 2 x^{3} - 2 x^{2} - 2 x + 1$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{10}$ |
$2$ |
$13.2801830364$ |
$17.477703781463642$ |
|
|
✓ |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$21.4899921701$ |
| 8.0.1121513121.1 |
$x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{5} + 8 x^{4} + 16 x^{3} + 18 x^{2} + 28 x + 13$ |
$8$ |
[0,4] |
$3^{4}\cdot 61^{4}$ |
$2$ |
$13.5277492585$ |
$26.839876760292654$ |
✓ |
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$6$ |
$3$ |
$63.6847948779$ |
| 8.0.1445900625.6 |
$x^{8} - x^{7} + x^{6} + 6 x^{5} - 7 x^{4} + 8 x^{3} + 9 x^{2} - 12 x + 16$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$13.9642400438$ |
$21.412852778309286$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$48.6909101532$ |
| 8.0.1445900625.7 |
$x^{8} - x^{7} + 6 x^{6} - 8 x^{5} + 13 x^{4} - 15 x^{3} + 17 x^{2} - 11 x + 4$ |
$8$ |
[0,4] |
$3^{4}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$13.9642400438$ |
$21.412852778309286$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$37.965510637$ |
| 8.0.1632240801.1 |
$x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + x^{4} - 6 x^{3} + 15 x^{2} - 18 x + 36$ |
$8$ |
[0,4] |
$3^{4}\cdot 67^{4}$ |
$2$ |
$14.1774468788$ |
$28.57220971835363$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$41.1496475247$ |
| 8.0.1698181681.2 |
$x^{8} - x^{7} + x^{6} - 3 x^{5} + 3 x^{4} + 3 x^{3} + x^{2} + x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 29^{4}$ |
$2$ |
$14.2478068488$ |
$19.705964328162043$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$36.8218141102$ |
| 8.0.1719926784.3 |
$x^{8} + 6 x^{4} - 8 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{8}$ |
$2$ |
$14.27048538$ |
$20.58160140743025$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$34.8341019306$ |
| 8.0.1719926784.4 |
$x^{8} + 6 x^{4} + 8 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{18}\cdot 3^{8}$ |
$2$ |
$14.27048538$ |
$20.58160140743025$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$100.637691627$ |
| 8.0.1908029761.1 |
$x^{8} - x^{7} - 5 x^{6} + 3 x^{5} + 13 x^{4} + 3 x^{3} - 5 x^{2} - x + 1$ |
$8$ |
[0,4] |
$11^{4}\cdot 19^{4}$ |
$2$ |
$14.4568322948$ |
$23.615586898971756$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$24.4754875268$ |
| 8.0.1927561216.9 |
$x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} + 4 x + 2$ |
$8$ |
[0,4] |
$2^{14}\cdot 7^{6}$ |
$2$ |
$14.4752483108$ |
$17.023578553967216$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$33.3153733951$ |
| 8.0.2135179264.1 |
$x^{8} - 4 x^{5} - 8 x^{4} - 8 x^{3} + 8 x^{2} + 24 x + 36$ |
$8$ |
[0,4] |
$2^{14}\cdot 19^{4}$ |
$2$ |
$14.6615299843$ |
$23.949965549560982$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$92.9183656505$ |
| 8.0.2300257521.2 |
$x^{8} + 2 x^{6} + 13 x^{4} + 15 x^{2} + 36$ |
$8$ |
[0,4] |
$3^{4}\cdot 73^{4}$ |
$2$ |
$14.7986485869$ |
$30.253516886595015$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$40.2377684215$ |
| 8.0.3016755625.2 |
$x^{8} - x^{7} - 3 x^{6} + 9 x^{5} - 4 x^{4} - 10 x^{3} + 17 x^{2} - 14 x + 9$ |
$8$ |
[0,4] |
$5^{4}\cdot 13^{6}$ |
$2$ |
$15.30884819$ |
$18.957066304919827$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$26.5769464125$ |
| 8.0.3016755625.3 |
$x^{8} - x^{7} - 2 x^{6} - 6 x^{5} + 18 x^{4} + 6 x^{3} - 2 x^{2} + x + 1$ |
$8$ |
[0,4] |
$5^{4}\cdot 13^{6}$ |
$2$ |
$15.30884819$ |
$18.957066304919827$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$51.9632534968$ |
| 8.0.3186376704.9 |
$x^{8} - 2 x^{7} + 8 x^{4} + 20 x^{3} + 16 x^{2} + 12 x + 6$ |
$8$ |
[0,4] |
$2^{14}\cdot 3^{4}\cdot 7^{4}$ |
$3$ |
$15.4138858981$ |
$21.31875374853333$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$25.506368139$ |
| 8.0.3360173089.1 |
$x^{8} - 2 x^{7} + 2 x^{6} - 8 x^{5} + 32 x^{4} - 51 x^{3} + 36 x^{2} - 7 x + 1$ |
$8$ |
[0,4] |
$7^{6}\cdot 13^{4}$ |
$2$ |
$15.5165514631$ |
$18.248200448594663$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$22.9514674902$ |
| 8.0.3360173089.2 |
$x^{8} - x^{7} + 8 x^{6} + 3 x^{5} + 9 x^{4} + 13 x^{3} + 18 x^{2} + 9 x + 4$ |
$8$ |
[0,4] |
$7^{6}\cdot 13^{4}$ |
$2$ |
$15.5165514631$ |
$18.248200448594663$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$56.3375372069$ |
| 8.0.3782742016.1 |
$x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} + 4 x^{2} - 16 x + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 31^{4}$ |
$2$ |
$15.748015748$ |
$27.911689339648817$ |
✓ |
|
|
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$76.9159796917$ |
| 8.0.3782742016.5 |
$x^{8} - 2 x^{7} + 11 x^{6} - 14 x^{5} + 39 x^{4} - 28 x^{3} + 54 x^{2} - 16 x + 28$ |
$8$ |
[0,4] |
$2^{12}\cdot 31^{4}$ |
$2$ |
$15.748015748$ |
$27.911689339648817$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$42.9387034214$ |
| 8.0.4032758016.4 |
$x^{8} - 2 x^{7} + 2 x^{6} - 4 x^{5} - x^{4} + 4 x^{3} + 2 x^{2} - 10 x + 25$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{8}\cdot 7^{4}$ |
$3$ |
$15.8745078664$ |
$31.66579252742446$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
trivial |
$4$ |
$3$ |
$120.87811487$ |
| 8.0.4569760000.9 |
$x^{8} + x^{6} + 2 x^{4} + 9 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$16.1245154966$ |
$24.725432631349385$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$4$ |
$3$ |
$59.9551527465$ |
| 8.0.4569760000.11 |
$x^{8} - 2 x^{6} + 3 x^{4} + 3 x^{2} + 1$ |
$8$ |
[0,4] |
$2^{8}\cdot 5^{4}\cdot 13^{4}$ |
$3$ |
$16.1245154966$ |
$24.725432631349385$ |
|
|
✓ |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$57.7860515992$ |
| 8.0.4931831529.1 |
$x^{8} - x^{7} + x^{6} + 5 x^{5} + 13 x^{4} + 5 x^{3} + x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{10}\cdot 17^{4}$ |
$2$ |
$16.2789364996$ |
$21.42428528562855$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$48.7234772798$ |
| 8.0.4931831529.2 |
$x^{8} - x^{7} - 5 x^{6} + 4 x^{5} + 23 x^{4} - 14 x^{3} - 23 x^{2} - 40 x + 64$ |
$8$ |
[0,4] |
$3^{10}\cdot 17^{4}$ |
$2$ |
$16.2789364996$ |
$21.42428528562855$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$118.96943902$ |
| 8.0.5554571841.4 |
$x^{8} - x^{7} - 4 x^{6} + 3 x^{5} + 18 x^{4} - 14 x^{3} + x^{2} - 12 x + 9$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{4}\cdot 13^{4}$ |
$3$ |
$16.5227116419$ |
$22.852356834621286$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2, 2]$ |
$6$ |
$3$ |
$51.2308049404$ |
| 8.0.5554571841.5 |
$x^{8} - x^{7} + 8 x^{6} - 6 x^{5} + 21 x^{4} - 11 x^{3} + 25 x^{2} - 9 x + 12$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{4}\cdot 13^{4}$ |
$3$ |
$16.5227116419$ |
$22.852356834621286$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[4]$ |
$2$ |
$3$ |
$52.1584722493$ |
| 8.0.5554571841.6 |
$x^{8} - 13 x^{6} + 46 x^{4} - 21 x^{2} + 36$ |
$8$ |
[0,4] |
$3^{4}\cdot 7^{4}\cdot 13^{4}$ |
$3$ |
$16.5227116419$ |
$35.04194650073235$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$96.6554616047$ |
| 8.0.6146560000.15 |
$x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} + 18 x^{4} + 16 x^{3} + 12 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{12}\cdot 5^{4}\cdot 7^{4}$ |
$3$ |
$16.7332005307$ |
$23.143481397064466$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$41.3399731494$ |
| 8.0.6784652161.1 |
$x^{8} - x^{7} - 4 x^{5} + 6 x^{4} + 4 x^{3} + x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 41^{4}$ |
$2$ |
$16.9410743461$ |
$23.430989084024507$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$168.225795064$ |
| 8.0.7487094784.2 |
$x^{8} - 8 x^{6} + 22 x^{4} - 16 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{18}\cdot 13^{4}$ |
$2$ |
$17.1509889212$ |
$26.299433382699032$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$136.128674343$ |
| 8.0.7487094784.3 |
$x^{8} + 8 x^{6} + 22 x^{4} + 16 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{18}\cdot 13^{4}$ |
$2$ |
$17.1509889212$ |
$26.299433382699032$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
trivial |
$2$ |
$3$ |
$80.6052912972$ |
| 8.0.7695324729.2 |
$x^{8} - 9 x^{6} + 18 x^{4} + 3 x^{2} + 36$ |
$8$ |
[0,4] |
$3^{10}\cdot 19^{4}$ |
$2$ |
$17.209900874$ |
$22.64950330581225$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[4]$ |
$6$ |
$3$ |
$78.5483433847$ |
| 8.0.7695324729.3 |
$x^{8} - x^{7} - 8 x^{6} - 4 x^{5} + 40 x^{4} - 4 x^{3} - 8 x^{2} - x + 1$ |
$8$ |
[0,4] |
$3^{10}\cdot 19^{4}$ |
$2$ |
$17.209900874$ |
$22.64950330581225$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[4]$ |
$2$ |
$3$ |
$70.5903508279$ |
| 8.0.8208541201.1 |
$x^{8} - x^{7} + 7 x^{6} + 3 x^{5} + 27 x^{4} - 3 x^{3} + 7 x^{2} + x + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 43^{4}$ |
$2$ |
$17.3493515729$ |
$23.99567223510292$ |
|
|
? |
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$2$ |
$3$ |
$25.061520038$ |
| 8.0.9116621361.1 |
$x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} - 12 x^{4} - 6 x^{3} + 5 x^{2} + 42 x + 49$ |
$8$ |
[0,4] |
$3^{4}\cdot 103^{4}$ |
$2$ |
$17.5783958312$ |
$38.0585388267201$ |
|
|
|
$A_4\times C_2$ (as 8T13) |
$[2]$ |
$6$ |
$3$ |
$287.869265868$ |
