Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| Weil polynomial: | $(1-2x+3x^{2})^{2}(1-3x+3x^{2})^{3}$ |
| Frobenius angles: | $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$ |
| Angle rank: | $1$ (numerical) |
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1, 1]$ |
Point counts
This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.
Point counts of the abelian variety
| $r$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| $A(\F_{q^r})$ | 4 | 49392 | 31698688 | 6944910336 | 1165570654204 | 225455270068224 | 51614165618530036 | 12492606163646988288 | 3012386135220532021504 | 720755591632702229851632 |
Point counts of the (virtual) curve
| $r$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| $C(\F_{q^r})$ | -9 | 5 | 48 | 137 | 321 | 800 | 2259 | 6737 | 20064 | 59285 |
Decomposition
1.3.ad 3 $\times$ 1.3.ac 2
Base change
This is a primitive isogeny class.