Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 2 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$ |
| $1 - 7 x + 26 x^{2} - 66 x^{3} + 128 x^{4} - 198 x^{5} + 234 x^{6} - 189 x^{7} + 81 x^{8}$ | |
| Frobenius angles: | $\pm0.0714477711956$, $\pm0.272071776080$, $\pm0.304086723985$, $\pm0.560185743604$ |
| Angle rank: | $4$ (numerical) |
| Isomorphism classes: | 1 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10$ | $9300$ | $621490$ | $46500000$ | $3863596550$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $13$ | $33$ | $89$ | $267$ | $673$ | $1922$ | $6417$ | $20229$ | $59993$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{3}$.
Endomorphism algebra over $\F_{3}$| The isogeny class factors as 1.3.ac $\times$ 3.3.af_n_az and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 4.3.ad_g_ao_bc | $2$ | (not in LMFDB) |
| 4.3.d_g_o_bc | $2$ | (not in LMFDB) |
| 4.3.h_ba_co_ey | $2$ | (not in LMFDB) |