Invariants
| Base field: | $\F_{11}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4} )$ |
| $1 - 15 x + 103 x^{2} - 426 x^{3} + 1133 x^{4} - 1815 x^{5} + 1331 x^{6}$ | |
| Frobenius angles: | $\pm0.0468428922585$, $\pm0.140218899004$, $\pm0.380176225592$ |
| Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $312$ | $1505088$ | $2325611808$ | $3102311467008$ | $4154340757959912$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-3$ | $103$ | $1314$ | $14471$ | $160167$ | $1770520$ | $19495725$ | $214403855$ | $2358013734$ | $25937228503$ |
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 $\F_{11^{6}}$.
Endomorphism algebra over $\F_{11}$| The isogeny class factors as 1.11.ag $\times$ 2.11.aj_bm and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
The base change of $A$ to $\F_{11^{6}}$ is 1.1771561.acna 2 $\times$ 1.1771561.dly. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{11^{2}}$
The base change of $A$ to $\F_{11^{2}}$ is 1.121.ao $\times$ 2.121.af_ads. The endomorphism algebra for each factor is: - Endomorphism algebra over $\F_{11^{3}}$
The base change of $A$ to $\F_{11^{3}}$ is 1.1331.as $\times$ 2.1331.a_acna. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.