Invariants
Base field: | $\F_{23}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$1 - 23 x + 241 x^{2} - 1474 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
Frobenius angles: | $\pm0.0252283536038$, $\pm0.186011988595$, $\pm0.308104979730$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4288$ | $135569408$ | $1806958037248$ | $21955079523926016$ | $266619757351864728128$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $1$ | $483$ | $12208$ | $280359$ | $6435971$ | $148015356$ | $3404691389$ | $78310493615$ | $1801151265424$ | $41426502984843$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23^{6}}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.ai $\times$ 2.23.ap_du 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 $\F_{23^{6}}$ is 1.148035889.abgac 2 $\times$ 1.148035889.bhqk. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{23^{2}}$
The base change of $A$ to $\F_{23^{2}}$ is 1.529.as $\times$ 2.529.abd_ma. The endomorphism algebra for each factor is: - Endomorphism algebra over $\F_{23^{3}}$
The base change of $A$ to $\F_{23^{3}}$ is 1.12167.bo $\times$ 2.12167.a_abgac. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.