Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
| $1 - 26 x + 294 x^{2} - 1844 x^{3} + 6762 x^{4} - 13754 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.186011988595$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3600$ | $125452800$ | $1775575468800$ | $21946123203840000$ | $266921851464714690000$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $442$ | $11992$ | $280242$ | $6443258$ | $148083964$ | $3405076358$ | $78312069794$ | $1801156630216$ | $41426523384682$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.aj 2 $\times$ 1.23.ai 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.