Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ |
| $1 - 23 x + 243 x^{2} - 1490 x^{3} + 5589 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.112386341891$, $\pm0.186011988595$, $\pm0.284877382774$ |
| Angle rank: | $3$ (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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4320$ | $136857600$ | $1820627383680$ | $22034402058240000$ | $266930683449174381600$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $487$ | $12298$ | $281367$ | $6443471$ | $148056424$ | $3404868209$ | $78311179919$ | $1801154483014$ | $41426522921407$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The isogeny class factors as 1.23.aj $\times$ 1.23.ai $\times$ 1.23.ag 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.