Invariants
| Base field: | $\F_{2^{3}}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 + 8 x^{2} )( 1 + x + 8 x^{2} )$ |
| $1 + x + 16 x^{2} + 8 x^{3} + 64 x^{4}$ | |
| Frobenius angles: | $\pm0.5$, $\pm0.556567041129$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $1$ |
| Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $90$ | $6480$ | $251370$ | $15876000$ | $1083015450$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $10$ | $96$ | $490$ | $3872$ | $33050$ | $263664$ | $2094410$ | $16767808$ | $134240890$ | $1073793936$ |
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 $\F_{2^{6}}$.
Endomorphism algebra over $\F_{2^{3}}$| The isogeny class factors as 1.8.a $\times$ 1.8.b 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 $\F_{2^{6}}$ is 1.64.p $\times$ 1.64.q. The endomorphism algebra for each factor is:
|
Base change
This is a primitive isogeny class.