Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
| $1 - 2 x + 5 x^{2} - 8 x^{3} + 10 x^{4} - 8 x^{5} + 8 x^{6}$ | |
| Frobenius angles: | $\pm0.174442860055$, $\pm0.5$, $\pm0.546783656212$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6$ | $252$ | $558$ | $2016$ | $58146$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $11$ | $7$ | $7$ | $51$ | $107$ | $127$ | $223$ | $547$ | $1051$ |
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 $\F_{2^{2}}$.
Endomorphism algebra over $\F_{2}$| The isogeny class factors as 1.2.a $\times$ 2.2.ac_d 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 $\F_{2^{2}}$ is 1.4.e $\times$ 2.4.c_b. The endomorphism algebra for each factor is:
|
Base change
This is a primitive isogeny class.