Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$ |
| $1 - 4 x + 8 x^{2} - 9 x^{3} + 10 x^{4} - 18 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8}$ | |
| Frobenius angles: | $\pm0.161334789180$, $\pm0.250000000000$, $\pm0.327009058845$, $\pm0.739882802642$ |
| Angle rank: | $3$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 2 |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4$ | $520$ | $7696$ | $275600$ | $1295764$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $5$ | $14$ | $41$ | $39$ | $62$ | $139$ | $225$ | $554$ | $1065$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2}$| The isogeny class factors as 1.2.ac $\times$ 3.2.ac_c_ab 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 $\F_{2^{4}}$ is 1.16.i $\times$ 3.16.q_ey_yp. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is 1.4.a $\times$ 3.4.a_i_ab. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.