Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
| $1 - 5 x + 15 x^{2} - 31 x^{3} + 50 x^{4} - 62 x^{5} + 60 x^{6} - 40 x^{7} + 16 x^{8}$ | |
| Frobenius angles: | $\pm0.174442860055$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.546783656212$ |
| Angle rank: | $3$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4$ | $1120$ | $11284$ | $89600$ | $1589324$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $10$ | $16$ | $22$ | $48$ | $82$ | $124$ | $254$ | $520$ | $930$ |
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 $\times$ 1.2.ab $\times$ 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 $\F_{2^{4}}$ is 1.16.ab $\times$ 1.16.i $\times$ 2.16.ac_b. 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 $\times$ 1.4.d $\times$ 2.4.c_b. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.