Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
| $1 - 5 x + 14 x^{2} - 29 x^{3} + 47 x^{4} - 58 x^{5} + 56 x^{6} - 40 x^{7} + 16 x^{8}$ | |
| Frobenius angles: | $\pm0.123548644961$, $\pm0.174442860055$, $\pm0.456881978294$, $\pm0.546783656212$ |
| Angle rank: | $3$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2$ | $532$ | $4712$ | $38304$ | $1693282$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $8$ | $7$ | $8$ | $48$ | $113$ | $166$ | $272$ | $547$ | $1048$ |
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 $\F_{2}$| The isogeny class factors as 2.2.ad_f $\times$ 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 $\F_{2^{6}}$ is 1.64.l 2 $\times$ 2.64.ba_ld. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is 2.4.b_ad $\times$ 2.4.c_b. The endomorphism algebra for each factor is: - Endomorphism algebra over $\F_{2^{3}}$
The base change of $A$ to $\F_{2^{3}}$ is 2.8.ac_p $\times$ 2.8.a_l. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.