Invariants
Base field: | $\F_{2}$ |
Dimension: | $4$ |
L-polynomial: | $1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8}$ |
Frobenius angles: | $\pm0.0635622003031$, $\pm0.165221137389$, $\pm0.365221137389$, $\pm0.663562200303$ |
Angle rank: | $2$ (numerical) |
Number field: | 8.0.13140625.1 |
Galois group: | $C_2^2:C_4$ |
Jacobians: | $0$ |
Isomorphism classes: | 1 |
This isogeny class is simple but not geometrically 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1$ | $211$ | $1861$ | $88831$ | $1046771$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $4$ | $4$ | $20$ | $33$ | $46$ | $159$ | $324$ | $508$ | $1019$ |
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 $\F_{2^{10}}$.
Endomorphism algebra over $\F_{2}$The endomorphism algebra of this simple isogeny class is 8.0.13140625.1. |
The base change of $A$ to $\F_{2^{10}}$ is 2.1024.ad_bwv 2 and its endomorphism algebra is $\mathrm{M}_{2}($4.0.3625.1$)$ |
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is the simple isogeny class 4.4.ab_c_ai_z and its endomorphism algebra is 8.0.13140625.1. - Endomorphism algebra over $\F_{2^{5}}$
The base change of $A$ to $\F_{2^{5}}$ is the simple isogeny class 4.32.a_ad_a_bwv and its endomorphism algebra is 8.0.13140625.1.
Base change
This is a primitive isogeny class.