Invariants
Base field: | $\F_{2}$ |
Dimension: | $4$ |
L-polynomial: | $1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8}$ |
Frobenius angles: | $\pm0.0755571399449$, $\pm0.203216343788$, $\pm0.424442860055$, $\pm0.703216343788$ |
Angle rank: | $2$ (numerical) |
Number field: | 8.0.18939904.2 |
Galois group: | $D_4\times C_2$ |
Jacobians: | $0$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $2$ | $292$ | $2402$ | $85264$ | $930082$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $5$ | $5$ | $21$ | $29$ | $65$ | $181$ | $253$ | $437$ | $1025$ |
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 endomorphism algebra of this simple isogeny class is 8.0.18939904.2. |
The base change of $A$ to $\F_{2^{4}}$ is 2.16.c_b 2 and its endomorphism algebra is $\mathrm{M}_{2}($4.0.1088.2$)$ |
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is the simple isogeny class 4.4.a_c_a_b and its endomorphism algebra is 8.0.18939904.2.
Base change
This is a primitive isogeny class.