Invariants
Base field: | $\F_{2}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 + x + 2 x^{2} )^{2}$ |
$1 + 2 x + 5 x^{2} + 4 x^{3} + 4 x^{4}$ | |
Frobenius angles: | $\pm0.615026728081$, $\pm0.615026728081$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $16$ | $64$ | $16$ | $256$ | $1936$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $5$ | $11$ | $-1$ | $15$ | $55$ | $47$ | $103$ | $319$ | $503$ | $911$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$The isogeny class factors as 1.2.b 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$ |
Base change
This is a primitive isogeny class.