Invariants
Base field: | $\F_{2^{6}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 8 x )^{2}( 1 - 11 x + 64 x^{2} )$ |
$1 - 27 x + 304 x^{2} - 1728 x^{3} + 4096 x^{4}$ | |
Frobenius angles: | $0$, $0$, $\pm0.258708130235$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $2646$ | $16288776$ | $68655500046$ | $281474121474000$ | $1152893643780692646$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $38$ | $3976$ | $261902$ | $16777168$ | $1073715878$ | $68718866776$ | $4398038840702$ | $281474910402208$ | $18014398103222678$ | $1152921503039558056$ |
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 $\F_{2^{6}}$The isogeny class factors as 1.64.aq $\times$ 1.64.al and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
|
Base change
This is a primitive isogeny class.