Invariants
Base field: | $\F_{2^{6}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 8 x )^{2}( 1 - 13 x + 64 x^{2} )$ |
$1 - 29 x + 336 x^{2} - 1856 x^{3} + 4096 x^{4}$ | |
Frobenius angles: | $0$, $0$, $\pm0.198106042756$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $2548$ | $16098264$ | $68529639724$ | $281446754425200$ | $1152921471322750948$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $36$ | $3928$ | $261420$ | $16775536$ | $1073741796$ | $68719387336$ | $4398043777884$ | $281474934317536$ | $18014398032634260$ | $1152921500315679928$ |
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.an 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.