Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 16 x )^{2}( 1 - 27 x + 256 x^{2} )$ |
$1 - 59 x + 1376 x^{2} - 15104 x^{3} + 65536 x^{4}$ | |
Frobenius angles: | $0$, $0$, $\pm0.180343027596$ |
Angle rank: | $1$ (numerical) |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $51750$ | $4247433000$ | $281355229086750$ | $18446541825576618000$ | $1208925710564174413593750$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $198$ | $64808$ | $16770078$ | $4294920208$ | $1099511528598$ | $281474975601848$ | $72057593865607758$ | $18446744066656407328$ | $4722366482680374610758$ | $1208925819610637278597448$ |
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 $\F_{2^{8}}$.
Endomorphism algebra over $\F_{2^{8}}$The isogeny class factors as 1.256.abg $\times$ 1.256.abb 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.