Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 4 x )^{2}( 1 - 9 x + 44 x^{2} - 144 x^{3} + 256 x^{4} )$ |
$1 - 17 x + 132 x^{2} - 640 x^{3} + 2112 x^{4} - 4352 x^{5} + 4096 x^{6}$ | |
Frobenius angles: | $0$, $0$, $\pm0.126935807746$, $\pm0.434779740724$ |
Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1332$ | $15118200$ | $67046618268$ | $277852348321200$ | $1149673953169893492$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $232$ | $3996$ | $64688$ | $1045620$ | $16777768$ | $268465932$ | $4294976096$ | $68718920292$ | $1099509955672$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$The isogeny class factors as 1.16.ai $\times$ 2.16.aj_bs 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.