Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 4 x )^{2}( 1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4} )$ |
$1 - 19 x + 163 x^{2} - 824 x^{3} + 2608 x^{4} - 4864 x^{5} + 4096 x^{6}$ | |
Frobenius angles: | $0$, $0$, $\pm0.133878927982$, $\pm0.347077071791$ |
Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1161$ | $14599575$ | $68032644876$ | $280282363458075$ | $1150297296203146311$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $222$ | $4057$ | $65258$ | $1046188$ | $16767783$ | $268427626$ | $4295064146$ | $68719857001$ | $1099510740222$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$The isogeny class factors as 1.16.ai $\times$ 2.16.al_ch 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.