Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 4 x )^{2}( 1 - 9 x + 41 x^{2} - 144 x^{3} + 256 x^{4} )$ |
$1 - 17 x + 129 x^{2} - 616 x^{3} + 2064 x^{4} - 4352 x^{5} + 4096 x^{6}$ | |
Frobenius angles: | $0$, $0$, $\pm0.0608845495576$, $\pm0.454248801212$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1305$ | $14713875$ | $65720368980$ | $275894116999875$ | $1147899425817065625$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $0$ | $226$ | $3915$ | $64226$ | $1044000$ | $16770991$ | $268422840$ | $4294777346$ | $68718526875$ | $1099510512946$ |
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.aj_bp 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.