Invariants
Base field: | $\F_{5}$ |
Dimension: | $4$ |
L-polynomial: | $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$1 - 13 x + 79 x^{2} - 299 x^{3} + 788 x^{4} - 1495 x^{5} + 1975 x^{6} - 1625 x^{7} + 625 x^{8}$ | |
Frobenius angles: | $\pm0.0878807261908$, $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.450170915301$ |
Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $4$ |
Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $36$ | $248400$ | $224644212$ | $144731750400$ | $97001204486976$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-7$ | $15$ | $113$ | $591$ | $3178$ | $16263$ | $79933$ | $393087$ | $1955453$ | $9772410$ |
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 $\F_{5}$.
Endomorphism algebra over $\F_{5}$The isogeny class factors as 1.5.ae 2 $\times$ 2.5.af_n 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.