Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$ |
$1 - 13 x + 81 x^{2} - 322 x^{3} + 891 x^{4} - 1573 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.451829325548$ |
Angle rank: | $2$ (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: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $396$ | $1667952$ | $2355076944$ | $3115894459392$ | $4187575203146676$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $115$ | $1328$ | $14535$ | $161449$ | $1777876$ | $19512499$ | $214402895$ | $2357984768$ | $25937637955$ |
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 $\F_{11}$.
Endomorphism algebra over $\F_{11}$The isogeny class factors as 1.11.ag 2 $\times$ 1.11.ab 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.