Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 11 x^{2} )( 1 - 8 x + 32 x^{2} - 88 x^{3} + 121 x^{4} )$ |
$1 - 13 x + 83 x^{2} - 336 x^{3} + 913 x^{4} - 1573 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.0750991438595$, $\pm0.228229222880$, $\pm0.424900856141$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $406$ | $1725500$ | $2416006936$ | $3127468750000$ | $4168862454145466$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $119$ | $1364$ | $14591$ | $160729$ | $1772624$ | $19494019$ | $214352111$ | $2357820284$ | $25937221079$ |
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 $\F_{11^{4}}$.
Endomorphism algebra over $\F_{11}$The isogeny class factors as 1.11.af $\times$ 2.11.ai_bg and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
The base change of $A$ to $\F_{11^{4}}$ is 1.14641.afm 2 $\times$ 1.14641.iz. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{11^{2}}$
The base change of $A$ to $\F_{11^{2}}$ is 1.121.ad $\times$ 2.121.a_afm. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.