Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 11 x^{2} )( 1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4} )$ |
$1 - 14 x + 94 x^{2} - 388 x^{3} + 1034 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.0468428922585$, $\pm0.228229222880$, $\pm0.380176225592$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $364$ | $1658384$ | $2428264384$ | $3141808488000$ | $4160796310194524$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $114$ | $1372$ | $14658$ | $160418$ | $1769244$ | $19484246$ | $214351682$ | $2357851972$ | $25936927554$ |
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 $\F_{11^{6}}$.
Endomorphism algebra over $\F_{11}$The isogeny class factors as 1.11.af $\times$ 2.11.aj_bm 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 $\F_{11^{6}}$ is 1.1771561.acna 2 $\times$ 1.1771561.bow. 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.af_ads. The endomorphism algebra for each factor is: - Endomorphism algebra over $\F_{11^{3}}$
The base change of $A$ to $\F_{11^{3}}$ is 1.1331.bo $\times$ 2.1331.a_acna. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.