Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 32 x^{2} - 88 x^{3} + 121 x^{4} )$ |
$1 - 14 x + 91 x^{2} - 368 x^{3} + 1001 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.0750991438595$, $\pm0.140218899004$, $\pm0.424900856141$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $348$ | $1566000$ | $2313872532$ | $3088152000000$ | $4162394387139708$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $108$ | $1306$ | $14404$ | $160478$ | $1773900$ | $19505498$ | $214404284$ | $2357982046$ | $25937522028$ |
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.ag $\times$ 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.bu. 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.ao $\times$ 2.121.a_afm. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.