Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 11 x^{2} )^{3}$ |
$1 - 15 x + 108 x^{2} - 455 x^{3} + 1188 x^{4} - 1815 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.228229222880$, $\pm0.228229222880$, $\pm0.228229222880$ |
Angle rank: | $1$ (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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $343$ | $1685159$ | $2582630848$ | $3291326171875$ | $4233994921204433$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-3$ | $113$ | $1452$ | $15341$ | $163227$ | $1774748$ | $19479177$ | $214283861$ | $2357660532$ | $25936814033$ |
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.af 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-19}) \)$)$ |
Base change
This is a primitive isogeny class.