Invariants
This isogeny class is simple and geometrically simple,
primitive,
not ordinary,
and supersingular.
It is principally polarizable and
contains a Jacobian.
This isogeny class is supersingular.
Point counts
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
Point counts of the abelian variety
$r$ |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$A(\F_{q^r})$ |
$4$ |
$16$ |
$28$ |
$64$ |
$244$ |
Point counts of the curve
$r$ |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
$9$ |
$10$ |
$C(\F_{q^r})$ |
$4$ |
$16$ |
$28$ |
$64$ |
$244$ |
$784$ |
$2188$ |
$6400$ |
$19684$ |
$59536$ |
Endomorphism algebra over $\F_{3}$
Endomorphism algebra over $\overline{\F}_{3}$
The base change of $A$ to $\F_{3^{2}}$ is the simple isogeny class 1.9.g and its endomorphism algebra is the quaternion algebra over \(\Q\) ramified at $3$ and $\infty$. |
All geometric endomorphisms are defined over $\F_{3^{2}}$.
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.