Invariants
This isogeny class is simple but not geometrically simple,
primitive,
ordinary,
and not supersingular.
It is principally polarizable and
contains a Jacobian.
This isogeny class is ordinary.
Point counts
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2+(x^2+x+1)y=x^5+x^3+x^2+1$
Point counts of the abelian variety
| $r$ |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
|---|
| $A(\F_{q^r})$ |
$6$ |
$36$ |
$54$ |
$576$ |
$1086$ |
Point counts of the curve
| $r$ |
$1$ |
$2$ |
$3$ |
$4$ |
$5$ |
$6$ |
$7$ |
$8$ |
$9$ |
$10$ |
|---|
| $C(\F_{q^r})$ |
$3$ |
$7$ |
$9$ |
$31$ |
$33$ |
$43$ |
$129$ |
$223$ |
$513$ |
$1147$ |
Endomorphism algebra over $\F_{2}$
Endomorphism algebra over $\overline{\F}_{2}$
| The base change of $A$ to $\F_{2^{2}}$ is 1.4.b 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-15}) \)$)$ |
All geometric endomorphisms are defined over $\F_{2^{2}}$.
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
