Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $( 1 - 2 x + 2 x^{2} )^{6}$ |
| $1 - 12 x + 72 x^{2} - 280 x^{3} + 780 x^{4} - 1632 x^{5} + 2624 x^{6} - 3264 x^{7} + 3120 x^{8} - 2240 x^{9} + 1152 x^{10} - 384 x^{11} + 64 x^{12}$ | |
| Frobenius angles: | $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$ |
| Angle rank: | $0$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not simple, primitive, not ordinary, and supersingular. It is principally polarizable.
Newton polygon
This isogeny class is supersingular.
| $p$-rank: | $0$ |
| Slopes: | $[1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1$ | $15625$ | $4826809$ | $244140625$ | $4750104241$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-9$ | $5$ | $33$ | $65$ | $81$ | $65$ | $33$ | $65$ | $321$ | $1025$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2}$| The isogeny class factors as 1.2.ac 6 and its endomorphism algebra is $\mathrm{M}_{6}($\(\Q(\sqrt{-1}) \)$)$ |
| The base change of $A$ to $\F_{2^{4}}$ is 1.16.i 6 and its endomorphism algebra is $\mathrm{M}_{6}(B)$, where $B$ is the quaternion algebra over \(\Q\) ramified at $2$ and $\infty$. |
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is 1.4.a 6 and its endomorphism algebra is $\mathrm{M}_{6}($\(\Q(\sqrt{-1}) \)$)$
Base change
This is a primitive isogeny class.