Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
| $1 - 5 x + 14 x^{2} - 27 x^{3} + 42 x^{4} - 54 x^{5} + 56 x^{6} - 40 x^{7} + 16 x^{8}$ | |
| Frobenius angles: | $\pm0.147012170705$, $\pm0.250000000000$, $\pm0.341962716420$, $\pm0.600633654388$ |
| Angle rank: | $3$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3$ | $765$ | $6669$ | $141525$ | $1923843$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $8$ | $13$ | $28$ | $53$ | $59$ | $110$ | $300$ | $562$ | $983$ |
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 $\times$ 3.2.ad_g_aj 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 $\F_{2^{4}}$ is 1.16.i $\times$ 3.16.d_bq_db. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{2^{2}}$
The base change of $A$ to $\F_{2^{2}}$ is 1.4.a $\times$ 3.4.d_g_h. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.