Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $5$ |
| L-polynomial: | $( 1 - x + 2 x^{2} )( 1 + x^{3} + x^{4} + 2 x^{5} + 16 x^{8} )$ |
| $1 - x + 2 x^{2} + x^{3} + 3 x^{5} + 4 x^{7} + 16 x^{8} - 16 x^{9} + 32 x^{10}$ | |
| Frobenius angles: | $\pm0.160761046163$, $\pm0.352134945401$, $\pm0.384973271919$, $\pm0.624242320844$, $\pm0.891697068324$ |
| Angle rank: | $5$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 30 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $5$ |
| Slopes: | $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $42$ | $2520$ | $80262$ | $1638000$ | $31522722$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $8$ | $17$ | $20$ | $32$ | $53$ | $135$ | $396$ | $503$ | $958$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$| The isogeny class factors as 1.2.ab $\times$ 4.2.a_a_b_b and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 5.2.ab_c_ab_c_af | $2$ | (not in LMFDB) |
| 5.2.b_c_ab_a_ad | $2$ | (not in LMFDB) |
| 5.2.b_c_b_c_f | $2$ | (not in LMFDB) |