Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 8 x + 17 x^{2} )( 1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4} )$ |
| $1 - 20 x + 178 x^{2} - 928 x^{3} + 3026 x^{4} - 5780 x^{5} + 4913 x^{6}$ | |
| Frobenius angles: | $\pm0.0157896134134$, $\pm0.0779791303774$, $\pm0.349122946747$ |
| Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1390$ | $20635940$ | $116056526560$ | $577733681491200$ | $2852802639769683950$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $246$ | $4810$ | $82818$ | $1415078$ | $24117792$ | $410299286$ | $6975799682$ | $118588284490$ | $2015993668086$ |
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 $\F_{17^{6}}$.
Endomorphism algebra over $\F_{17}$| The isogeny class factors as 1.17.ai $\times$ 2.17.am_cn 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 $\F_{17^{6}}$ is 1.24137569.anxi 2 $\times$ 1.24137569.abmc. The endomorphism algebra for each factor is:
|
- Endomorphism algebra over $\F_{17^{2}}$
The base change of $A$ to $\F_{17^{2}}$ is 1.289.abe $\times$ 2.289.ao_adp. The endomorphism algebra for each factor is: - Endomorphism algebra over $\F_{17^{3}}$
The base change of $A$ to $\F_{17^{3}}$ is 1.4913.aea $\times$ 2.4913.a_anxi. The endomorphism algebra for each factor is:
Base change
This is a primitive isogeny class.