Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 4 x + 17 x^{2} )( 1 - x + 17 x^{2} )( 1 + 2 x + 17 x^{2} )$ |
| $1 - 3 x + 45 x^{2} - 94 x^{3} + 765 x^{4} - 867 x^{5} + 4913 x^{6}$ | |
| Frobenius angles: | $\pm0.338793663197$, $\pm0.461304015105$, $\pm0.577979130377$ |
| Angle rank: | $3$ (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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4760$ | $31834880$ | $120924429920$ | $578600217395200$ | $2861449338510947800$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $15$ | $371$ | $5010$ | $82943$ | $1419375$ | $24136112$ | $410313135$ | $6975829247$ | $118588499970$ | $2015993680211$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{17}$.
Endomorphism algebra over $\F_{17}$| The isogeny class factors as 1.17.ae $\times$ 1.17.ab $\times$ 1.17.c 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.