Invariants
| Base field: | $\F_{17}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
| $1 - 23 x + 227 x^{2} - 1230 x^{3} + 3859 x^{4} - 6647 x^{5} + 4913 x^{6}$ | |
| Frobenius angles: | $\pm0.0779791303774$, $\pm0.0779791303774$, $\pm0.177280642489$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1100$ | $18590000$ | $114014700800$ | $580602880000000$ | $2863668774319127500$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-5$ | $215$ | $4720$ | $83231$ | $1420475$ | $24145220$ | $410379755$ | $6975926591$ | $118588488880$ | $2015996127575$ |
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 $\F_{17}$.
Endomorphism algebra over $\F_{17}$The isogeny class factors as 1.17.ai 2 $\times$ 1.17.ah 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.