Invariants
Base field: | $\F_{17}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$ |
$1 - 15 x + 90 x^{2} - 255 x^{3} + 289 x^{4}$ | |
Frobenius angles: | $\pm0.0779791303774$, $\pm0.177280642489$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 1 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $110$ | $71500$ | $23703680$ | $6978400000$ | $2018018233550$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $3$ | $245$ | $4824$ | $83553$ | $1421283$ | $24146210$ | $410373939$ | $6975863233$ | $118588080888$ | $2015993940725$ |
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 $\times$ 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.