Invariants
Base field: | $\F_{17}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 6 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$1 - 22 x + 211 x^{2} - 1132 x^{3} + 3587 x^{4} - 6358 x^{5} + 4913 x^{6}$ | |
Frobenius angles: | $\pm0.0779791303774$, $\pm0.0779791303774$, $\pm0.240632536990$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1200$ | $19468800$ | $115773044400$ | $582132695040000$ | $2863026403093230000$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-4$ | $228$ | $4796$ | $83452$ | $1420156$ | $24137316$ | $410328124$ | $6975721724$ | $118588094972$ | $2015997450468$ |
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.ag 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.