Invariants
Base field: | $\F_{13^{2}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 13 x )^{2}( 1 - 24 x + 169 x^{2} )$ |
$1 - 50 x + 962 x^{2} - 8450 x^{3} + 28561 x^{4}$ | |
Frobenius angles: | $0$, $0$, $\pm0.125665916378$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21024$ | $799416576$ | $23268899852064$ | $665370404536320000$ | $19004901566295727075104$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $27986$ | $4820760$ | $815674078$ | $137858040600$ | $23298082380146$ | $3937376376837240$ | $665416609182951358$ | $112455406950186673080$ | $19004963774795922773906$ |
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 $\F_{13^{2}}$.
Endomorphism algebra over $\F_{13^{2}}$The isogeny class factors as 1.169.aba $\times$ 1.169.ay 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.