Invariants
Base field: | $\F_{13}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$1 - 16 x + 121 x^{2} - 549 x^{3} + 1573 x^{4} - 2704 x^{5} + 2197 x^{6}$ | |
Frobenius angles: | $\pm0.0772104791556$, $\pm0.215685987913$, $\pm0.344616475996$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $623$ | $4461303$ | $10920532112$ | $23496688030431$ | $51181625711781488$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $156$ | $2263$ | $28804$ | $371263$ | $4824657$ | $62745730$ | $815755460$ | $10604610859$ | $137858522871$ |
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 $\F_{13}$.
Endomorphism algebra over $\F_{13}$The isogeny class factors as 1.13.ah $\times$ 2.13.aj_bt 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.