Invariants
Base field: | $\F_{13}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$1 - 9 x + 46 x^{2} - 117 x^{3} + 169 x^{4}$ | |
Frobenius angles: | $\pm0.256122854178$, $\pm0.312832958189$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 6 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $90$ | $30780$ | $5193720$ | $832291200$ | $138056202450$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $5$ | $181$ | $2360$ | $29137$ | $371825$ | $4822234$ | $62722805$ | $815674753$ | $10604553320$ | $137859316861$ |
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.af $\times$ 1.13.ae 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.