Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 17 x + 79 x^{2} )( 1 - 16 x + 79 x^{2} )$ |
$1 - 33 x + 430 x^{2} - 2607 x^{3} + 6241 x^{4}$ | |
Frobenius angles: | $\pm0.0944227114288$, $\pm0.143514932644$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4032$ | $37545984$ | $242502978816$ | $1517038725242880$ | $9468461809993983552$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $6013$ | $491852$ | $38948281$ | $3077116757$ | $243088553806$ | $19203921995123$ | $1517108935530961$ | $119851597020907748$ | $9468276089931882853$ |
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 $\F_{79}$.
Endomorphism algebra over $\F_{79}$The isogeny class factors as 1.79.ar $\times$ 1.79.aq 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.