Invariants
Base field: | $\F_{163}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 25 x + 163 x^{2}$ |
Frobenius angles: | $\pm0.0652307277549$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-3}) \) |
Galois group: | $C_2$ |
Jacobians: | $2$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $1$ |
Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $139$ | $26271$ | $4327348$ | $705875499$ | $115063264669$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $139$ | $26271$ | $4327348$ | $705875499$ | $115063264669$ | $18755366679504$ | $3057125226189943$ | $498311414414939475$ | $81224760538723362124$ | $13239635967124119157311$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \). |
Base change
This is a primitive isogeny class.