Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 25 x + 163 x^{2} )^{2}$ |
$1 - 50 x + 951 x^{2} - 8150 x^{3} + 26569 x^{4}$ | |
Frobenius angles: | $\pm0.0652307277549$, $\pm0.0652307277549$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $2$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $19321$ | $690165441$ | $18725940713104$ | $498260220088499001$ | $13239554876288343679561$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $114$ | $25972$ | $4323948$ | $705839236$ | $115062912294$ | $18755363780998$ | $3057125211164418$ | $498311414511757828$ | $81224760543592981524$ | $13239635967230078250772$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=2x^6+59x^3+122$
- $y^2=129x^6+4x^5+27x^4+153x^3+27x^2+4x+129$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The isogeny class factors as 1.163.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$ |
Base change
This is a primitive isogeny class.