Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 24 x + 163 x^{2} )( 1 - 23 x + 163 x^{2} )$ |
$1 - 47 x + 878 x^{2} - 7661 x^{3} + 26569 x^{4}$ | |
Frobenius angles: | $\pm0.110906256499$, $\pm0.143017980409$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $19740$ | $693979440$ | $18742353270480$ | $498313227693758400$ | $13239698099694485531700$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $117$ | $26117$ | $4327740$ | $705914329$ | $115064157027$ | $18755381694854$ | $3057125436187401$ | $498311416911820081$ | $81224760563052570180$ | $13239635967284984818757$ |
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 $\F_{163}$.
Endomorphism algebra over $\F_{163}$The isogeny class factors as 1.163.ay $\times$ 1.163.ax 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.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.163.ab_ais | $2$ | (not in LMFDB) |
2.163.b_ais | $2$ | (not in LMFDB) |
2.163.bv_bhu | $2$ | (not in LMFDB) |