Properties

Label 2.163.abv_bhu
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 24 x + 163 x^{2} )( 1 - 23 x + 163 x^{2} )$
Frobenius angles:  $\pm0.110906256499$, $\pm0.143017980409$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19740 693979440 18742353270480 498313227693758400 13239698099694485531700 351764115263663963149175040 9346015336530360438784279602660 248314266932195966611174320862252800 6597461726153552308901435593049585388240 175287960542693552979991658817632889078913200

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

Decomposition and endomorphism algebra

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:
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon 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)