# Properties

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

## 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.

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

 $r$ 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.
 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)