Properties

Label 2.163.abs_bes
Base field $\F_{163}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $1 - 44 x + 798 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0236068181920$, $\pm0.241413415058$
Angle rank:  $2$ (numerical)
Number field:  4.0.39744.5
Galois group:  $D_{4}$
Jacobians:  $28$

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:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $20152$ $696936768$ $18749460156856$ $498312833339802624$ $13239625329965910743032$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $120$ $26230$ $4329384$ $705913774$ $115063524600$ $18755363155750$ $3057125083076520$ $498311411768505694$ $81224760504261240312$ $13239635966787143560150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 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 4.0.39744.5.

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.bs_bes$2$(not in LMFDB)