Properties

Label 2.167.abv_bhz
Base field $\F_{167}$
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:  $\F_{167}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 883 x^{2} - 7849 x^{3} + 27889 x^{4}$
Frobenius angles:  $\pm0.0653585255984$, $\pm0.182853389423$
Angle rank:  $2$ (numerical)
Number field:  4.0.925613.1
Galois group:  $D_{4}$
Jacobians:  $9$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $20877$ $765538713$ $21678615651267$ $604966396090831389$ $16871969707024828628112$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $121$ $27447$ $4654597$ $777795395$ $129892307276$ $21691967385051$ $3622557647310527$ $604967117254049395$ $101029508529127859407$ $16871927924826638687262$

Jacobians and polarizations

This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$
The endomorphism algebra of this simple isogeny class is 4.0.925613.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.167.bv_bhz$2$(not in LMFDB)