Properties

Label 2.181.abw_bjx
Base field $\F_{181}$
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:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 933 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0712454186694$, $\pm0.200090328096$
Angle rank:  $2$ (numerical)
Number field:  4.0.223225.1
Galois group:  $D_{4}$
Jacobians:  $26$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $24959$ $1059035329$ $35148172307600$ $1151949625203197689$ $37738693348157251730159$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $134$ $32324$ $5927438$ $1073295204$ $194264741654$ $35161835230838$ $6364290975562094$ $1151936657623560004$ $208500535055041922198$ $37738596846807669294404$

Jacobians and polarizations

This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.223225.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.181.bw_bjx$2$(not in LMFDB)