Properties

Label 2.181.ar_iu
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:  $1 - 17 x + 228 x^{2} - 3077 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.176820765591$, $\pm0.569900268738$
Angle rank:  $2$ (numerical)
Number field:  4.0.37805724.1
Galois group:  $D_{4}$
Jacobians:  $480$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $29896$ $1078767264$ $35146919568256$ $1151934390461587584$ $37738909326496693369576$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $165$ $32929$ $5927226$ $1073281009$ $194265853425$ $35161842940918$ $6364290884818605$ $1151936658789683329$ $208500535084412010066$ $37738596846438330998329$

Jacobians and polarizations

This isogeny class contains the Jacobians of 480 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 4.0.37805724.1.

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.r_iu$2$(not in LMFDB)