Properties

Label 2.181.abw_bju
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 930 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0243701074205$, $\pm0.211718100097$
Angle rank:  $2$ (numerical)
Number field:  4.0.4672.2
Galois group:  $D_{4}$
Jacobians:  22

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24956 1058833168 35145606897884 1151931946774930432 37738606348488341996156 1236354072995272239737235472 40504198190295030097281813967964 1326958060200524631699489979049852928 43472473112425408450271867368045814264444 1424201691952803815817146231007914228122021648

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32318 5927006 1073278734 194264293814 35161825531214 6364290799022990 1151936654839784350 208500535016148491750 37738596846313093815518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.4672.2.
All geometric endomorphisms are defined over $\F_{181}$.

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_bju$2$(not in LMFDB)