Properties

Label 2.181.abw_bjw
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:  $1 - 48 x + 932 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0587985007366$, $\pm0.204345036706$
Angle rank:  $2$ (numerical)
Number field:  4.0.3651840.3
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24958 1058967940 35147317165438 1151943736680090000 37738664441509340762158 1236354301431439325606384260 40504198947853787926218760298638 1326958062392017732815407870691840000 43472473118113649270503952774262224104798 1424201691966530412748623893438633235855458500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32322 5927294 1073289718 194264592854 35161832027922 6364290918055694 1151936656742226718 208500535043430152294 37738596846676822148802

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.3651840.3.
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_bjw$2$(not in LMFDB)