Properties

Label 2.181.abw_bjz
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:  $1 - 48 x + 935 x^{2} - 8688 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0944233419094$, $\pm0.189715959479$
Angle rank:  $2$ (numerical)
Number field:  4.0.2032272.2
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24961 1059170113 35149882608724 1151961389390580777 37738750881728090235481 1236354636099404393406354832 40504200020296488608663229122689 1326958065277741375241222235588753033 43472473124541872291051467651226809334644 1424201691977589214683319513218661928945313073

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 134 32328 5927726 1073306164 194265037814 35161841545854 6364291086565070 1151936659247332900 208500535074260879030 37738596846969859062168

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.2032272.2.
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_bjz$2$(not in LMFDB)