Properties

Label 2.181.abv_biz
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:  $1 - 47 x + 909 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0919956722480$, $\pm0.211005189210$
Angle rank:  $2$ (numerical)
Number field:  4.0.284445.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25117 1060565325 35154866511025 1151970369193277925 37738744066132427475712 1236354518735855879699593125 40504199523033080728821168027697 1326958063930020675666160674233852325 43472473122272700693738551503864412684725 1424201691977461542223496191630637775828480000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32371 5928567 1073314531 194265002730 35161838208043 6364291008431715 1151936658077372131 208500535063377589947 37738596846966475988326

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.284445.1.
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.bv_biz$2$(not in LMFDB)