Properties

Label 2.181.abv_bjc
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:  $( 1 - 25 x + 181 x^{2} )( 1 - 22 x + 181 x^{2} )$
Frobenius angles:  $\pm0.120568372405$, $\pm0.195291079027$
Angle rank:  $2$ (numerical)
Jacobians:  24

This isogeny class is not 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
$A(\F_{q^r})$ 25120 1060767360 35157378359680 1151987094432576000 37738821994604977348000 1236354798297031772995952640 40504200313880881812351672722080 1326958065613867935854030242288896000 43472473124279575131677789025002677467520 1424201691974259127235077150178790576090384000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32377 5928990 1073330113 194265403875 35161846158742 6364291132695015 1151936659539125473 208500535073002862310 37738596846881618170177

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.az $\times$ 1.181.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_ahg$2$(not in LMFDB)
2.181.d_ahg$2$(not in LMFDB)
2.181.bv_bjc$2$(not in LMFDB)