Properties

Label 2.181.abx_bla
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 181 x^{2} )( 1 - 24 x + 181 x^{2} )$
Frobenius angles:  $\pm0.120568372405$, $\pm0.149335043618$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24806 1057777452 35144989483400 1151953917217444800 37738771034746308795806 1236354835482079799582995200 40504200907100258103785614856606 1326958068119436112570739794294675200 43472473131471969430989119699032637558600 1424201691989067777523831732304639802015408012

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32285 5926900 1073299201 194265141553 35161847216282 6364291225905613 1151936661714217441 208500535107498669700 37738596847274018829605

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.az $\times$ 1.181.ay 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.ab_aje$2$(not in LMFDB)
2.181.b_aje$2$(not in LMFDB)
2.181.bx_bla$2$(not in LMFDB)