Properties

Label 2.181.abv_bje
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:  $( 1 - 24 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$
Frobenius angles:  $\pm0.149335043618$, $\pm0.173686936480$
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
$A(\F_{q^r})$ 25122 1060902060 35159052952800 1151998223159010240 37738873490422887496362 1236354979603990374674784000 40504200802083358208141825233002 1326958066503335699349987336399394560 43472473124477292370272943458912535423200 1424201691967429743954485698682674204645951500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32381 5929272 1073340481 194265668955 35161851315098 6364291209404655 1151936660311275361 208500535073951143992 37738596846700652690501

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.ay $\times$ 1.181.ax 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_ahi$2$(not in LMFDB)
2.181.b_ahi$2$(not in LMFDB)
2.181.bv_bje$2$(not in LMFDB)