Properties

Label 2.181.abu_bhx
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:  $1 - 46 x + 881 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0750770395501$, $\pm0.236117797856$
Angle rank:  $2$ (numerical)
Number field:  4.0.20904000.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25271 1061761065 35157464922716 1151964633686097465 37738675923132130311791 1236354214545056348418785040 40504198618435684403686755501911 1326958062082509757099229093665349865 43472473120425426998535617199244135501436 1424201691981254214565677837215671604173415625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32408 5929006 1073309188 194264651956 35161829556878 6364290866295316 1151936656473541828 208500535054517786806 37738596847066974487448

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.20904000.1.
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.bu_bhx$2$(not in LMFDB)