Properties

Label 2.181.abv_bja
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:  $1 - 47 x + 910 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.101095234702$, $\pm0.206548865791$
Angle rank:  $2$ (numerical)
Number field:  4.0.5395052.1
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
$A(\F_{q^r})$ 25118 1060632668 35155703788448 1151975948559692672 37738770133589417846358 1236354612936908884486068992 40504199794471643475908992301702 1326958064538181042526605543263723008 43472473123172449886687161457327389299872 1424201691977355590243605134031641656775780348

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32373 5928708 1073319729 194265136915 35161840887114 6364291051081959 1151936658605318145 208500535067692922724 37738596846963668465293

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.5395052.1.
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_bja$2$(not in LMFDB)