Properties

Label 2.181.abv_bjd
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:  $1 - 47 x + 913 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.132251908937$, $\pm0.187299602773$
Angle rank:  $2$ (numerical)
Number field:  4.0.657725.1
Galois group:  $D_{4}$
Jacobians:  13

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 13 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25121 1060834709 35158215653501 1151992660939088309 37738847788163620114176 1236354889456945618976835725 40504200561876683682439253479781 1326958066081782287175268691651760389 43472473124491079096512385428025539779041 1424201691971302584625386989687300753842089984

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32379 5929131 1073335299 194265536650 35161848751323 6364291171661775 1151936659945323459 208500535074017267211 37738596846803275495654

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.657725.1.
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_bjd$2$(not in LMFDB)