Properties

Label 2.181.abv_bit
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:  $1 - 47 x + 903 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0200095723598$, $\pm0.230670495285$
Angle rank:  $2$ (numerical)
Number field:  4.0.22725.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25111 1060161309 35149842960811 1151936802973792629 37738585744099234253776 1236353932209071229509137725 40504197729335016350367027062731 1326958059284396400250512853058811429 43472473111897230916929348353752667355031 1424201691956828754890205921641259113068771584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32359 5927721 1073283259 194264187750 35161821527263 6364290726593865 1151936654044490419 208500535013615272671 37738596846419746934854

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.22725.1.
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_bit$2$(not in LMFDB)