Properties

Label 2.181.abv_biw
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:  $1 - 47 x + 906 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0635793485401$, $\pm0.221935502645$
Angle rank:  $2$ (numerical)
Number field:  4.0.9265212.2
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
$A(\F_{q^r})$ 25114 1060363308 35152354711456 1151953605373879488 37738665315964174366594 1236354230043666854621468928 40504198661630860494554980168354 1326958061821943784027104142041832192 43472473118163894905683421251379226902944 1424201691971805592242839605423461969531376908

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32365 5928144 1073298913 194264597355 35161829997658 6364290873082431 1151936656247343649 208500535043671137936 37738596846816604226965

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.9265212.2.
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_biw$2$(not in LMFDB)