Properties

Label 2.181.abx_bkv
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:  $1 - 49 x + 957 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0295624989655$, $\pm0.190960746979$
Angle rank:  $2$ (numerical)
Number field:  4.0.633717.2
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
$A(\F_{q^r})$ 24801 1057440237 35140624323525 1151922971588050725 37738613257322806255056 1236354191423556302210480325 40504198696075677902666066110581 1326958061601746947605982935485727525 43472473114974760620822484479000918069225 1424201691954199136940811324280520006349811712

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32275 5926165 1073270371 194264329378 35161828899307 6364290878494633 1151936656056190051 208500535028375569105 37738596846350067133030

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.633717.2.
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.bx_bkv$2$(not in LMFDB)