Properties

Label 2.181.abv_biv
Base Field $\F_{181}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 905 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0525515266489$, $\pm0.225033026600$
Angle rank:  $2$ (numerical)
Number field:  4.0.8177037.2
Galois group:  $D_{4}$
Jacobians:  12

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25113 1060295973 35151517455813 1151948008860622677 37738638883308874545408 1236354131781853908338566557 40504198358759399288038960007997 1326958061024072536623697374735302853 43472473116317535690473921893305252875817 1424201691967871905432422042333472488275202048

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32363 5928003 1073293699 194264461290 35161827203099 6364290825493239 1151936655554708995 208500535034815720779 37738596846712369116518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.8177037.2.
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_biv$2$(not in LMFDB)