Properties

Label 2.191.abw_bkp
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 951 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0856585252156$, $\pm0.218971105078$
Angle rank:  $2$ (numerical)
Number field:  4.0.13040272.1
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
$A(\F_{q^r})$ 28217 1316294833 48543204099908 1771241026132892713 64615235944826395314857 2357221975771722891140516368 85993800555309607637244314794313 3137139823941346827281520078088440777 114445997941912288409691746189053389715268 4175104451031945569148965860833601732926905233

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36080 6966720 1330896228 254195640624 48551234577158 9273284257555728 1771197285222884164 338298681550606970688 64615048177915421324240

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.13040272.1.
All geometric endomorphisms are defined over $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.bw_bkp$2$(not in LMFDB)