Properties

Label 2.191.abw_bks
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:  $( 1 - 26 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$
Frobenius angles:  $\pm0.110219473395$, $\pm0.206981219725$
Angle rank:  $2$ (numerical)
Jacobians:  32

This isogeny class is not 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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28220 1316519440 48546218097020 1771262611568296960 64615343927199401685500 2357222391444081281408554000 85993801820228015174863848245180 3137139826877520012295100310355722240 114445997946079346068453192529234692526780 4175104451028668523346007002184744155763626000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36086 6967152 1330912446 254196065424 48551243138678 9273284393960304 1771197286880617726 338298681562924658832 64615048177864704875126

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.aba $\times$ 1.191.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ae_ahi$2$(not in LMFDB)
2.191.e_ahi$2$(not in LMFDB)
2.191.bw_bks$2$(not in LMFDB)