Properties

Label 2.191.abw_bkn
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:  $( 1 - 27 x + 191 x^{2} )( 1 - 21 x + 191 x^{2} )$
Frobenius angles:  $\pm0.0686610702072$, $\pm0.225319681555$
Angle rank:  $2$ (numerical)
Jacobians:  56

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 56 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28215 1316145105 48541194797040 1771226609260596345 64615163346536461275375 2357221691360552948005536000 85993799651427907735931749462335 3137139821592665603258026237554590505 114445997937055231688557018298209488597360 4175104451024740279854947565026894669016782625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36076 6966432 1330885396 254195355024 48551228719198 9273284160084144 1771197283896842596 338298681536249667552 64615048177803910314076

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.abb $\times$ 1.191.av 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.ag_ahd$2$(not in LMFDB)
2.191.g_ahd$2$(not in LMFDB)
2.191.bw_bkn$2$(not in LMFDB)