Properties

Label 2.191.aby_bmp
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:  $( 1 - 27 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$
Frobenius angles:  $\pm0.0686610702072$, $\pm0.187132320568$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27885 1312965225 48528938755440 1771202484229689225 64615178135059740742125 2357222014703926385561145600 85993801084779398672571394192365 3137139825472435623978491604036297225 114445997942646222604358486211305390891760 4175104451017532153406827147668336467369515625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35988 6964672 1330867268 254195413202 48551235379038 9273284314651982 1771197286087321348 338298681552776456512 64615048177692355395348

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.abb $\times$ 1.191.ax 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_ajf$2$(not in LMFDB)
2.191.e_ajf$2$(not in LMFDB)
2.191.by_bmp$2$(not in LMFDB)