Properties

Label 2.191.abz_bns
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 191 x^{2} )( 1 - 25 x + 191 x^{2} )$
Frobenius angles:  $\pm0.110219473395$, $\pm0.140267993779$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27722 1311416932 48523525494968 1771197872375495200 64615240680028026608702 2357222495526466821096692800 85993803317669414895780060408542 3137139833466253119636570289357852800 114445997965836145111240378905074452148888 4175104451070618955899687190963038843686059012

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 141 35945 6963894 1330863801 254195659251 48551245282442 9273284555439381 1771197290600549521 338298681621325120074 64615048178513941140305

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.aba $\times$ 1.191.az 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.ab_aki$2$(not in LMFDB)
2.191.b_aki$2$(not in LMFDB)
2.191.bz_bns$2$(not in LMFDB)