# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)