# Properties

 Label 2.191.acb_bps 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: $( 1 - 27 x + 191 x^{2} )( 1 - 26 x + 191 x^{2} )$ Frobenius angles: $\pm0.0686610702072$, $\pm0.110219473395$ 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 $A(\F_{q^r})$ 27390 1307653380 48503242850040 1771116211426367520 64614968004475421222250 2357221716233344218075048000 85993801425938674696922673965610 3137139829821755679412752395845476480 114445997961892754664401194219749895590360 4175104451078905149532492301467672141225654500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 139 35841 6960982 1330802441 254194586549 48551229231498 9273284351441459 1771197288542903281 338298681609668585002 64615048178642180519001

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.abb $\times$ 1.191.aba 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_ami $2$ (not in LMFDB) 2.191.b_ami $2$ (not in LMFDB) 2.191.cb_bps $2$ (not in LMFDB)