# Properties

 Label 2.191.abx_blu 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: $( 1 - 25 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$ Frobenius angles: $\pm0.140267993779$, $\pm0.165219579186$ 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 $A(\F_{q^r})$ 28056 1315040832 48541680381600 1771262819186515200 64615418719063270735656 2357222843468917663095628800 85993803546637026146941936872456 3137139831577488006404260044738892800 114445997953904547172083030979154795690400 4175104451024332861346539288135320686116264512

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 143 36045 6966500 1330912601 254196359653 48551252448942 9273284580130483 1771197289534171921 338298681586055701100 64615048177797604994805

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.az $\times$ 1.191.ay 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_aik $2$ (not in LMFDB) 2.191.b_aik $2$ (not in LMFDB) 2.191.bx_blu $2$ (not in LMFDB)