Properties

Label 2.191.abx_blu
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:  $( 1 - 25 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28056 1315040832 48541680381600 1771262819186515200 64615418719063270735656 2357222843468917663095628800 85993803546637026146941936872456 3137139831577488006404260044738892800 114445997953904547172083030979154795690400 4175104451024332861346539288135320686116264512

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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)