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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27390 1307653380 48503242850040 1771116211426367520 64614968004475421222250 2357221716233344218075048000 85993801425938674696922673965610 3137139829821755679412752395845476480 114445997961892754664401194219749895590360 4175104451078905149532492301467672141225654500

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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)