Properties

Label 2.191.acb_bpr
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 53 x + 1083 x^{2} - 10123 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0128489088744$, $\pm0.129572401751$
Angle rank:  $2$ (numerical)
Number field:  4.0.3725.1
Galois group:  $D_{4}$
Jacobians:  1

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27389 1307578249 48502133155475 1771107024866409149 64614911891852335078384 2357221433561431885089397225 85993800184336856401664715420239 3137139824914372357573477299909048149 114445997944100630064167549228390492513225 4175104451019014422541328004456339766516195584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 139 35839 6960823 1330795539 254194365804 48551223409363 9273284217551269 1771197285772244499 338298681557075638093 64615048177715295394254

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.3725.1.
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.cb_bpr$2$(not in LMFDB)