Properties

Label 2.191.aca_boq
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:  $1 - 52 x + 1056 x^{2} - 9932 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0407629633776$, $\pm0.151065030898$
Angle rank:  $2$ (numerical)
Number field:  4.0.127232.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27554 1309421188 48511750095746 1771143887259580688 64615026883385448761794 2357221733620401461778092548 85993800830980474943173177986914 3137139825990975068538543245031391232 114445997945204380090285217468755161476834 4175104451019061812564125558087986967299701508

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 140 35890 6962204 1330823238 254194818180 48551229589618 9273284287283156 1771197286380083454 338298681560338287596 64615048177716028815090

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.127232.1.
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.ca_boq$2$(not in LMFDB)