Properties

Label 2.191.abw_bkr
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:  $1 - 48 x + 953 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.101907512735$, $\pm0.211431110568$
Angle rank:  $2$ (numerical)
Number field:  4.0.549225.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28219 1316444569 48545213425600 1771255421739537129 64615308055083265449259 2357222254345104476029849600 85993801410684171669669158195659 3137139825976627643900308084164394569 114445997945101379038014880917267363505600 4175104451031596744408389159085757771428945209

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36084 6967008 1330907044 254195924304 48551240314878 9273284349796464 1771197286371983044 338298681560033819808 64615048177910022818004

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.549225.1.
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.bw_bkr$2$(not in LMFDB)