Properties

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

Learn more about

Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 956 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.128631181971$, $\pm0.195566501682$
Angle rank:  $2$ (numerical)
Number field:  4.0.39168.3
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
$A(\F_{q^r})$ 28222 1316669188 48548227457038 1771276975276806288 64615415305407277763182 2357222661269520214844362948 85993802603122300046112233242078 3137139828447362151080372544109842432 114445997946819910873591892934748147439518 4175104451017461779655012085238515448135325508

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36090 6967440 1330923238 254196346224 48551248696218 9273284478385008 1771197287766934654 338298681565113744528 64615048177691266272090

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.39168.3.
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_bku$2$(not in LMFDB)