Properties

Label 2.191.abw_bko
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:  $1 - 48 x + 950 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0773520389145$, $\pm0.222263726252$
Angle rank:  $2$ (numerical)
Number field:  4.0.223488.6
Galois group:  $D_{4}$
Jacobians:  56

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 56 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28216 1316219968 48542199445624 1771233820354962432 64615199706685581252856 2357221834296152793680345152 85993800109441497157976638529464 3137139822806336731276335092211007488 114445997939694039364682257746307969152184 4175104451029303022855407328094076858758672448

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36078 6966576 1330890814 254195498064 48551231663214 9273284209474800 1771197284582068990 338298681544049898000 64615048177874524561518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.223488.6.
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_bko$2$(not in LMFDB)