Properties

Label 2.191.abw_bkq
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:  $1 - 48 x + 952 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0937844041757$, $\pm0.215386779040$
Angle rank:  $2$ (numerical)
Number field:  4.0.444672.4
Galois group:  $D_{4}$
Jacobians:  84

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 84 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28218 1316369700 48544208759898 1771248226594410000 64615272060958943372058 2357222115787845898975035300 85993800989050934149197552868218 3137139824998006842689799500636160000 114445997943713546808368440784280980373498 4175104451032699605577901594208560439163342500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36082 6966864 1330901638 254195782704 48551237461042 9273284304328944 1771197285819463678 338298681555931432464 64615048177927090996402

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.444672.4.
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_bkq$2$(not in LMFDB)