Properties

Label 2.191.abw_bkv
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:  $( 1 - 25 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$
Frobenius angles:  $\pm0.140267993779$, $\pm0.187132320568$
Angle rank:  $2$ (numerical)
Jacobians:  18

This isogeny class is not 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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28223 1316744065 48549232145648 1771284149156601625 64615450811499098454983 2357222793997147662403068160 85993802976510131366451921168503 3137139829116933059149590566099291625 114445997946589613050534505805565532049008 4175104451009245959774143842147430281923816625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36092 6967584 1330928628 254196485904 48551251429982 9273284518649904 1771197288144967588 338298681564432991584 64615048177564116016652

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.az $\times$ 1.191.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_ahl$2$(not in LMFDB)
2.191.c_ahl$2$(not in LMFDB)
2.191.bw_bkv$2$(not in LMFDB)