Properties

Label 2.191.abv_bjm
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:  $( 1 - 27 x + 191 x^{2} )( 1 - 20 x + 191 x^{2} )$
Frobenius angles:  $\pm0.0686610702072$, $\pm0.242497774430$
Angle rank:  $2$ (numerical)
Jacobians:  56

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 56 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28380 1317626640 48545985795120 1771230810646440000 64615128331508560294500 2357221483191554677050312960 85993799042228598890905835228820 3137139820797983078389802988251040000 114445997938997081888210383357938972354480 4175104451040063199201578635538579059228106000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36117 6967120 1330888553 254195217275 48551224431582 9273284094390125 1771197283448172913 338298681541989714160 64615048178041051967277

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.abb $\times$ 1.191.au 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.ah_agc$2$(not in LMFDB)
2.191.h_agc$2$(not in LMFDB)
2.191.bv_bjm$2$(not in LMFDB)