Properties

Label 2.191.aby_bms
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:  $( 1 - 26 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$
Frobenius angles:  $\pm0.110219473395$, $\pm0.165219579186$
Angle rank:  $2$ (numerical)
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27888 1313190144 48532078753200 1771226369864146944 64615308156361728468528 2357222577326361061057440000 85993803108915737884757379086448 3137139831598782921868545048276762624 114445997957895256771082915698280749330800 4175104451045616280079780861295669540591638784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35994 6965122 1330885214 254195924702 48551246967258 9273284532928082 1771197289546194814 338298681597852110062 64615048178126992952154

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.aba $\times$ 1.191.ay 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_aji$2$(not in LMFDB)
2.191.c_aji$2$(not in LMFDB)
2.191.by_bms$2$(not in LMFDB)