Properties

Label 2.191.abz_bnp
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:  $1 - 51 x + 1029 x^{2} - 9741 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0498136467200$, $\pm0.172118248730$
Angle rank:  $2$ (numerical)
Number field:  4.0.634933.1
Galois group:  $C_4$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27719 1311191857 48520322483789 1771172788704310813 64615098529676835926384 2357221845991117542368665513 85993800800661972880824456866081 3137139825001429940664072326564248053 114445997941023473548179175988619731910851 4175104451008334786712855060698950315502924032

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 141 35939 6963435 1330844955 254195100036 48551231904095 9273284284013709 1771197285821396323 338298681547979662599 64615048177550014455374

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.634933.1.
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.bz_bnp$2$(not in LMFDB)