Properties

Label 2.191.aby_bmo
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:  $1 - 50 x + 1002 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0545220769588$, $\pm0.191978923746$
Angle rank:  $2$ (numerical)
Number field:  4.0.136400.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27884 1312890256 48527892101564 1771194511720582400 64615134540443980747804 2357221823963014166468359696 85993800381765225721498380209804 3137139823233247083236094816925798400 114445997936416658187735806752023229535564 4175104451002399053723510769475922175590086416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35986 6964522 1330861278 254195241702 48551231450386 9273284238841282 1771197284823098238 338298681534362064862 64615048177458151442706

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.136400.1.
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.by_bmo$2$(not in LMFDB)