Properties

Label 2.191.aby_bmr
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:  $1 - 50 x + 1005 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0951733851509$, $\pm0.174595285009$
Angle rank:  $2$ (numerical)
Number field:  4.0.17984.1
Galois group:  $D_{4}$
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27887 1313115169 48531032081252 1771218413301447401 64615264943018569540927 2357222391385017164437202704 85993802448335180810802086370527 3137139829654863813454209314238055625 114445997953381403955313265880380268313892 4175104451039101844216784154835286428328947329

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35992 6964972 1330879236 254195754702 48551243137462 9273284461693282 1771197288448677828 338298681584509306612 64615048178026173776952

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.17984.1.
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_bmr$2$(not in LMFDB)