Properties

Label 2.191.abv_bjk
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:  $1 - 47 x + 920 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0518315516314$, $\pm0.247050510603$
Angle rank:  $2$ (numerical)
Number field:  4.0.24458472.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28378 1317477028 48544018516168 1771217096646108832 64615061666215091756158 2357221231611336477208101952 85993798264722370366806863321662 3137139818751303461863876472784263808 114445997934135609993764846341372051933672 4175104451028409726565153731632487543087052548

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36113 6966838 1330878249 254194955015 48551219249834 9273284010546449 1771197282292638385 338298681527619359914 64615048177860699665993

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.24458472.1.
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.bv_bjk$2$(not in LMFDB)