Properties

Label 2.191.abv_bjp
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:  $1 - 47 x + 925 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0900686723414$, $\pm0.234746497408$
Angle rank:  $2$ (numerical)
Number field:  4.0.28164437.1
Galois group:  $D_{4}$
Jacobians:  62

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 62 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28383 1317851073 48548936755053 1771251341770094877 64615227433446386854608 2357221850113431927785480937 85993800124191289974996326417217 3137139823340910717533259333879276213 114445997943579385668859436708070551281227 4175104451045677766555460324854578195027822848

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36123 6967543 1330903979 254195607140 48551231988999 9273284211065369 1771197284883884035 338298681555534856459 64615048178127944533518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.28164437.1.
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_bjp$2$(not in LMFDB)