Properties

Label 2.191.abv_bji
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 918 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0283325455262$, $\pm0.251234528562$
Angle rank:  $2$ (numerical)
Number field:  4.0.2454725.2
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28376 1317327424 48542051259296 1771203361377922304 64614994523053342297576 2357220974453173484932326400 85993797442087076346985207601096 3137139816420733567700049639611945984 114445997927797848569610168002626249094816 4175104451010160270251477522750190355779345984

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36109 6966556 1330867929 254194690875 48551213953198 9273283921836205 1771197280976822289 338298681508885141396 64615048177578266133429

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.2454725.2.
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_bji$2$(not in LMFDB)