Properties

Label 2.191.abv_bjj
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:  $1 - 47 x + 919 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0415744860853$, $\pm0.249183751291$
Angle rank:  $2$ (numerical)
Number field:  4.0.733037.1
Galois group:  $D_{4}$
Jacobians:  25

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 25 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28377 1317402225 48543034884975 1771210231670508525 64615028154367770644112 2357221103729789406710270625 85993797859055009289398614294467 3137139817621653505676007301365964725 114445997931152929157483854606656556344525 4175104451020123887825978043047648861102240000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36111 6966697 1330873091 254194823180 48551216615883 9273283966800635 1771197281654849491 338298681518802651487 64615048177732465779726

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.733037.1.
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_bjj$2$(not in LMFDB)