Properties

Label 2.191.abv_bjo
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:  $1 - 47 x + 924 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0832068261027$, $\pm0.237476928001$
Angle rank:  $2$ (numerical)
Number field:  4.0.30190760.1
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
$A(\F_{q^r})$ 28382 1317776260 48547953096200 1771244503379092640 64615194518934045052762 2357221729198489312223656000 85993799774752205851157765284922 3137139822563150866135261937902828160 114445997942408848862190322656041772405800 4175104451045350237844073213676004174177486500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36121 6967402 1330898841 254195477655 48551229498538 9273284173383025 1771197284444768721 338298681552074787382 64615048178122875610401

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.30190760.1.
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_bjo$2$(not in LMFDB)