Properties

Label 2.191.abx_blm
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:  $1 - 49 x + 974 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0443842198615$, $\pm0.213962896348$
Angle rank:  $2$ (numerical)
Number field:  4.0.1190277.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28048 1314441472 48533475090112 1771202212439569408 64615101848591844452848 2357221544337283187461132288 85993799201191142765111007258928 3137139819719285676562126063570341888 114445997928973061430933266142179501848768 4175104450994055134230546310993576097173477632

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36029 6965324 1330867065 254195113093 48551225690990 9273284111532115 1771197282839151313 338298681512359032740 64615048177329018682949

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.1190277.1.
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.bx_blm$2$(not in LMFDB)