Properties

Label 2.191.abx_bln
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:  $1 - 49 x + 975 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0573856553654$, $\pm0.210617421473$
Angle rank:  $2$ (numerical)
Number field:  4.0.5958485.4
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
$A(\F_{q^r})$ 28049 1314516385 48534500731031 1771209806888796365 64615141893324404297104 2357221712080479134960148625 85993799790282623778366500911259 3137139821509877036166511533358544885 114445997933808573872913313896271651283381 4175104451006074838465713572981551345501344000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36031 6965471 1330872771 254195270628 48551229145963 9273284175057773 1771197283850101011 338298681526652651681 64615048177515038883726

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.5958485.4.
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_bln$2$(not in LMFDB)