Properties

Label 2.193.abz_bnv
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 51 x + 1035 x^{2} - 9843 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0925765054042$, $\pm0.159192387568$
Angle rank:  $2$ (numerical)
Number field:  4.0.281725.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28391 1367849989 51655058081759 1925125054047145621 71709094761259877212016 2671085862175250757305152381 99495247835335771294733059097951 3706098391007995042460506945968929349 138048458715638620210583547965923200028031 5142167038151395748279475296393249830501690624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36719 7185233 1387489515 267785893298 51682557277343 9974730602585045 1925122956634332019 371548729954826443019 71708904873647483475614

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.281725.1.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.bz_bnv$2$(not in LMFDB)