Properties

Label 2.193.abw_bky
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:  $1 - 48 x + 960 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.132444567603$, $\pm0.197898328146$
Angle rank:  $2$ (numerical)
Number field:  4.0.2113792.1
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
$A(\F_{q^r})$ 28898 1373290756 51681517058594 1925214602462699536 71709317079284242891298 2671086209407757337468619012 99495247719524810152557866818274 3706098387724135972543280808940535808 138048458700961042127037383961433314864098 5142167038106769844193284659358008624150650116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36866 7188914 1387554054 267786723506 51682563995906 9974730590974610 1925122954928540158 371548729915322666258 71708904873025163218946

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.2113792.1.
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.bw_bky$2$(not in LMFDB)