Properties

Label 2.193.aca_bot
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:  $1 - 52 x + 1059 x^{2} - 10036 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0196335768550$, $\pm0.161895347612$
Angle rank:  $2$ (numerical)
Number field:  4.0.77328.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28221 1365811737 51642930110292 1925068943929166169 71708869768475963786901 2671085044931361742772659728 99495245087286115504297160550597 3706098382355958349535659936285458537 138048458689986462100035752447340735747732 5142167038079619052975076384337386375648685897

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 36664 7183546 1387449076 267785053102 51682541464582 9974730327083902 1925122952140054564 371548729885785275482 71708904872646538119784

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.77328.1.
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.ca_bot$2$(not in LMFDB)