Properties

Label 2.193.abx_blt
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:  $1 - 49 x + 981 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0853826055493$, $\pm0.205199049154$
Angle rank:  $2$ (numerical)
Number field:  4.0.6666597.1
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
$A(\F_{q^r})$ 28725 1371245325 51669514082925 1925161005311143125 71709118018795601538000 2671085581879924099541796525 99495246073874189313324140114325 3706098384462457454849939394833953125 138048458698234305463424619408050850774525 5142167038121500015149235552768992545972736000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36811 7187245 1387515427 267785980150 51682551853939 9974730425992645 1925122953234269923 371548729907983826305 71708904873230579421886

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.6666597.1.
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.bx_blt$2$(not in LMFDB)