Properties

Label 2.193.abw_bkm
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:  $1 - 48 x + 948 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0177587632772$, $\pm0.239932532337$
Angle rank:  $2$ (numerical)
Number field:  4.0.2722048.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28886 1372373860 51669078950918 1925124687459859600 71708862828564593649446 2671084435944357955538276260 99495242169023085972128906008502 3706098373864556970033512033996083200 138048458675112028888295571180663169320182 5142167038080440870649076506965438990901547300

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36842 7187186 1387489254 267785027186 51682529681354 9974730034518290 1925122947729218686 371548729845751675538 71708904872657998588682

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.2722048.1.
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_bkm$2$(not in LMFDB)