Properties

Label 2.193.abw_bkn
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:  $1 - 48 x + 949 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0361850571721$, $\pm0.237645444107$
Angle rank:  $2$ (numerical)
Number field:  4.0.66417.2
Galois group:  $D_{4}$
Jacobians:  40

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 40 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28887 1372450257 51670115428464 1925132210862845049 71708901389715393421647 2671084592273086214623527168 99495242703233567604911231167263 3706098375487632822867720785491008297 138048458679791007216272817652897096943088 5142167038094283125700168257933411335193220897

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36844 7187330 1387494676 267785171186 51682532706142 9974730088074674 1925122948572321124 371548729858344850946 71708904872851032565084

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.66417.2.
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_bkn$2$(not in LMFDB)