Properties

Label 2.193.abx_blv
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:  $1 - 49 x + 983 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.104436197114$, $\pm0.195695727417$
Angle rank:  $2$ (numerical)
Number field:  4.0.3479541.1
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
$A(\F_{q^r})$ 28727 1371398253 51671630448071 1925176757215549509 71709200684399348610032 2671085920079988635888445525 99495247191110325918374732219183 3706098387407299277965078128753731109 138048458703821738079017046346227946078439 5142167038124945903681988544140582266220496128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36815 7187539 1387526779 267786288850 51682558397735 9974730537999295 1925122954763960179 371548729923022049197 71708904873278633265950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.3479541.1.
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_blv$2$(not in LMFDB)