Properties

Label 2.193.abz_bns
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:  $1 - 51 x + 1032 x^{2} - 9843 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0403859860472$, $\pm0.180450830900$
Angle rank:  $2$ (numerical)
Number field:  4.0.49708.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28388 1367620288 51651753544208 1925098953201074944 71708945830468264883588 2671085177800605442004463616 99495245169024428285528865699524 3706098381978392268086641804924996608 138048458688833571732628872547016051001872 5142167038082156588264057462510315958977745088

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36713 7184774 1387470705 267785337143 51682544035454 9974730335278439 1925122951943928865 371548729882682343686 71708904872681924733113

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.49708.1.
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.bz_bns$2$(not in LMFDB)