Properties

Label 2.193.abx_blu
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:  $1 - 49 x + 982 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0948069130604$, $\pm0.200778298609$
Angle rank:  $2$ (numerical)
Number field:  4.0.5159228.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28726 1371321788 51670572262552 1925168884034538944 71709159417201855643126 2671085751792249182038198016 99495246639502567194730868150278 3706098385982078172649754904399550208 138048458701290606182487006081476382684376 5142167038124469195335573052025340052802062588

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36813 7187392 1387521105 267786134745 51682555141554 9974730482698777 1925122954023632865 371548729916209667152 71708904873271985439613

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.5159228.1.
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_blu$2$(not in LMFDB)