Properties

Label 2.193.aby_bmu
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:  $1 - 50 x + 1008 x^{2} - 9650 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0879067867460$, $\pm0.184056049243$
Angle rank:  $2$ (numerical)
Number field:  4.0.1905984.1
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
$A(\F_{q^r})$ 28558 1369584564 51662781846286 1925146358155782096 71709121043208505833118 2671085765140176913194227796 99495247011937365360038383859902 3706098387501366783968727852792443904 138048458704820329443284085546638526194014 5142167038126947124500884359042411389853467924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36766 7186308 1387504870 267785991444 51682555399822 9974730520036608 1925122954812823294 371548729925709694944 71708904873306540829486

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.1905984.1.
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.by_bmu$2$(not in LMFDB)