Properties

Label 2.199.abz_boi
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 199 x^{2} )( 1 - 25 x + 199 x^{2} )$
Frobenius angles:  $\pm0.126927281034$, $\pm0.153403448314$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30450 1548382500 62082154625400 2459420600508900000 97394079861932880699750 3856888682341671641563080000 152736588020186326573400179021350 6048521427612679158841575598400400000 239527496546341870738284301539218362867800 9485528389678191877127926206456581872119562500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 149 39097 7877846 1568268793 312080890739 62103867412282 12358664704382621 2459374197056601553 489415464175171417274 97393677360042264635377

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.aba $\times$ 1.199.az and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ab_ajs$2$(not in LMFDB)
2.199.b_ajs$2$(not in LMFDB)
2.199.bz_boi$2$(not in LMFDB)