# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)