# Properties

 Label 2.199.acb_bqi 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: $( 1 - 27 x + 199 x^{2} )( 1 - 26 x + 199 x^{2} )$ Frobenius angles: $\pm0.0936959350875$, $\pm0.126927281034$ 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 $A(\F_{q^r})$ 30102 1544292804 62059590469656 2459329592340224160 97393786012966189230402 3856887923923467324839727936 152736586638371737259817904612962 6048521427229326783669064148522547840 239527496557492143221170658064709901481336 9485528389744280111620696896397238091954053604

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 147 38993 7874982 1568210761 312079949157 62103855200186 12358664592573243 2459374196900727601 489415464197954253738 97393677360720832652153

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The isogeny class factors as 1.199.abb $\times$ 1.199.aba 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_als $2$ (not in LMFDB) 2.199.b_als $2$ (not in LMFDB) 2.199.cb_bqi $2$ (not in LMFDB)