# Properties

 Label 1.199.ar Base Field $\F_{199}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{199}$ Dimension: $1$ L-polynomial: $1 - 17 x + 199 x^{2}$ Frobenius angles: $\pm0.294151794293$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 5

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class contains the Jacobians of 5 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 183 39711 7885836 1568306523 312079703493 62103828944304 12358664060638827 2459374190157479763 489415464138830696964 97393677360308696184951

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 183 39711 7885836 1568306523 312079703493 62103828944304 12358664060638827 2459374190157479763 489415464138830696964 97393677360308696184951

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{199}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 1.199.r $2$ (not in LMFDB) 1.199.al $3$ (not in LMFDB) 1.199.bc $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.199.r $2$ (not in LMFDB) 1.199.al $3$ (not in LMFDB) 1.199.bc $3$ (not in LMFDB) 1.199.abc $6$ (not in LMFDB) 1.199.l $6$ (not in LMFDB)