# Properties

 Label 1.283.az Base Field $\F_{283}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{283}$ Dimension: $1$ L-polynomial: $1 - 25 x + 283 x^{2}$ Frobenius angles: $\pm0.233379450635$ 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 $A(\F_{q^r})$ 259 80031 22670788 6414404619 1815234494269 513710715715344 145380128282952703 41142576380327368275 11643349118745789552604 3295067800661307805392111

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 259 80031 22670788 6414404619 1815234494269 513710715715344 145380128282952703 41142576380327368275 11643349118745789552604 3295067800661307805392111

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{283}$.

## 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 1.283.z $2$ (not in LMFDB) 1.283.ah $3$ (not in LMFDB) 1.283.bg $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.283.z $2$ (not in LMFDB) 1.283.ah $3$ (not in LMFDB) 1.283.bg $3$ (not in LMFDB) 1.283.abg $6$ (not in LMFDB) 1.283.h $6$ (not in LMFDB)