# Properties

 Label 1.283.ae 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: $1 - 4 x + 283 x^{2}$ Frobenius angles: $\pm0.462067163245$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-31})$$ Galois group: $C_2$ Jacobians: 30

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 30 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 280 80640 22668520 6414105600 1815230649400 513710735973120 145380129158703880 41142576384625766400 11643349118761380095320 3295067800664462062867200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 280 80640 22668520 6414105600 1815230649400 513710735973120 145380129158703880 41142576384625766400 11643349118761380095320 3295067800664462062867200

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-31})$$.
All geometric endomorphisms are defined over $\F_{283}$.

## 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 1.283.e $2$ (not in LMFDB)