# Properties

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

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## Invariants

 Base field: $\F_{283}$ Dimension: $1$ L-polynomial: $1 + 3 x + 283 x^{2}$ Frobenius angles: $\pm0.528420082361$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1123})$$ 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 $A(\F_{q^r})$ 287 80647 22662668 6414097851 1815233325017 513710740724944 145380128147651747 41142576382360013043 11643349119106294499924 3295067800665395508045607

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 287 80647 22662668 6414097851 1815233325017 513710740724944 145380128147651747 41142576382360013043 11643349119106294499924 3295067800665395508045607

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1123})$$.
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.ad $2$ (not in LMFDB)