# Properties

 Label 1.283.am 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: $1 - 12 x + 283 x^{2}$ Frobenius angles: $\pm0.383914450053$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-247})$$ Galois group: $C_2$ Jacobians: 12

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 12 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 272 80512 22673648 6414230016 1815229552592 513710675503744 145380129017293232 41142576404560693248 11643349118981201984144 3295067800659941792444032

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 272 80512 22673648 6414230016 1815229552592 513710675503744 145380129017293232 41142576404560693248 11643349118981201984144 3295067800659941792444032

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-247})$$.
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.m $2$ (not in LMFDB)