# Properties

 Label 1.227.az Base Field $\F_{227}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

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## Invariants

 Base field: $\F_{227}$ Dimension: $1$ L-polynomial: $1 - 25 x + 227 x^{2}$ Frobenius angles: $\pm0.188537632524$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-283})$$ Galois group: $C_2$ Jacobians: 3

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 3 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 203 51359 11698484 2655311659 602740517533 136821772143056 31058537600001079 7050287992139867475 1600415374200799722188 363294289952982487707839

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 203 51359 11698484 2655311659 602740517533 136821772143056 31058537600001079 7050287992139867475 1600415374200799722188 363294289952982487707839

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{227}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-283})$$.
All geometric endomorphisms are defined over $\F_{227}$.

## 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 1.227.z $2$ (not in LMFDB)