# Properties

 Label 1.467.abr Base Field $\F_{467}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{467}$ Dimension: $1$ L-polynomial: $1 - 43 x + 467 x^{2}$ Frobenius angles: $\pm0.0321571444691$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-19})$$ Galois group: $C_2$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 425 217175 101828300 47562410875 22211824918375 10372925921632400 4844156480234874325 2262221077766706637875 1056457243346477075971700 493365532643370964256978375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 425 217175 101828300 47562410875 22211824918375 10372925921632400 4844156480234874325 2262221077766706637875 1056457243346477075971700 493365532643370964256978375

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{467}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-19})$$.
All geometric endomorphisms are defined over $\F_{467}$.

## 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 1.467.br $2$ (not in LMFDB)