# Properties

 Label 1.167.at Base Field $\F_{167}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{167}$ Dimension: $1$ L-polynomial: $1 - 19 x + 167 x^{2}$ Frobenius angles: $\pm0.237120127213$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-307})$$ 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 $A(\F_{q^r})$ 149 27863 4660124 777851371 129892587319 21691963835696 3622557528655081 604967115486335283 101029508514164093108 16871927924826823002143

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 149 27863 4660124 777851371 129892587319 21691963835696 3622557528655081 604967115486335283 101029508514164093108 16871927924826823002143

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{167}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-307})$$.
All geometric endomorphisms are defined over $\F_{167}$.

## 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 1.167.t $2$ (not in LMFDB)