# Properties

 Label 1.193.at Base Field $\F_{193}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{193}$ Dimension: $1$ L-polynomial: $1 - 19 x + 193 x^{2}$ Frobenius angles: $\pm0.260315182816$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-411})$$ Galois group: $C_2$ Jacobians: 6

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 6 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 175 37275 7193200 1387561875 267785788375 51682537771200 9974730156615175 1925122950236731875 371548729895091977200 71708904873449472748875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 175 37275 7193200 1387561875 267785788375 51682537771200 9974730156615175 1925122950236731875 371548729895091977200 71708904873449472748875

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-411})$$.
All geometric endomorphisms are defined over $\F_{193}$.

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