# Properties

 Label 1.179.t Base Field $\F_{179}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{179}$ Dimension: $1$ L-polynomial: $1 + 19 x + 179 x^{2}$ Frobenius angles: $\pm0.751333716250$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-355})$$ Galois group: $C_2$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 199 32039 5731996 1026689755 183765378089 32894113733264 5888046411929531 1053960286836615795 188658891731222952484 33769941616267882556279

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 199 32039 5731996 1026689755 183765378089 32894113733264 5888046411929531 1053960286836615795 188658891731222952484 33769941616267882556279

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{179}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-355})$$.
All geometric endomorphisms are defined over $\F_{179}$.

## 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 1.179.at $2$ (not in LMFDB)