# Properties

 Label 1.347.aba Base Field $\F_{347}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{347}$ Dimension: $1$ L-polynomial: $1 - 26 x + 347 x^{2}$ Frobenius angles: $\pm0.254128400961$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-178})$$ Galois group: $C_2$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 322 120428 41791414 14498567776 5030922526322 1745729083081676 605767992887583302 210201493918148143488 72939918399270270978658 25310151684664282136399468

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 322 120428 41791414 14498567776 5030922526322 1745729083081676 605767992887583302 210201493918148143488 72939918399270270978658 25310151684664282136399468

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{347}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-178})$$.
All geometric endomorphisms are defined over $\F_{347}$.

## 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 1.347.ba $2$ (not in LMFDB)