# Properties

 Label 1.313.ar Base Field $\F_{313}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{313}$ Dimension: $1$ L-polynomial: $1 - 17 x + 313 x^{2}$ Frobenius angles: $\pm0.340473932128$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-107})$$ Galois group: $C_2$ Jacobians: 9

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 9 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 297 98307 30675348 9598007331 3004148454417 940299049730304 294313621198933017 92120163569398049283 28833611193669595705524 9024920303516216241812307

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 297 98307 30675348 9598007331 3004148454417 940299049730304 294313621198933017 92120163569398049283 28833611193669595705524 9024920303516216241812307

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{313}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-107})$$.
All geometric endomorphisms are defined over $\F_{313}$.

## 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 1.313.r $2$ (not in LMFDB)