# Properties

 Label 1.317.aw Base Field $\F_{317}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{317}$ Dimension: $1$ L-polynomial: $1 - 22 x + 317 x^{2}$ Frobenius angles: $\pm0.288015407848$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 296 100640 31865288 10098217600 3201079071016 1014741811385120 321673166341090888 101970394077588134400 32324614926393763127336 10246902931640240494407200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 296 100640 31865288 10098217600 3201079071016 1014741811385120 321673166341090888 101970394077588134400 32324614926393763127336 10246902931640240494407200

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{317}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
All geometric endomorphisms are defined over $\F_{317}$.

## 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 1.317.w $2$ (not in LMFDB) 1.317.abc $4$ (not in LMFDB) 1.317.bc $4$ (not in LMFDB)