# Properties

 Label 1.317.abi 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: $1 - 34 x + 317 x^{2}$ Frobenius angles: $\pm0.0960529433044$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-7})$$ 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 $A(\F_{q^r})$ 284 99968 31848044 10097967616 3201078179644 1014741868359296 321673168058637196 101970394104329422848 32324614926618604936028 10246902931640639779146368

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 284 99968 31848044 10097967616 3201078179644 1014741868359296 321673168058637196 101970394104329422848 32324614926618604936028 10246902931640639779146368

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{317}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-7})$$.
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.bi $2$ (not in LMFDB)