# Properties

 Label 1.17.c Base field $\F_{17}$ Dimension $1$ $p$-rank $1$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

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## Invariants

 Base field: $\F_{17}$ Dimension: $1$ L-polynomial: $1 + 2 x + 17 x^{2}$ Frobenius angles: $\pm0.577979130377$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ 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:

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $20$ $320$ $4820$ $83200$ $1422100$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $20$ $320$ $4820$ $83200$ $1422100$ $24138560$ $410298580$ $6975820800$ $118588431380$ $2015991713600$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
All geometric endomorphisms are defined over $\F_{17}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
1.17.ac$2$1.289.be
1.17.ai$4$(not in LMFDB)
1.17.i$4$(not in LMFDB)