# Properties

 Label 1.17.a Base Field $\F_{17}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{17}$ Dimension: $1$ L-polynomial: $1 + 17 x^{2}$ Frobenius angles: $\pm0.5$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-17})$$ Galois group: $C_2$ Jacobians: 4

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is supersingular.

 $p$-rank: $0$ Slopes: $[1/2, 1/2]$

## 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 $A(\F_{q^r})$ 18 324 4914 82944 1419858 24147396 410338674 6975590400 118587876498 2015996740164

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 18 324 4914 82944 1419858 24147396 410338674 6975590400 118587876498 2015996740164

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-17})$$.
Endomorphism algebra over $\overline{\F}_{17}$
 The base change of $A$ to $\F_{17^{2}}$ is the simple isogeny class 1.289.bi and its endomorphism algebra is the quaternion algebra over $$\Q$$ ramified at $17$ and $\infty$.
All geometric endomorphisms are defined over $\F_{17^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

This isogeny class has no twists.