# Properties

 Label 2.17.an_cy Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ Frobenius angles: $\pm0.177280642489$, $\pm0.240632536990$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary. $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 132 79200 24659712 7053552000 2021889165252 582896408371200 168380808657984516 48660354784857024000 14062989450255637909248 4064225418633377836476000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 273 5018 84449 1424005 24148926 410345941 6975637441 118587075386 2015990930193

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah $\times$ 1.17.ag and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.
 Twist Extension Degree Common base change 2.17.ab_ai $2$ (not in LMFDB) 2.17.b_ai $2$ (not in LMFDB) 2.17.n_cy $2$ (not in LMFDB)