# Properties

 Label 2.17.aj_cc 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: $( 1 - 5 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ Frobenius angles: $\pm0.292637436158$, $\pm0.338793663197$ 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 $A(\F_{q^r})$ 182 92092 25492376 7038775744 2014450139702 582215684866816 168354868337287814 48661349247531820800 14063198471181701378264 4064238953138390667693052

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 317 5184 84273 1418769 24120722 410282721 6975780001 118588837968 2015997643757

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.af $\times$ 1.17.ae 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_o $2$ (not in LMFDB) 2.17.b_o $2$ (not in LMFDB) 2.17.j_cc $2$ (not in LMFDB)