# Properties

 Label 2.17.al_cm 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: $( 1 - 6 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ Frobenius angles: $\pm0.240632536990$, $\pm0.292637436158$ 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 $A(\F_{q^r})$ 156 86112 25240176 7065661824 2019105335676 582493185570816 168352294123689468 48659500972028044800 14063046909587100522864 4064235318498004170329952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 297 5134 84593 1422047 24132222 410276447 6975515041 118587559918 2015995840857

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ag $\times$ 1.17.af 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_e $2$ (not in LMFDB) 2.17.b_e $2$ (not in LMFDB) 2.17.l_cm $2$ (not in LMFDB)