# Properties

 Label 2.17.ak_ch Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{17}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 17 x^{2} )^{2}$ Frobenius angles: $\pm0.292637436158$, $\pm0.292637436158$ Angle rank: $1$ (numerical) Jacobians: 2

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 contains the Jacobians of 2 curves, and hence is principally polarizable:

• $y^2=14x^6+5x^5+8x^4+5x^3+7x^2+14x+6$
• $y^2=8x^6+4x^5+2x^4+5x^3+9x^2+13x+15$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 169 89401 25441936 7059192361 2016777737689 582280837206016 168344964959279641 48660076235222375625 14063151082168111575184 4064242551432373300082521

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 308 5174 84516 1420408 24123422 410258584 6975597508 118588438358 2015999428628

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.af 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-43})$$$)$
All geometric endomorphisms are defined over $\F_{17}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.a_j $2$ (not in LMFDB) 2.17.k_ch $2$ (not in LMFDB) 2.17.f_i $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.a_j $2$ (not in LMFDB) 2.17.k_ch $2$ (not in LMFDB) 2.17.f_i $3$ (not in LMFDB) 2.17.a_aj $4$ (not in LMFDB) 2.17.af_i $6$ (not in LMFDB)