Properties

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

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)