Properties

Label 2.17.ak_ca
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:  $1 - 10 x + 52 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.122222492446$, $\pm0.407842140074$
Angle rank:  $2$ (numerical)
Number field:  4.0.467264.1
Galois group:  $D_{4}$
Jacobians:  8

This isogeny class is simple and geometrically 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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 162 84564 24386994 6954881616 2013794032482 582741707504436 168407697256754418 48663144646229873664 14063120425706884270866 4064230240118967136503924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 294 4964 83270 1418308 24142518 410411464 6976037374 118588179848 2015993321814

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.467264.1.
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.
TwistExtension DegreeCommon base change
2.17.k_ca$2$(not in LMFDB)