Properties

Label 2.17.ak_bx
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:  $1 - 10 x + 49 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0454542879392$, $\pm0.428461841097$
Angle rank:  $2$ (numerical)
Number field:  4.0.142400.3
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 159 82521 23939676 6905439801 2010392171439 582519252414096 168385462895412831 48660970239290954025 14062987964585295365724 4064227007104482349060521

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 288 4874 82676 1415908 24133302 410357284 6975725668 118587062858 2015991718128

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.142400.3.
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_bx$2$(not in LMFDB)