Properties

Label 2.17.ak_cc
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:  $1 - 10 x + 54 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.159208333631$, $\pm0.391204221240$
Angle rank:  $2$ (numerical)
Number field:  4.0.23600.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 164 85936 24686756 6986253056 2015353294564 582747563627056 168404709712798436 48663022317189017600 14063096205542845055204 4064224265858270698670896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 298 5024 83646 1419408 24142762 410404184 6976019838 118587975608 2015990358378

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.23600.1.
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_cc$2$(not in LMFDB)