Properties

Label 2.16.an_cv
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 13 x + 73 x^{2} - 208 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.0987587980325$, $\pm0.265114785720$
Angle rank:  $2$ (numerical)
Number field:  4.0.5225.1
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
$A(\F_{q^r})$ 109 60059 16884100 4317100979 1100590570909 281475776609600 72054659224004629 18446666146098631139 4722387710775253128100 1208929177941864573589659

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 234 4123 65874 1049604 16777263 268424524 4294949154 68719785643 1099514682154

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.5225.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.16.n_cv$2$2.256.ax_qr