Properties

Label 2.16.al_ch
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:  $1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.133878927982$, $\pm0.347077071791$
Angle rank:  $2$ (numerical)
Number field:  4.0.90753.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 129 64887 17141004 4310378523 1099154725959 281454120091728 72064288318624941 18447723008335638963 4722428643550675277076 1208927149582990251323607

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 254 4185 65770 1048236 16775975 268460394 4295195218 68720381289 1099512837374

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.90753.1.
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.l_ch$2$2.256.ad_er