Properties

Label 2.16.ah_bk
Base Field $\F_{2^{4}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 7 x + 36 x^{2} - 112 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.206663904003$, $\pm0.474998167614$
Angle rank:  $2$ (numerical)
Number field:  4.0.101277.1
Galois group:  $D_{4}$
Jacobians:  8

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 174 71688 17102286 4291673808 1100825995494 281697704301528 72063658356938814 18446027890056000672 4722310484285499085014 1208925194500744065536808

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 280 4174 65488 1049830 16790488 268458046 4294800544 68718661846 1099511059240

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.101277.1.
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.h_bk$2$2.256.x_jg