Properties

Label 2.16.ai_bp
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:  $1 - 8 x + 41 x^{2} - 128 x^{3} + 256 x^{4}$
Frobenius angles:  $\pm0.187929673264$, $\pm0.445855430413$
Angle rank:  $2$ (numerical)
Number field:  4.0.107408.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 162 70308 17147538 4292725248 1100005557282 281673449940708 72070580954571858 18446620653567977472 4722310104054457245858 1208923378193570628425508

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 275 4185 65503 1049049 16789043 268483833 4294938559 68718656313 1099509407315

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.107408.1.
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.i_bp$2$2.256.s_fp