Properties

Label 2.64.ax_jl
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 23 x + 245 x^{2} - 1472 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0870708726221$, $\pm0.342563904315$
Angle rank:  $2$ (numerical)
Number field:  4.0.13786305.2
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
$A(\F_{q^r})$ 2847 16617939 68803699536 281466424902195 1152863693810239827 4722333534335393735616 19342813521597079347520167 79228174459424129507851541955 324518562091328092050540349182096 1329227998632498254827659834370107579

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 4058 262467 16776706 1073687982 68718997271 4398046603818 281475019148386 18014398977602043 1152921507076730978

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.13786305.2.
All geometric endomorphisms are defined over $\F_{2^{6}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.x_jl$2$(not in LMFDB)