Properties

Label 2.64.az_kt
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:  $1 - 25 x + 279 x^{2} - 1600 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.124520053775$, $\pm0.279743569050$
Angle rank:  $2$ (numerical)
Number field:  4.0.2491209.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2751 16508751 68850718524 281602130861499 1152969959859007101 4722372569663602758576 19342811792983502624418051 79228165031871123674983366419 324518558419371083808393406394964 1329227999553065001650035675704342951

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 40 4030 262645 16784794 1073786950 68719565311 4398046210780 281474985654994 18014398773767485 1152921507875195350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.2491209.1.
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.z_kt$2$(not in LMFDB)