Properties

Label 2.64.abd_mz
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:  $1 - 29 x + 337 x^{2} - 1856 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0696923787592$, $\pm0.184671871212$
Angle rank:  $2$ (numerical)
Number field:  4.0.23225.1
Galois group:  $D_{4}$
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2549 16107131 68552612276 281480634897299 1152957594379246749 4722391294383123317696 19342823591656104908403869 79228164883005478003360636259 324518553183424854658279455623156 1329227995026455015981906837933016651

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3930 261507 16777554 1073775436 68719837791 4398048893484 281474985126114 18014398483114083 1152921503948987050

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.23225.1.
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.bd_mz$2$(not in LMFDB)