Properties

Label 2.64.aw_it
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:  $1 - 22 x + 227 x^{2} - 1408 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0627187389289$, $\pm0.370970111216$
Angle rank:  $2$ (numerical)
Number field:  4.0.16425024.1
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
$A(\F_{q^r})$ 2894 16652076 68748020522 281385048432096 1152819436840274174 4722325496728590420684 19342815125323616372359994 79228171962519124399365619584 324518556977633197980970811371502 1329227995232443786616099641025698476

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 43 4067 262255 16771855 1073646763 68718880307 4398046968463 281475010277599 18014398693734955 1152921504127653827

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.16425024.1.
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.w_it$2$(not in LMFDB)