Properties

Label 2.64.aba_lf
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:  $1 - 26 x + 291 x^{2} - 1664 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0837415506466$, $\pm0.270807474395$
Angle rank:  $2$ (numerical)
Number field:  4.0.1442880.5
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
$A(\F_{q^r})$ 2698 16398444 68753465854 281539637533920 1152934878654743098 4722352988837506773516 19342800583566403268565838 79228159137852150206390033280 324518556170156862931127676376234 1329227999450414235208219499178381804

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 4003 262275 16781071 1073754279 68719280371 4398043662051 281474964715231 18014398648911015 1152921507786160003

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.1442880.5.
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.ba_lf$2$(not in LMFDB)