Properties

Label 2.64.ax_jw
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 23 x + 256 x^{2} - 1472 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.178048525745$, $\pm0.299165991752$
Angle rank:  $2$ (numerical)
Number field:  4.0.54332.1
Galois group:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2858 16713584 69003486266 281672058949088 1152988655399793738 4722372874184682990416 19342808661288122194103642 79228161630532184254744369088 324518554878270321786318198751082 1329227996349844068896785019549565744

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 4080 263226 16788960 1073804362 68719569744 4398045498714 281474973571008 18014398577196906 1152921505096844080

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.54332.1.
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.x_jw$2$(not in LMFDB)