Properties

Label 2.64.aba_lj
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:  $1 - 26 x + 295 x^{2} - 1664 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.142916203509$, $\pm0.242250011848$
Angle rank:  $2$ (numerical)
Number field:  4.0.375872.1
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
$A(\F_{q^r})$ 2702 16433564 68835716978 281642495355872 1153020866492287422 4722404205775274588444 19342820918051898155605346 79228161751443638203004056448 324518552586238656816694880832686 1329227995734499348520048032454545884

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 4011 262587 16787199 1073834359 68720025675 4398048285579 281474974000575 18014398449963591 1152921504563117611

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.375872.1.
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.ba_lj$2$(not in LMFDB)