Properties

Label 2.64.abc_ml
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:  $( 1 - 15 x + 64 x^{2} )( 1 - 13 x + 64 x^{2} )$
Frobenius angles:  $\pm0.113134082257$, $\pm0.198106042756$
Angle rank:  $2$ (numerical)
Jacobians:  18

This isogeny class is not 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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2600 16224000 68668472600 281563820928000 1153006260223493000 4722415559142843744000 19342834184132098626279800 79228169054238310587366912000 324518554731800158569284137620200 1329227995581505494130367664981600000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 37 3959 261949 16782511 1073820757 68720190887 4398051301933 281474999945311 18014398569066181 1152921504430416599

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.ap $\times$ 1.64.an and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_acp$2$(not in LMFDB)
2.64.c_acp$2$(not in LMFDB)
2.64.bc_ml$2$(not in LMFDB)