Properties

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

Learn more about

Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $( 1 - 8 x )^{2}( 1 - 13 x + 64 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.198106042756$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2548 16098264 68529639724 281446754425200 1152921471322750948 4722360339189138367176 19342801093003651533130588 79228150581662450953622200800 324518545068301872267320028815764 1329227990837537109160771672142904504

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3928 261420 16775536 1073741796 68719387336 4398043777884 281474934317536 18014398032634260 1152921500315679928

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.aq $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.ad_adc$2$(not in LMFDB)
2.64.d_adc$2$(not in LMFDB)
2.64.bd_my$2$(not in LMFDB)
2.64.af_y$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.ad_adc$2$(not in LMFDB)
2.64.d_adc$2$(not in LMFDB)
2.64.bd_my$2$(not in LMFDB)
2.64.af_y$3$(not in LMFDB)
2.64.an_ey$4$(not in LMFDB)
2.64.n_ey$4$(not in LMFDB)
2.64.av_iy$6$(not in LMFDB)
2.64.f_y$6$(not in LMFDB)
2.64.v_iy$6$(not in LMFDB)