Properties

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

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Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $( 1 - 8 x )^{2}( 1 - 11 x + 64 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.258708130235$
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
$A(\F_{q^r})$ 2646 16288776 68655500046 281474121474000 1152893643780692646 4722324566851251515736 19342779379068289784935806 79228143850096861591146084000 324518546339909745324777175316886 1329227993977954773010729652811272616

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3976 261902 16777168 1073715878 68718866776 4398038840702 281474910402208 18014398103222678 1152921503039558056

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.aq $\times$ 1.64.al 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.af_abw$2$(not in LMFDB)
2.64.f_abw$2$(not in LMFDB)
2.64.bb_ls$2$(not in LMFDB)
2.64.ad_bo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.af_abw$2$(not in LMFDB)
2.64.f_abw$2$(not in LMFDB)
2.64.bb_ls$2$(not in LMFDB)
2.64.ad_bo$3$(not in LMFDB)
2.64.al_ey$4$(not in LMFDB)
2.64.l_ey$4$(not in LMFDB)
2.64.at_ii$6$(not in LMFDB)
2.64.d_bo$6$(not in LMFDB)
2.64.t_ii$6$(not in LMFDB)