# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2646 16288776 68655500046 281474121474000 1152893643780692646 4722324566851251515736 19342779379068289784935806 79228143850096861591146084000 324518546339909745324777175316886 1329227993977954773010729652811272616

 $r$ 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: 1.64.aq : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.64.al : $$\Q(\sqrt{-15})$$.
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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)