# 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

## 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.

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

 $r$ 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: 1.64.aq : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.64.an : $$\Q(\sqrt{-87})$$.
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.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.
 Twist Extension Degree Common 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)