# Properties

 Label 2.64.abf_oe 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: $( 1 - 8 x )^{2}( 1 - 15 x + 64 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.113134082257$ 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 $A(\F_{q^r})$ 2450 15876000 68322309650 281317163400000 1152865552114267250 4722349644870882444000 19342809311458203331120850 79228162097374332559280400000 324518553650518532056123744800050 1329227995577124107633773961178900000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 34 3872 260626 16767808 1073689714 68719231712 4398045646546 281474975229568 18014398509042994 1152921504426616352

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
 The isogeny class factors as 1.64.aq $\times$ 1.64.ap 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.ap : $$\Q(\sqrt{-31})$$.
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.ab_aei $2$ (not in LMFDB) 2.64.b_aei $2$ (not in LMFDB) 2.64.bf_oe $2$ (not in LMFDB) 2.64.ah_i $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.64.ab_aei $2$ (not in LMFDB) 2.64.b_aei $2$ (not in LMFDB) 2.64.bf_oe $2$ (not in LMFDB) 2.64.ah_i $3$ (not in LMFDB) 2.64.ap_ey $4$ (not in LMFDB) 2.64.p_ey $4$ (not in LMFDB) 2.64.ax_jo $6$ (not in LMFDB) 2.64.h_i $6$ (not in LMFDB) 2.64.x_jo $6$ (not in LMFDB)