# Properties

 Label 2.2.a_d Base field $\F_{2}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple No Geometrically simple No Primitive Yes Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $2$ L-polynomial: $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$ Frobenius angles: $\pm0.384973271919$, $\pm0.615026728081$ Angle rank: $1$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary. $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## 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 $A(\F_{q^r})$ 8 64 56 256 968 3136 16472 82944 263144 937024

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 11 9 15 33 47 129 319 513 911

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
 The isogeny class factors as 1.2.ab $\times$ 1.2.b and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2}$
 The base change of $A$ to $\F_{2^{2}}$ is 1.4.d 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-7})$$$)$
All geometric endomorphisms are defined over $\F_{2^{2}}$.

## 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 2.2.ac_f $2$ 2.4.g_r 2.2.c_f $2$ 2.4.g_r 2.2.a_ad $4$ 2.16.ac_bh
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.2.ac_f $2$ 2.4.g_r 2.2.c_f $2$ 2.4.g_r 2.2.a_ad $4$ 2.16.ac_bh 2.2.ab_ab $6$ 2.64.as_ib 2.2.b_ab $6$ 2.64.as_ib