# Properties

 Label 2.256.ack_cer Base Field $\F_{2^{8}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $( 1 - 31 x + 256 x^{2} )^{2}$ Frobenius angles: $\pm0.0797861753495$, $\pm0.0797861753495$ Angle rank: $1$ (numerical)

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 contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 51076 4236447744 281274289882756 18446138247776845824 1208924379804581299596676 79228161252211611842173440000 5192296872675221101264372445983876 340282367054330365605229844832623591424 22300745199351984843516283006769043752360836 1461501637335183299916426696252531589500595113984

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 195 64639 16765251 4294826239 1099510318275 281474972226943 72057594234165315 18446744080940741119 4722366483043575319491 1208925819618169823473279

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abf 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-7})$$$)$
All geometric endomorphisms are defined over $\F_{2^{8}}$.

## 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 2.256.a_arh $2$ (not in LMFDB) 2.256.ck_cer $2$ (not in LMFDB) 2.256.bf_bbd $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.a_arh $2$ (not in LMFDB) 2.256.ck_cer $2$ (not in LMFDB) 2.256.bf_bbd $3$ (not in LMFDB) 2.256.a_rh $4$ (not in LMFDB) 2.256.abf_bbd $6$ (not in LMFDB)