# Properties

 Label 2.256.acm_chc Base Field $\F_{2^{8}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $( 1 - 16 x )^{4}$ Frobenius angles: $0$, $0$, $0$, $0$ Angle rank: $0$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is supersingular.

 $p$-rank: $0$ Slopes: $[1/2, 1/2, 1/2, 1/2]$

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 50625 4228250625 281200199450625 18445618199572250625 1208921207935207812890625 79228143624800094964756250625 5192296781163575605539792301850625 340282366604025813516997721482669850625 22300745197232548926930345564412680417050625 1461501637325586006220552422779585474791812890625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 193 64513 16760833 4294705153 1099507433473 281474909601793 72057592964186113 18446744056529682433 4722366482594767306753 1208925819610231128195073

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The isogeny class factors as 1.256.abg 2 and its endomorphism algebra is $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^{8}}$.

 Subfield Primitive Model $\F_{2}$ 2.2.ae_i $\F_{2}$ 2.2.ac_e $\F_{2}$ 2.2.a_ae $\F_{2}$ 2.2.a_a $\F_{2}$ 2.2.a_e $\F_{2}$ 2.2.c_e $\F_{2}$ 2.2.e_i

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.a_ats $2$ (not in LMFDB) 2.256.cm_chc $2$ (not in LMFDB) 2.256.aq_a $3$ (not in LMFDB) 2.256.bg_bdo $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.a_ats $2$ (not in LMFDB) 2.256.cm_chc $2$ (not in LMFDB) 2.256.aq_a $3$ (not in LMFDB) 2.256.bg_bdo $3$ (not in LMFDB) 2.256.abg_ts $4$ (not in LMFDB) 2.256.a_ts $4$ (not in LMFDB) 2.256.bg_ts $4$ (not in LMFDB) 2.256.q_jw $5$ (not in LMFDB) 2.256.abw_bnk $6$ (not in LMFDB) 2.256.abg_bdo $6$ (not in LMFDB) 2.256.a_jw $6$ (not in LMFDB) 2.256.q_a $6$ (not in LMFDB) 2.256.bw_bnk $6$ (not in LMFDB) 2.256.a_a $8$ (not in LMFDB) 2.256.aq_jw $10$ (not in LMFDB) 2.256.aq_ts $12$ (not in LMFDB) 2.256.a_ajw $12$ (not in LMFDB) 2.256.q_ts $12$ (not in LMFDB)