# Properties

 Label 2.64.abg_ou Base Field $\F_{2^{6}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{6}}$ Dimension: $2$ L-polynomial: $( 1 - 8 x )^{4}$ Frobenius angles: $0$, $0$, $0$, $0$ Angle rank: $0$ (numerical) Jacobians: 1

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 the Jacobians of 1 curves, and hence is principally polarizable:

• $y^2+y=x^5+x^4+x^3$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2401 15752961 68184176641 281200199450625 1152780773560811521 4722294425687923097601 19342776220372307646873601 79228143624800094964756250625 324518543987020277952513142947841 1329227990833155722679814984029962241

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 33 3841 260097 16760833 1073610753 68718428161 4398038122497 281474909601793 18014397972611073 1152921500311879681

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
 The isogeny class factors as 1.64.aq 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 $\F_{2^{6}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^{6}}$.

 Subfield Primitive Model $\F_{2}$ 2.2.a_ae $\F_{2}$ 2.2.a_c

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.64.a_aey $2$ (not in LMFDB) 2.64.bg_ou $2$ (not in LMFDB) 2.64.ai_a $3$ (not in LMFDB) 2.64.q_hk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.64.a_aey $2$ (not in LMFDB) 2.64.bg_ou $2$ (not in LMFDB) 2.64.ai_a $3$ (not in LMFDB) 2.64.q_hk $3$ (not in LMFDB) 2.64.aq_ey $4$ (not in LMFDB) 2.64.a_ey $4$ (not in LMFDB) 2.64.q_ey $4$ (not in LMFDB) 2.64.i_cm $5$ (not in LMFDB) 2.64.ay_jw $6$ (not in LMFDB) 2.64.aq_hk $6$ (not in LMFDB) 2.64.a_cm $6$ (not in LMFDB) 2.64.i_a $6$ (not in LMFDB) 2.64.y_jw $6$ (not in LMFDB) 2.64.a_a $8$ (not in LMFDB) 2.64.ai_cm $10$ (not in LMFDB) 2.64.ai_ey $12$ (not in LMFDB) 2.64.a_acm $12$ (not in LMFDB) 2.64.i_ey $12$ (not in LMFDB)