# Properties

 Label 2.16.aq_ds Base Field $\F_{2^{4}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 4 x )^{4}$ 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:

• $y^2+y=x^5+a^3+a^2+a$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 81 50625 15752961 4228250625 1095222947841 281200199450625 72040003462430721 18445618199572250625 4722294425687923097601 1208921207935207812890625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 193 3841 64513 1044481 16760833 268369921 4294705153 68718428161 1099507433473

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai 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 $\F_{2^{4}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^{4}}$.

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

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.a_abg $2$ 2.256.acm_chc 2.16.q_ds $2$ 2.256.acm_chc 2.16.ae_a $3$ (not in LMFDB) 2.16.i_bw $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.16.a_abg $2$ 2.256.acm_chc 2.16.q_ds $2$ 2.256.acm_chc 2.16.ae_a $3$ (not in LMFDB) 2.16.i_bw $3$ (not in LMFDB) 2.16.ai_bg $4$ (not in LMFDB) 2.16.a_bg $4$ (not in LMFDB) 2.16.i_bg $4$ (not in LMFDB) 2.16.e_q $5$ (not in LMFDB) 2.16.am_cm $6$ (not in LMFDB) 2.16.ai_bw $6$ (not in LMFDB) 2.16.a_q $6$ (not in LMFDB) 2.16.e_a $6$ (not in LMFDB) 2.16.m_cm $6$ (not in LMFDB) 2.16.a_a $8$ (not in LMFDB) 2.16.ae_q $10$ (not in LMFDB) 2.16.ae_bg $12$ (not in LMFDB) 2.16.a_aq $12$ (not in LMFDB) 2.16.e_bg $12$ (not in LMFDB)