# Properties

 Label 3.16.ay_jg_abxg Base Field $\F_{2^{4}}$ Dimension $3$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{4}}$ Dimension: $3$ L-polynomial: $( 1 - 4 x )^{6}$ Frobenius angles: $0$, $0$, $0$, $0$, $0$, $0$ Angle rank: $0$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is supersingular.

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

## 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 $A(\F_{q^r})$ 729 11390625 62523502209 274941996890625 1146182576381093889 4715453174592516890625 19335730644885715992608769 79220909236042181489028890625 324511126089026151457611904974849 1329220389899448367763203918212890625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -7 161 3713 64001 1042433 16752641 268337153 4294574081 68717903873 1099505336321

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The isogeny class factors as 1.16.ai 3 and its endomorphism algebra is $\mathrm{M}_{3}(B)$, 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 $\F_{2}$ 3.2.a_ac_a $\F_{2}$ 3.2.a_g_a

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ai_aq_jw $2$ (not in LMFDB) 3.16.i_aq_ajw $2$ (not in LMFDB) 3.16.y_jg_bxg $2$ (not in LMFDB) 3.16.am_bw_aey $3$ (not in LMFDB) 3.16.a_a_aey $3$ (not in LMFDB) 3.16.m_ds_rg $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.16.ai_aq_jw $2$ (not in LMFDB) 3.16.i_aq_ajw $2$ (not in LMFDB) 3.16.y_jg_bxg $2$ (not in LMFDB) 3.16.am_bw_aey $3$ (not in LMFDB) 3.16.a_a_aey $3$ (not in LMFDB) 3.16.m_ds_rg $3$ (not in LMFDB) 3.16.aq_ei_ats $4$ (not in LMFDB) 3.16.ai_bw_ajw $4$ (not in LMFDB) 3.16.a_aq_a $4$ (not in LMFDB) 3.16.a_bw_a $4$ (not in LMFDB) 3.16.i_bw_jw $4$ (not in LMFDB) 3.16.q_ei_ts $4$ (not in LMFDB) 3.16.ae_a_a $5$ (not in LMFDB) 3.16.au_gu_abim $6$ (not in LMFDB) 3.16.aq_ey_ayq $6$ (not in LMFDB) 3.16.am_ds_arg $6$ (not in LMFDB) 3.16.ai_bg_aey $6$ (not in LMFDB) 3.16.ae_aq_ey $6$ (not in LMFDB) 3.16.ae_bg_acm $6$ (not in LMFDB) 3.16.a_a_ey $6$ (not in LMFDB) 3.16.e_aq_aey $6$ (not in LMFDB) 3.16.e_bg_cm $6$ (not in LMFDB) 3.16.i_bg_ey $6$ (not in LMFDB) 3.16.m_bw_ey $6$ (not in LMFDB) 3.16.q_ey_yq $6$ (not in LMFDB) 3.16.u_gu_bim $6$ (not in LMFDB) 3.16.ai_q_a $8$ (not in LMFDB) 3.16.a_q_a $8$ (not in LMFDB) 3.16.i_q_a $8$ (not in LMFDB) 3.16.a_a_cm $9$ (not in LMFDB) 3.16.am_cm_ajw $10$ (not in LMFDB) 3.16.e_a_a $10$ (not in LMFDB) 3.16.m_cm_jw $10$ (not in LMFDB) 3.16.am_dc_aou $12$ (not in LMFDB) 3.16.ai_a_ey $12$ (not in LMFDB) 3.16.ai_cm_ajw $12$ (not in LMFDB) 3.16.ae_a_cm $12$ (not in LMFDB) 3.16.ae_q_aey $12$ (not in LMFDB) 3.16.ae_bw_aey $12$ (not in LMFDB) 3.16.a_a_a $12$ (not in LMFDB) 3.16.a_bg_a $12$ (not in LMFDB) 3.16.e_a_acm $12$ (not in LMFDB) 3.16.e_q_ey $12$ (not in LMFDB) 3.16.e_bw_ey $12$ (not in LMFDB) 3.16.i_a_aey $12$ (not in LMFDB) 3.16.i_cm_jw $12$ (not in LMFDB) 3.16.m_dc_ou $12$ (not in LMFDB) 3.16.i_bw_hk $15$ (not in LMFDB) 3.16.a_a_acm $18$ (not in LMFDB) 3.16.ae_bg_aey $20$ (not in LMFDB) 3.16.e_bg_ey $20$ (not in LMFDB) 3.16.ae_q_a $24$ (not in LMFDB) 3.16.e_q_a $24$ (not in LMFDB) 3.16.ai_bw_ahk $30$ (not in LMFDB) 3.16.a_q_acm $30$ (not in LMFDB) 3.16.a_q_cm $30$ (not in LMFDB)