# Properties

 Label 6.2.aj_bo_aek_jc_apc_we Base Field $\F_{2}$ Dimension $6$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $6$ L-polynomial: $( 1 - 2 x + 2 x^{2} )^{4}( 1 - x - 2 x^{3} + 4 x^{4} )$ Frobenius angles: $\pm0.139386741866$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.686170398078$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

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

## 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 $A(\F_{q^r})$ 2 10000 742586 162500000 3961716922 70545670000 3643456328906 189776925000000 13829578483078202 1250416903506250000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -6 4 18 56 74 64 106 160 378 1104

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
 The isogeny class factors as 1.2.ac 4 $\times$ 2.2.ab_a and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.2.ac 4 : $\mathrm{M}_{4}($$$\Q(\sqrt{-1})$$$)$ 2.2.ab_a : 4.0.2312.1.
Endomorphism algebra over $\overline{\F}_{2}$
 The base change of $A$ to $\F_{2^{4}}$ is 1.16.i 4 $\times$ 2.16.h_bo. The endomorphism algebra for each factor is: 1.16.i 4 : $\mathrm{M}_{4}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 2.16.h_bo : 4.0.2312.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{2^{2}}$  The base change of $A$ to $\F_{2^{2}}$ is 1.4.a 4 $\times$ 2.4.ab_e. The endomorphism algebra for each factor is: 1.4.a 4 : $\mathrm{M}_{4}($$$\Q(\sqrt{-1})$$$)$ 2.4.ab_e : 4.0.2312.1.

## 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 6.2.ah_y_abu_bs_i_acm $2$ (not in LMFDB) 6.2.af_m_as_bc_ace_ds $2$ (not in LMFDB) 6.2.ad_e_c_ae_ai_bg $2$ (not in LMFDB) 6.2.ab_a_ac_m_ai_a $2$ (not in LMFDB) 6.2.b_a_c_m_i_a $2$ (not in LMFDB) 6.2.d_e_ac_ae_i_bg $2$ (not in LMFDB) 6.2.f_m_s_bc_ce_ds $2$ (not in LMFDB) 6.2.h_y_bu_bs_ai_acm $2$ (not in LMFDB) 6.2.j_bo_ek_jc_pc_we $2$ (not in LMFDB) 6.2.ad_e_a_ae_e_a $3$ (not in LMFDB) 6.2.d_e_g_i_e_a $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 6.2.ah_y_abu_bs_i_acm $2$ (not in LMFDB) 6.2.af_m_as_bc_ace_ds $2$ (not in LMFDB) 6.2.ad_e_c_ae_ai_bg $2$ (not in LMFDB) 6.2.ab_a_ac_m_ai_a $2$ (not in LMFDB) 6.2.b_a_c_m_i_a $2$ (not in LMFDB) 6.2.d_e_ac_ae_i_bg $2$ (not in LMFDB) 6.2.f_m_s_bc_ce_ds $2$ (not in LMFDB) 6.2.h_y_bu_bs_ai_acm $2$ (not in LMFDB) 6.2.j_bo_ek_jc_pc_we $2$ (not in LMFDB) 6.2.ad_e_a_ae_e_a $3$ (not in LMFDB) 6.2.d_e_g_i_e_a $3$ (not in LMFDB) 6.2.b_a_ae_ae_i_q $5$ (not in LMFDB) 6.2.ah_y_ace_ee_ahg_lc $6$ (not in LMFDB) 6.2.af_m_aba_ce_ado_ey $6$ (not in LMFDB) 6.2.af_m_aq_m_ae_a $6$ (not in LMFDB) 6.2.ad_e_ai_u_abc_bg $6$ (not in LMFDB) 6.2.ad_e_ag_i_ae_a $6$ (not in LMFDB) 6.2.ab_a_ac_a_e_a $6$ (not in LMFDB) 6.2.ab_a_a_e_ae_a $6$ (not in LMFDB) 6.2.ab_a_i_ae_ae_bg $6$ (not in LMFDB) 6.2.b_a_ai_ae_e_bg $6$ (not in LMFDB) 6.2.b_a_a_e_e_a $6$ (not in LMFDB) 6.2.b_a_c_a_ae_a $6$ (not in LMFDB) 6.2.d_e_a_ae_ae_a $6$ (not in LMFDB) 6.2.d_e_i_u_bc_bg $6$ (not in LMFDB) 6.2.f_m_q_m_e_a $6$ (not in LMFDB) 6.2.f_m_ba_ce_do_ey $6$ (not in LMFDB) 6.2.h_y_ce_ee_hg_lc $6$ (not in LMFDB) 6.2.ah_ba_aco_fc_aiq_my $8$ (not in LMFDB) 6.2.af_i_c_au_q_a $8$ (not in LMFDB) 6.2.af_o_aw_u_a_aq $8$ (not in LMFDB) 6.2.af_q_abm_cy_aey_hk $8$ (not in LMFDB) 6.2.ad_a_o_au_aq_cm $8$ (not in LMFDB) 6.2.ad_c_c_ae_i_aq $8$ (not in LMFDB) 6.2.ad_g_ak_u_abg_bw $8$ (not in LMFDB) 6.2.ad_i_ak_m_a_a $8$ (not in LMFDB) 6.2.ad_k_aw_bs_acu_ei $8$ (not in LMFDB) 6.2.ab_ai_g_bc_ai_acm $8$ (not in LMFDB) 6.2.ab_ae_c_m_a_abg $8$ (not in LMFDB) 6.2.ab_ac_g_ae_ai_q $8$ (not in LMFDB) 6.2.ab_a_ac_ae_i_a $8$ (not in LMFDB) 6.2.ab_c_c_e_a_q $8$ (not in LMFDB) 6.2.ab_e_ag_m_aq_bg $8$ (not in LMFDB) 6.2.ab_g_ac_m_i_q $8$ (not in LMFDB) 6.2.ab_i_ak_bc_abo_cm $8$ (not in LMFDB) 6.2.b_ai_ag_bc_i_acm $8$ (not in LMFDB) 6.2.b_ae_ac_m_a_abg $8$ (not in LMFDB) 6.2.b_ac_ag_ae_i_q $8$ (not in LMFDB) 6.2.b_a_c_ae_ai_a $8$ (not in LMFDB) 6.2.b_c_ac_e_a_q $8$ (not in LMFDB) 6.2.b_e_g_m_q_bg $8$ (not in LMFDB) 6.2.b_g_c_m_ai_q $8$ (not in LMFDB) 6.2.b_i_k_bc_bo_cm $8$ (not in LMFDB) 6.2.d_a_ao_au_q_cm $8$ (not in LMFDB) 6.2.d_c_ac_ae_ai_aq $8$ (not in LMFDB) 6.2.d_g_k_u_bg_bw $8$ (not in LMFDB) 6.2.d_i_k_m_a_a $8$ (not in LMFDB) 6.2.d_k_w_bs_cu_ei $8$ (not in LMFDB) 6.2.f_i_ac_au_aq_a $8$ (not in LMFDB) 6.2.f_o_w_u_a_aq $8$ (not in LMFDB) 6.2.f_q_bm_cy_ey_hk $8$ (not in LMFDB) 6.2.h_ba_co_fc_iq_my $8$ (not in LMFDB) 6.2.ad_e_ae_e_ai_q $10$ (not in LMFDB) 6.2.ab_a_e_ae_ai_q $10$ (not in LMFDB) 6.2.d_e_e_e_i_q $10$ (not in LMFDB) 6.2.ab_a_ac_e_a_a $16$ (not in LMFDB) 6.2.b_a_c_e_a_a $16$ (not in LMFDB) 6.2.af_k_ai_e_au_bw $24$ (not in LMFDB) 6.2.af_o_abg_cm_aee_ge $24$ (not in LMFDB) 6.2.af_o_abc_ca_ado_fo $24$ (not in LMFDB) 6.2.ad_a_e_e_e_abg $24$ (not in LMFDB) 6.2.ad_c_ac_m_am_a $24$ (not in LMFDB) 6.2.ad_c_i_am_am_bw $24$ (not in LMFDB) 6.2.ad_e_ae_i_am_q $24$ (not in LMFDB) 6.2.ad_g_ao_bc_abs_cm $24$ (not in LMFDB) 6.2.ad_g_ai_i_ae_a $24$ (not in LMFDB) 6.2.ad_g_ae_e_ae_q $24$ (not in LMFDB) 6.2.ad_i_au_bk_aci_ds $24$ (not in LMFDB) 6.2.ad_i_aq_bg_aca_dc $24$ (not in LMFDB) 6.2.ab_ag_e_u_ae_abw $24$ (not in LMFDB) 6.2.ab_ae_c_q_ae_abg $24$ (not in LMFDB) 6.2.ab_ae_e_e_ae_a $24$ (not in LMFDB) 6.2.ab_ac_a_e_e_aq $24$ (not in LMFDB) 6.2.ab_ac_a_m_ae_aq $24$ (not in LMFDB) 6.2.ab_ac_c_e_ae_a $24$ (not in LMFDB) 6.2.ab_a_ac_i_ae_a $24$ (not in LMFDB) 6.2.ab_a_e_a_ae_q $24$ (not in LMFDB) 6.2.ab_c_ai_i_am_bg $24$ (not in LMFDB) 6.2.ab_c_ae_e_ae_q $24$ (not in LMFDB) 6.2.ab_c_ae_m_am_q $24$ (not in LMFDB) 6.2.ab_c_ac_e_ae_a $24$ (not in LMFDB) 6.2.ab_c_a_a_e_a $24$ (not in LMFDB) 6.2.ab_e_ag_q_au_bg $24$ (not in LMFDB) 6.2.ab_e_ae_e_ae_a $24$ (not in LMFDB) 6.2.ab_e_a_i_e_q $24$ (not in LMFDB) 6.2.ab_g_ai_u_abc_bw $24$ (not in LMFDB) 6.2.b_ag_ae_u_e_abw $24$ (not in LMFDB) 6.2.b_ae_ae_e_e_a $24$ (not in LMFDB) 6.2.b_ae_ac_q_e_abg $24$ (not in LMFDB) 6.2.b_ac_ac_e_e_a $24$ (not in LMFDB) 6.2.b_ac_a_e_ae_aq $24$ (not in LMFDB) 6.2.b_ac_a_m_e_aq $24$ (not in LMFDB) 6.2.b_a_ae_a_e_q $24$ (not in LMFDB) 6.2.b_a_c_i_e_a $24$ (not in LMFDB) 6.2.b_c_a_a_ae_a $24$ (not in LMFDB) 6.2.b_c_c_e_e_a $24$ (not in LMFDB) 6.2.b_c_e_e_e_q $24$ (not in LMFDB) 6.2.b_c_e_m_m_q $24$ (not in LMFDB) 6.2.b_c_i_i_m_bg $24$ (not in LMFDB) 6.2.b_e_a_i_ae_q $24$ (not in LMFDB) 6.2.b_e_e_e_e_a $24$ (not in LMFDB) 6.2.b_e_g_q_u_bg $24$ (not in LMFDB) 6.2.b_g_i_u_bc_bw $24$ (not in LMFDB) 6.2.d_a_ae_e_ae_abg $24$ (not in LMFDB) 6.2.d_c_ai_am_m_bw $24$ (not in LMFDB) 6.2.d_c_c_m_m_a $24$ (not in LMFDB) 6.2.d_e_e_i_m_q $24$ (not in LMFDB) 6.2.d_g_e_e_e_q $24$ (not in LMFDB) 6.2.d_g_i_i_e_a $24$ (not in LMFDB) 6.2.d_g_o_bc_bs_cm $24$ (not in LMFDB) 6.2.d_i_q_bg_ca_dc $24$ (not in LMFDB) 6.2.d_i_u_bk_ci_ds $24$ (not in LMFDB) 6.2.f_k_i_e_u_bw $24$ (not in LMFDB) 6.2.f_o_bc_ca_do_fo $24$ (not in LMFDB) 6.2.f_o_bg_cm_ee_ge $24$ (not in LMFDB) 6.2.ab_ac_a_i_a_aq $40$ (not in LMFDB) 6.2.ab_c_ae_i_ai_q $40$ (not in LMFDB) 6.2.b_ac_a_i_a_aq $40$ (not in LMFDB) 6.2.b_c_e_i_i_q $40$ (not in LMFDB)