# Properties

 Label 5.2.ah_bd_add_go_akm Base Field $\F_{2}$ Dimension $5$ Ordinary No $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $5$ L-polynomial: $( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{3}$ Frobenius angles: $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.384973271919$, $\pm0.384973271919$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 8 12800 463736 2560000 17899288 741977600 36561324472 1209323520000 32157289243352 952958093120000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 14 32 30 16 38 136 286 464 854

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
 The isogeny class factors as 1.2.ac 2 $\times$ 1.2.ab 3 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 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$ 1.2.ab 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-7})$$$)$
Endomorphism algebra over $\overline{\F}_{2}$
 The base change of $A$ to $\F_{2^{4}}$ is 1.16.ab 3 $\times$ 1.16.i 2 . The endomorphism algebra for each factor is: 1.16.ab 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-7})$$$)$ 1.16.i 2 : $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$.
All geometric endomorphisms are defined over $\F_{2^{4}}$.
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 2 $\times$ 1.4.d 3 . The endomorphism algebra for each factor is: 1.4.a 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$ 1.4.d 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-7})$$$)$

## 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 5.2.af_r_abn_cw_aei $2$ (not in LMFDB) 5.2.ad_j_ar_bi_abw $2$ (not in LMFDB) 5.2.ad_j_an_w_ay $2$ (not in LMFDB) 5.2.ab_f_ah_s_aq $2$ (not in LMFDB) 5.2.ab_f_ad_o_ai $2$ (not in LMFDB) 5.2.b_f_d_o_i $2$ (not in LMFDB) 5.2.b_f_h_s_q $2$ (not in LMFDB) 5.2.d_j_n_w_y $2$ (not in LMFDB) 5.2.d_j_r_bi_bw $2$ (not in LMFDB) 5.2.f_r_bn_cw_ei $2$ (not in LMFDB) 5.2.h_bd_dd_go_km $2$ (not in LMFDB) 5.2.ae_i_ad_aq_bo $3$ (not in LMFDB) 5.2.ab_f_d_c_w $3$ (not in LMFDB) 5.2.c_c_j_o_k $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 5.2.af_r_abn_cw_aei $2$ (not in LMFDB) 5.2.ad_j_ar_bi_abw $2$ (not in LMFDB) 5.2.ad_j_an_w_ay $2$ (not in LMFDB) 5.2.ab_f_ah_s_aq $2$ (not in LMFDB) 5.2.ab_f_ad_o_ai $2$ (not in LMFDB) 5.2.b_f_d_o_i $2$ (not in LMFDB) 5.2.b_f_h_s_q $2$ (not in LMFDB) 5.2.d_j_n_w_y $2$ (not in LMFDB) 5.2.d_j_r_bi_bw $2$ (not in LMFDB) 5.2.f_r_bn_cw_ei $2$ (not in LMFDB) 5.2.h_bd_dd_go_km $2$ (not in LMFDB) 5.2.ae_i_ad_aq_bo $3$ (not in LMFDB) 5.2.ab_f_d_c_w $3$ (not in LMFDB) 5.2.c_c_j_o_k $3$ (not in LMFDB) 5.2.af_l_aj_ak_bg $4$ (not in LMFDB) 5.2.ad_d_b_ac_a $4$ (not in LMFDB) 5.2.ab_ab_d_c_ai $4$ (not in LMFDB) 5.2.b_ab_ad_c_i $4$ (not in LMFDB) 5.2.d_d_ab_ac_a $4$ (not in LMFDB) 5.2.f_l_j_ak_abg $4$ (not in LMFDB) 5.2.ag_s_abj_ca_acu $6$ (not in LMFDB) 5.2.af_r_abp_da_aes $6$ (not in LMFDB) 5.2.ae_i_ap_ba_abm $6$ (not in LMFDB) 5.2.ae_i_an_y_abo $6$ (not in LMFDB) 5.2.ad_j_at_bi_acc $6$ (not in LMFDB) 5.2.ac_c_aj_o_ak $6$ (not in LMFDB) 5.2.ac_c_ad_i_aq $6$ (not in LMFDB) 5.2.ac_c_b_ag_k $6$ (not in LMFDB) 5.2.ac_c_d_ae_i $6$ (not in LMFDB) 5.2.ab_f_aj_o_aba $6$ (not in LMFDB) 5.2.a_a_af_e_a $6$ (not in LMFDB) 5.2.a_a_ab_ac_g $6$ (not in LMFDB) 5.2.a_a_b_ac_ag $6$ (not in LMFDB) 5.2.a_a_f_e_a $6$ (not in LMFDB) 5.2.b_f_ad_c_aw $6$ (not in LMFDB) 5.2.b_f_j_o_ba $6$ (not in LMFDB) 5.2.c_c_ad_ae_ai $6$ (not in LMFDB) 5.2.c_c_ab_ag_ak $6$ (not in LMFDB) 5.2.c_c_d_i_q $6$ (not in LMFDB) 5.2.d_j_t_bi_cc $6$ (not in LMFDB) 5.2.e_i_d_aq_abo $6$ (not in LMFDB) 5.2.e_i_n_y_bo $6$ (not in LMFDB) 5.2.e_i_p_ba_bm $6$ (not in LMFDB) 5.2.f_r_bp_da_es $6$ (not in LMFDB) 5.2.g_s_bj_ca_cu $6$ (not in LMFDB) 5.2.ah_w_abn_bs_abw $7$ (not in LMFDB) 5.2.a_b_d_c_i $7$ (not in LMFDB) 5.2.af_t_abv_ds_afs $8$ (not in LMFDB) 5.2.ad_f_ad_ae_m $8$ (not in LMFDB) 5.2.ad_f_ab_ao_bc $8$ (not in LMFDB) 5.2.ad_l_av_bs_aci $8$ (not in LMFDB) 5.2.ad_n_az_cg_acy $8$ (not in LMFDB) 5.2.ab_af_h_g_au $8$ (not in LMFDB) 5.2.ab_b_ab_a_e $8$ (not in LMFDB) 5.2.ab_b_b_ag_e $8$ (not in LMFDB) 5.2.ab_d_ab_ac_e $8$ (not in LMFDB) 5.2.ab_h_ah_y_au $8$ (not in LMFDB) 5.2.ab_h_ad_u_ae $8$ (not in LMFDB) 5.2.ab_j_ah_bi_au $8$ (not in LMFDB) 5.2.b_af_ah_g_u $8$ (not in LMFDB) 5.2.b_b_ab_ag_ae $8$ (not in LMFDB) 5.2.b_b_b_a_ae $8$ (not in LMFDB) 5.2.b_d_b_ac_ae $8$ (not in LMFDB) 5.2.b_h_d_u_e $8$ (not in LMFDB) 5.2.b_h_h_y_u $8$ (not in LMFDB) 5.2.b_j_h_bi_u $8$ (not in LMFDB) 5.2.d_f_b_ao_abc $8$ (not in LMFDB) 5.2.d_f_d_ae_am $8$ (not in LMFDB) 5.2.d_l_v_bs_ci $8$ (not in LMFDB) 5.2.d_n_z_cg_cy $8$ (not in LMFDB) 5.2.f_t_bv_ds_fs $8$ (not in LMFDB) 5.2.ad_d_ab_ac_g $12$ (not in LMFDB) 5.2.ab_ab_ad_c_k $12$ (not in LMFDB) 5.2.b_ab_d_c_ak $12$ (not in LMFDB) 5.2.d_d_b_ac_ag $12$ (not in LMFDB) 5.2.ai_bh_adn_he_alk $14$ (not in LMFDB) 5.2.ae_j_ap_w_abg $14$ (not in LMFDB) 5.2.ad_c_b_i_ay $14$ (not in LMFDB) 5.2.ab_ac_h_e_aq $14$ (not in LMFDB) 5.2.a_b_ad_c_ai $14$ (not in LMFDB) 5.2.b_ac_ah_e_q $14$ (not in LMFDB) 5.2.d_c_ab_i_y $14$ (not in LMFDB) 5.2.e_j_p_w_bg $14$ (not in LMFDB) 5.2.h_w_bn_bs_bw $14$ (not in LMFDB) 5.2.i_bh_dn_he_lk $14$ (not in LMFDB) 5.2.ab_ac_d_c_ag $21$ (not in LMFDB) 5.2.g_t_bt_di_fe $21$ (not in LMFDB) 5.2.ae_k_at_be_abs $24$ (not in LMFDB) 5.2.ad_h_ah_e_c $24$ (not in LMFDB) 5.2.ad_l_at_bo_aby $24$ (not in LMFDB) 5.2.ac_ac_f_a_ae $24$ (not in LMFDB) 5.2.ac_a_b_e_ak $24$ (not in LMFDB) 5.2.ac_e_aj_o_au $24$ (not in LMFDB) 5.2.ac_e_ah_m_aw $24$ (not in LMFDB) 5.2.ac_e_b_ag_u $24$ (not in LMFDB) 5.2.ac_g_al_q_abc $24$ (not in LMFDB) 5.2.ab_ad_f_e_ao $24$ (not in LMFDB) 5.2.ab_b_b_a_ac $24$ (not in LMFDB) 5.2.ab_d_ab_e_ac $24$ (not in LMFDB) 5.2.ab_h_af_y_ao $24$ (not in LMFDB) 5.2.a_ae_af_e_u $24$ (not in LMFDB) 5.2.a_ae_f_e_au $24$ (not in LMFDB) 5.2.a_ac_af_e_k $24$ (not in LMFDB) 5.2.a_ac_f_e_ak $24$ (not in LMFDB) 5.2.a_c_af_e_ak $24$ (not in LMFDB) 5.2.a_c_ad_c_am $24$ (not in LMFDB) 5.2.a_c_d_c_m $24$ (not in LMFDB) 5.2.a_c_f_e_k $24$ (not in LMFDB) 5.2.a_e_af_e_au $24$ (not in LMFDB) 5.2.a_e_f_e_u $24$ (not in LMFDB) 5.2.b_ad_af_e_o $24$ (not in LMFDB) 5.2.b_b_ab_a_c $24$ (not in LMFDB) 5.2.b_d_b_e_c $24$ (not in LMFDB) 5.2.b_h_f_y_o $24$ (not in LMFDB) 5.2.c_ac_af_a_e $24$ (not in LMFDB) 5.2.c_a_ab_e_k $24$ (not in LMFDB) 5.2.c_e_ab_ag_au $24$ (not in LMFDB) 5.2.c_e_h_m_w $24$ (not in LMFDB) 5.2.c_e_j_o_u $24$ (not in LMFDB) 5.2.c_g_l_q_bc $24$ (not in LMFDB) 5.2.d_h_h_e_ac $24$ (not in LMFDB) 5.2.d_l_t_bo_by $24$ (not in LMFDB) 5.2.e_k_t_be_bs $24$ (not in LMFDB) 5.2.ag_t_abt_di_afe $42$ (not in LMFDB) 5.2.af_k_an_w_abm $42$ (not in LMFDB) 5.2.ac_d_ab_ag_k $42$ (not in LMFDB) 5.2.b_ac_ad_c_g $42$ (not in LMFDB) 5.2.c_d_b_ag_ak $42$ (not in LMFDB) 5.2.f_k_n_w_bm $42$ (not in LMFDB) 5.2.ag_v_acb_ea_agi $56$ (not in LMFDB) 5.2.af_m_at_ba_abk $56$ (not in LMFDB) 5.2.ae_f_b_ao_bc $56$ (not in LMFDB) 5.2.ae_n_abf_cg_ado $56$ (not in LMFDB) 5.2.ad_ac_n_a_abc $56$ (not in LMFDB) 5.2.ad_g_al_q_au $56$ (not in LMFDB) 5.2.ac_f_aj_m_au $56$ (not in LMFDB) 5.2.ab_a_ad_g_ae $56$ (not in LMFDB) 5.2.b_a_d_g_e $56$ (not in LMFDB) 5.2.c_f_j_m_u $56$ (not in LMFDB) 5.2.d_ac_an_a_bc $56$ (not in LMFDB) 5.2.d_g_l_q_u $56$ (not in LMFDB) 5.2.e_f_ab_ao_abc $56$ (not in LMFDB) 5.2.e_n_bf_cg_do $56$ (not in LMFDB) 5.2.f_m_t_ba_bk $56$ (not in LMFDB) 5.2.g_v_cb_ea_gi $56$ (not in LMFDB) 5.2.ae_h_ah_e_ac $168$ (not in LMFDB) 5.2.ae_l_ax_bo_ack $168$ (not in LMFDB) 5.2.ad_a_h_e_aba $168$ (not in LMFDB) 5.2.ad_e_af_m_aw $168$ (not in LMFDB) 5.2.d_a_ah_e_ba $168$ (not in LMFDB) 5.2.d_e_f_m_w $168$ (not in LMFDB) 5.2.e_h_h_e_c $168$ (not in LMFDB) 5.2.e_l_x_bo_ck $168$ (not in LMFDB)