Properties

Label 6.2.aj_bs_afr_of_abby_bsa
Base Field $\F_{2}$
Dimension $6$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.384973271919$, $\pm0.456881978294$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 30400 2517424 27360000 781873444 76529689600 5677561731916 293676658560000 16225401053666896 1096491499131160000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 12 27 24 24 69 162 272 459 972

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 1.2.ab 2 $\times$ 2.2.ad_f and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{2}$
The base change of $A$ to $\F_{2^{12}}$ is 1.4096.h 2 $\times$ 1.4096.bv 2 $\times$ 1.4096.ey 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ah_bc_adb_gt_amg_su$2$(not in LMFDB)
6.2.af_q_abn_dd_afm_ii$2$(not in LMFDB)
6.2.af_q_abj_cj_adm_ey$2$(not in LMFDB)
6.2.ad_i_ap_bb_abq_cm$2$(not in LMFDB)
6.2.ab_e_ah_n_as_bg$2$(not in LMFDB)
6.2.ab_e_ad_j_ao_y$2$(not in LMFDB)
6.2.ab_e_ab_h_g_i$2$(not in LMFDB)
6.2.b_e_b_h_ag_i$2$(not in LMFDB)
6.2.b_e_d_j_o_y$2$(not in LMFDB)
6.2.b_e_h_n_s_bg$2$(not in LMFDB)
6.2.d_i_j_j_ag_ai$2$(not in LMFDB)
6.2.d_i_p_bb_bq_cm$2$(not in LMFDB)
6.2.f_q_bj_cj_dm_ey$2$(not in LMFDB)
6.2.f_q_bn_dd_fm_ii$2$(not in LMFDB)
6.2.h_bc_db_gt_mg_su$2$(not in LMFDB)
6.2.j_bs_fr_of_bby_bsa$2$(not in LMFDB)
6.2.ag_r_ay_d_ci_aey$3$(not in LMFDB)
6.2.ag_u_abq_cl_acu_dk$3$(not in LMFDB)
6.2.ad_c_j_ap_ag_bo$3$(not in LMFDB)
6.2.ad_i_aj_d_s_abm$3$(not in LMFDB)
6.2.ad_i_aj_j_g_ai$3$(not in LMFDB)
6.2.a_ab_g_ad_ag_w$3$(not in LMFDB)
6.2.a_ab_g_d_a_q$3$(not in LMFDB)
6.2.a_c_g_d_g_w$3$(not in LMFDB)
6.2.d_c_d_p_s_k$3$(not in LMFDB)
6.2.d_i_v_bn_co_ec$3$(not in LMFDB)
6.2.g_r_bk_cr_ek_gk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ah_bc_adb_gt_amg_su$2$(not in LMFDB)
6.2.af_q_abn_dd_afm_ii$2$(not in LMFDB)
6.2.af_q_abj_cj_adm_ey$2$(not in LMFDB)
6.2.ad_i_ap_bb_abq_cm$2$(not in LMFDB)
6.2.ab_e_ah_n_as_bg$2$(not in LMFDB)
6.2.ab_e_ad_j_ao_y$2$(not in LMFDB)
6.2.ab_e_ab_h_g_i$2$(not in LMFDB)
6.2.b_e_b_h_ag_i$2$(not in LMFDB)
6.2.b_e_d_j_o_y$2$(not in LMFDB)
6.2.b_e_h_n_s_bg$2$(not in LMFDB)
6.2.d_i_j_j_ag_ai$2$(not in LMFDB)
6.2.d_i_p_bb_bq_cm$2$(not in LMFDB)
6.2.f_q_bj_cj_dm_ey$2$(not in LMFDB)
6.2.f_q_bn_dd_fm_ii$2$(not in LMFDB)
6.2.h_bc_db_gt_mg_su$2$(not in LMFDB)
6.2.j_bs_fr_of_bby_bsa$2$(not in LMFDB)
6.2.ag_r_ay_d_ci_aey$3$(not in LMFDB)
6.2.ag_u_abq_cl_acu_dk$3$(not in LMFDB)
6.2.ad_c_j_ap_ag_bo$3$(not in LMFDB)
6.2.ad_i_aj_d_s_abm$3$(not in LMFDB)
6.2.ad_i_aj_j_g_ai$3$(not in LMFDB)
6.2.a_ab_g_ad_ag_w$3$(not in LMFDB)
6.2.a_ab_g_d_a_q$3$(not in LMFDB)
6.2.a_c_g_d_g_w$3$(not in LMFDB)
6.2.d_c_d_p_s_k$3$(not in LMFDB)
6.2.d_i_v_bn_co_ec$3$(not in LMFDB)
6.2.g_r_bk_cr_ek_gk$3$(not in LMFDB)
6.2.ah_w_abl_z_be_adk$4$(not in LMFDB)
6.2.ad_c_d_ad_ag_q$4$(not in LMFDB)
6.2.ab_ac_f_b_ag_i$4$(not in LMFDB)
6.2.b_ac_af_b_g_i$4$(not in LMFDB)
6.2.d_c_ad_ad_g_q$4$(not in LMFDB)
6.2.h_w_bl_z_abe_adk$4$(not in LMFDB)
6.2.ai_bf_ada_fr_aiy_my$6$(not in LMFDB)
6.2.ah_bc_add_hb_ana_uc$6$(not in LMFDB)
6.2.ag_r_abk_cr_aek_gk$6$(not in LMFDB)
6.2.af_k_aj_j_abi_cu$6$(not in LMFDB)
6.2.af_q_abp_dh_afu_iw$6$(not in LMFDB)
6.2.ae_h_ak_t_abk_ce$6$(not in LMFDB)
6.2.ae_h_ag_ad_w_abq$6$(not in LMFDB)
6.2.ae_k_as_bb_abm_cc$6$(not in LMFDB)
6.2.ae_k_aq_z_abk_ce$6$(not in LMFDB)
6.2.ad_c_ad_p_as_k$6$(not in LMFDB)
6.2.ad_i_av_bn_aco_ec$6$(not in LMFDB)
6.2.ac_b_a_ad_c_g$6$(not in LMFDB)
6.2.ac_b_a_d_ae_a$6$(not in LMFDB)
6.2.ac_b_e_af_a_i$6$(not in LMFDB)
6.2.ac_e_ai_n_as_ba$6$(not in LMFDB)
6.2.ac_e_ag_p_aq_y$6$(not in LMFDB)
6.2.ac_e_ac_h_am_bg$6$(not in LMFDB)
6.2.ab_ac_ab_n_ag_aq$6$(not in LMFDB)
6.2.ab_ac_d_d_ac_ag$6$(not in LMFDB)
6.2.ab_e_ad_d_ac_ag$6$(not in LMFDB)
6.2.ab_e_ab_b_g_ak$6$(not in LMFDB)
6.2.a_ab_ag_ad_g_w$6$(not in LMFDB)
6.2.a_ab_ag_d_a_q$6$(not in LMFDB)
6.2.a_ab_g_ad_ag_w$6$(not in LMFDB)
6.2.a_c_ag_d_ag_w$6$(not in LMFDB)
6.2.a_c_a_j_a_q$6$(not in LMFDB)
6.2.b_ac_ad_d_c_ag$6$(not in LMFDB)
6.2.b_ac_b_n_g_aq$6$(not in LMFDB)
6.2.b_e_b_b_ag_ak$6$(not in LMFDB)
6.2.b_e_d_d_c_ag$6$(not in LMFDB)
6.2.c_b_ae_af_a_i$6$(not in LMFDB)
6.2.c_b_a_ad_ac_g$6$(not in LMFDB)
6.2.c_b_a_d_e_a$6$(not in LMFDB)
6.2.c_e_c_h_m_bg$6$(not in LMFDB)
6.2.c_e_g_p_q_y$6$(not in LMFDB)
6.2.c_e_i_n_s_ba$6$(not in LMFDB)
6.2.d_c_aj_ap_g_bo$6$(not in LMFDB)
6.2.d_i_j_d_as_abm$6$(not in LMFDB)
6.2.e_h_g_ad_aw_abq$6$(not in LMFDB)
6.2.e_h_k_t_bk_ce$6$(not in LMFDB)
6.2.e_k_q_z_bk_ce$6$(not in LMFDB)
6.2.e_k_s_bb_bm_cc$6$(not in LMFDB)
6.2.f_k_j_j_bi_cu$6$(not in LMFDB)
6.2.f_q_bp_dh_fu_iw$6$(not in LMFDB)
6.2.g_r_y_d_aci_aey$6$(not in LMFDB)
6.2.g_u_bq_cl_cu_dk$6$(not in LMFDB)
6.2.h_bc_dd_hb_na_uc$6$(not in LMFDB)
6.2.i_bf_da_fr_iy_my$6$(not in LMFDB)
6.2.ah_be_adn_ih_aps_ym$8$(not in LMFDB)
6.2.af_m_ar_l_m_abk$8$(not in LMFDB)
6.2.af_m_ap_ad_by_adw$8$(not in LMFDB)
6.2.af_s_abv_dx_agy_kq$8$(not in LMFDB)
6.2.af_u_acd_ev_aiw_ns$8$(not in LMFDB)
6.2.ad_ac_p_al_as_bs$8$(not in LMFDB)
6.2.ad_e_ad_af_s_abc$8$(not in LMFDB)
6.2.ad_g_aj_f_g_am$8$(not in LMFDB)
6.2.ad_k_ax_bv_adc_eu$8$(not in LMFDB)
6.2.ad_k_at_bj_aca_cy$8$(not in LMFDB)
6.2.ad_m_abb_ch_ady_ga$8$(not in LMFDB)
6.2.ab_a_ad_ad_k_ae$8$(not in LMFDB)
6.2.ab_a_ab_ab_a_m$8$(not in LMFDB)
6.2.ab_g_ah_r_ay_bk$8$(not in LMFDB)
6.2.ab_g_ab_l_m_m$8$(not in LMFDB)
6.2.ab_i_al_bd_abu_cq$8$(not in LMFDB)
6.2.b_a_b_ab_a_m$8$(not in LMFDB)
6.2.b_a_d_ad_ak_ae$8$(not in LMFDB)
6.2.b_g_b_l_am_m$8$(not in LMFDB)
6.2.b_g_h_r_y_bk$8$(not in LMFDB)
6.2.b_i_l_bd_bu_cq$8$(not in LMFDB)
6.2.d_ac_ap_al_s_bs$8$(not in LMFDB)
6.2.d_e_d_af_as_abc$8$(not in LMFDB)
6.2.d_g_j_f_ag_am$8$(not in LMFDB)
6.2.d_k_t_bj_ca_cy$8$(not in LMFDB)
6.2.d_k_x_bv_dc_eu$8$(not in LMFDB)
6.2.d_m_bb_ch_dy_ga$8$(not in LMFDB)
6.2.f_m_p_ad_aby_adw$8$(not in LMFDB)
6.2.f_m_r_l_am_abk$8$(not in LMFDB)
6.2.f_s_bv_dx_gy_kq$8$(not in LMFDB)
6.2.f_u_cd_ev_iw_ns$8$(not in LMFDB)
6.2.h_be_dn_ih_ps_ym$8$(not in LMFDB)
6.2.ag_w_acc_eb_agm_jo$12$(not in LMFDB)
6.2.af_k_al_h_g_aw$12$(not in LMFDB)
6.2.af_m_at_bf_ack_ea$12$(not in LMFDB)
6.2.ae_e_i_ar_am_ce$12$(not in LMFDB)
6.2.ae_g_a_ah_ae_y$12$(not in LMFDB)
6.2.ae_m_aba_bx_ade_es$12$(not in LMFDB)
6.2.ae_m_ay_bv_acy_eq$12$(not in LMFDB)
6.2.ad_e_aj_v_abe_bm$12$(not in LMFDB)
6.2.ad_e_d_aj_g_i$12$(not in LMFDB)
6.2.ac_ac_e_h_ag_ak$12$(not in LMFDB)
6.2.ac_a_a_f_ac_ag$12$(not in LMFDB)
6.2.ac_g_am_x_abm_cc$12$(not in LMFDB)
6.2.ac_g_ak_z_abg_ce$12$(not in LMFDB)
6.2.ac_g_ag_r_au_bw$12$(not in LMFDB)
6.2.ab_ac_f_af_ag_ba$12$(not in LMFDB)
6.2.ab_a_ad_l_ak_a$12$(not in LMFDB)
6.2.ab_a_b_b_c_ak$12$(not in LMFDB)
6.2.a_ae_a_p_a_abg$12$(not in LMFDB)
6.2.a_ac_a_j_a_aq$12$(not in LMFDB)
6.2.a_ab_g_ad_ag_w$12$(not in LMFDB)
6.2.a_e_ag_j_as_ba$12$(not in LMFDB)
6.2.a_e_a_p_a_bg$12$(not in LMFDB)
6.2.a_e_g_j_s_ba$12$(not in LMFDB)
6.2.b_ac_af_af_g_ba$12$(not in LMFDB)
6.2.b_a_ab_b_ac_ak$12$(not in LMFDB)
6.2.b_a_d_l_k_a$12$(not in LMFDB)
6.2.c_ac_ae_h_g_ak$12$(not in LMFDB)
6.2.c_a_a_f_c_ag$12$(not in LMFDB)
6.2.c_g_g_r_u_bw$12$(not in LMFDB)
6.2.c_g_k_z_bg_ce$12$(not in LMFDB)
6.2.c_g_m_x_bm_cc$12$(not in LMFDB)
6.2.d_e_ad_aj_ag_i$12$(not in LMFDB)
6.2.d_e_j_v_be_bm$12$(not in LMFDB)
6.2.e_e_ai_ar_m_ce$12$(not in LMFDB)
6.2.e_g_a_ah_e_y$12$(not in LMFDB)
6.2.e_m_y_bv_cy_eq$12$(not in LMFDB)
6.2.e_m_ba_bx_de_es$12$(not in LMFDB)
6.2.f_k_l_h_ag_aw$12$(not in LMFDB)
6.2.f_m_t_bf_ck_ea$12$(not in LMFDB)
6.2.g_w_cc_eb_gm_jo$12$(not in LMFDB)
6.2.ag_t_abs_df_afe_ho$24$(not in LMFDB)
6.2.af_o_az_bd_au_o$24$(not in LMFDB)
6.2.af_s_abt_dp_age_ji$24$(not in LMFDB)
6.2.ae_d_g_aj_e_ae$24$(not in LMFDB)
6.2.ae_f_ac_f_aq_ba$24$(not in LMFDB)
6.2.ae_j_as_bh_ace_di$24$(not in LMFDB)
6.2.ae_j_ak_ab_be_aci$24$(not in LMFDB)
6.2.ae_l_aba_bv_acy_em$24$(not in LMFDB)
6.2.ae_m_aw_bj_abq_ci$24$(not in LMFDB)
6.2.ae_o_abe_cj_adq_fs$24$(not in LMFDB)
6.2.ad_a_j_ah_am_be$24$(not in LMFDB)
6.2.ad_e_af_l_au_bc$24$(not in LMFDB)
6.2.ad_e_ad_b_a_c$24$(not in LMFDB)
6.2.ad_g_al_v_abk_ca$24$(not in LMFDB)
6.2.ad_g_aj_l_am_s$24$(not in LMFDB)
6.2.ad_k_av_br_acu_eg$24$(not in LMFDB)
6.2.ac_ad_m_aj_aq_bs$24$(not in LMFDB)
6.2.ac_ab_i_ah_ai_ba$24$(not in LMFDB)
6.2.ac_a_e_ab_ag_m$24$(not in LMFDB)
6.2.ac_a_g_aj_ae_u$24$(not in LMFDB)
6.2.ac_c_a_b_ac_e$24$(not in LMFDB)
6.2.ac_c_c_ah_e_ae$24$(not in LMFDB)
6.2.ac_c_c_ab_ai_ba$24$(not in LMFDB)
6.2.ac_d_ai_l_as_bk$24$(not in LMFDB)
6.2.ac_d_a_ad_i_ak$24$(not in LMFDB)
6.2.ac_e_ac_f_ai_w$24$(not in LMFDB)
6.2.ac_f_ae_ab_q_abc$24$(not in LMFDB)
6.2.ac_g_ai_r_as_bk$24$(not in LMFDB)
6.2.ac_g_ag_p_aq_bm$24$(not in LMFDB)
6.2.ac_i_am_bf_abm_cy$24$(not in LMFDB)
6.2.ac_i_ak_x_au_bs$24$(not in LMFDB)
6.2.ac_i_ak_bd_abg_cw$24$(not in LMFDB)
6.2.ac_k_ao_bp_abs_dw$24$(not in LMFDB)
6.2.ab_ag_d_v_ac_aca$24$(not in LMFDB)
6.2.ab_ae_b_l_c_abc$24$(not in LMFDB)
6.2.ab_ae_b_r_ae_abi$24$(not in LMFDB)
6.2.ab_ac_ab_l_ae_ao$24$(not in LMFDB)
6.2.ab_a_ad_j_ai_c$24$(not in LMFDB)
6.2.ab_a_f_ab_a_m$24$(not in LMFDB)
6.2.ab_c_af_f_ak_u$24$(not in LMFDB)
6.2.ab_c_af_f_ae_o$24$(not in LMFDB)
6.2.ab_c_af_l_aq_o$24$(not in LMFDB)
6.2.ab_c_d_b_i_e$24$(not in LMFDB)
6.2.ab_e_ah_l_aw_bc$24$(not in LMFDB)
6.2.ab_g_aj_v_abg_by$24$(not in LMFDB)
6.2.a_ai_a_bf_a_acy$24$(not in LMFDB)
6.2.a_ag_a_r_a_abk$24$(not in LMFDB)
6.2.a_ag_a_x_a_acc$24$(not in LMFDB)
6.2.a_ae_a_n_a_aba$24$(not in LMFDB)
6.2.a_ac_a_b_a_ae$24$(not in LMFDB)
6.2.a_ac_a_h_a_ak$24$(not in LMFDB)
6.2.a_a_a_ab_a_am$24$(not in LMFDB)
6.2.a_a_a_ab_a_m$24$(not in LMFDB)
6.2.a_a_a_f_a_ag$24$(not in LMFDB)
6.2.a_a_a_f_a_g$24$(not in LMFDB)
6.2.a_b_ac_ab_ac_e$24$(not in LMFDB)
6.2.a_b_c_ab_c_e$24$(not in LMFDB)
6.2.a_c_a_b_a_e$24$(not in LMFDB)
6.2.a_c_a_h_a_k$24$(not in LMFDB)
6.2.a_e_ac_l_ac_bc$24$(not in LMFDB)
6.2.a_e_a_n_a_ba$24$(not in LMFDB)
6.2.a_e_c_l_c_bc$24$(not in LMFDB)
6.2.a_g_ac_v_ag_ca$24$(not in LMFDB)
6.2.a_g_a_r_a_bk$24$(not in LMFDB)
6.2.a_g_a_x_a_cc$24$(not in LMFDB)
6.2.a_g_c_v_g_ca$24$(not in LMFDB)
6.2.a_i_a_bf_a_cy$24$(not in LMFDB)
6.2.b_ag_ad_v_c_aca$24$(not in LMFDB)
6.2.b_ae_ab_l_ac_abc$24$(not in LMFDB)
6.2.b_ae_ab_r_e_abi$24$(not in LMFDB)
6.2.b_ac_b_l_e_ao$24$(not in LMFDB)
6.2.b_a_af_ab_a_m$24$(not in LMFDB)
6.2.b_a_d_j_i_c$24$(not in LMFDB)
6.2.b_c_ad_b_ai_e$24$(not in LMFDB)
6.2.b_c_f_f_e_o$24$(not in LMFDB)
6.2.b_c_f_f_k_u$24$(not in LMFDB)
6.2.b_c_f_l_q_o$24$(not in LMFDB)
6.2.b_e_h_l_w_bc$24$(not in LMFDB)
6.2.b_g_j_v_bg_by$24$(not in LMFDB)
6.2.c_ad_am_aj_q_bs$24$(not in LMFDB)
6.2.c_ab_ai_ah_i_ba$24$(not in LMFDB)
6.2.c_a_ag_aj_e_u$24$(not in LMFDB)
6.2.c_a_ae_ab_g_m$24$(not in LMFDB)
6.2.c_c_ac_ah_ae_ae$24$(not in LMFDB)
6.2.c_c_ac_ab_i_ba$24$(not in LMFDB)
6.2.c_c_a_b_c_e$24$(not in LMFDB)
6.2.c_d_a_ad_ai_ak$24$(not in LMFDB)
6.2.c_d_i_l_s_bk$24$(not in LMFDB)
6.2.c_e_c_f_i_w$24$(not in LMFDB)
6.2.c_f_e_ab_aq_abc$24$(not in LMFDB)
6.2.c_g_g_p_q_bm$24$(not in LMFDB)
6.2.c_g_i_r_s_bk$24$(not in LMFDB)
6.2.c_i_k_x_u_bs$24$(not in LMFDB)
6.2.c_i_k_bd_bg_cw$24$(not in LMFDB)
6.2.c_i_m_bf_bm_cy$24$(not in LMFDB)
6.2.c_k_o_bp_bs_dw$24$(not in LMFDB)
6.2.d_a_aj_ah_m_be$24$(not in LMFDB)
6.2.d_e_d_b_a_c$24$(not in LMFDB)
6.2.d_e_f_l_u_bc$24$(not in LMFDB)
6.2.d_g_j_l_m_s$24$(not in LMFDB)
6.2.d_g_l_v_bk_ca$24$(not in LMFDB)
6.2.d_k_v_br_cu_eg$24$(not in LMFDB)
6.2.e_d_ag_aj_ae_ae$24$(not in LMFDB)
6.2.e_f_c_f_q_ba$24$(not in LMFDB)
6.2.e_j_k_ab_abe_aci$24$(not in LMFDB)
6.2.e_j_s_bh_ce_di$24$(not in LMFDB)
6.2.e_l_ba_bv_cy_em$24$(not in LMFDB)
6.2.e_m_w_bj_bq_ci$24$(not in LMFDB)
6.2.e_o_be_cj_dq_fs$24$(not in LMFDB)
6.2.f_o_z_bd_u_o$24$(not in LMFDB)
6.2.f_s_bt_dp_ge_ji$24$(not in LMFDB)
6.2.g_t_bs_df_fe_ho$24$(not in LMFDB)