Properties

Label 6.2.ak_bz_ags_qz_abho_cay
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$
Frobenius angles:  $\pm0.123548644961$, $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.456881978294$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 1 9025 976144 18275625 1552438801 140955193600 6208882848169 247630350875625 15804533776295056 1303350965653800625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 17 19 43 109 175 227 449 1147

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 2.2.ad_f 2 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 4 $\times$ 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.ag_t_abq_cv_aee_fw$2$(not in LMFDB)
6.2.ae_j_am_j_e_aq$2$(not in LMFDB)
6.2.ac_d_ag_j_aq_bg$2$(not in LMFDB)
6.2.a_b_a_b_a_i$2$(not in LMFDB)
6.2.c_d_g_j_q_bg$2$(not in LMFDB)
6.2.e_j_m_j_ae_aq$2$(not in LMFDB)
6.2.g_t_bq_cv_ee_fw$2$(not in LMFDB)
6.2.k_bz_gs_qz_bho_cay$2$(not in LMFDB)
6.2.ah_y_abz_cx_adi_ea$3$(not in LMFDB)
6.2.ae_g_a_ad_au_ce$3$(not in LMFDB)
6.2.ae_j_am_d_w_abu$3$(not in LMFDB)
6.2.ab_a_d_ad_ac_o$3$(not in LMFDB)
6.2.ab_a_d_d_ac_i$3$(not in LMFDB)
6.2.c_a_a_j_k_c$3$(not in LMFDB)
6.2.c_d_g_d_ac_c$3$(not in LMFDB)
6.2.f_m_v_bh_bu_ck$3$(not in LMFDB)
6.2.i_bh_ds_il_pq_yc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ag_t_abq_cv_aee_fw$2$(not in LMFDB)
6.2.ae_j_am_j_e_aq$2$(not in LMFDB)
6.2.ac_d_ag_j_aq_bg$2$(not in LMFDB)
6.2.a_b_a_b_a_i$2$(not in LMFDB)
6.2.c_d_g_j_q_bg$2$(not in LMFDB)
6.2.e_j_m_j_ae_aq$2$(not in LMFDB)
6.2.g_t_bq_cv_ee_fw$2$(not in LMFDB)
6.2.k_bz_gs_qz_bho_cay$2$(not in LMFDB)
6.2.ah_y_abz_cx_adi_ea$3$(not in LMFDB)
6.2.ae_g_a_ad_au_ce$3$(not in LMFDB)
6.2.ae_j_am_d_w_abu$3$(not in LMFDB)
6.2.ab_a_d_ad_ac_o$3$(not in LMFDB)
6.2.ab_a_d_d_ac_i$3$(not in LMFDB)
6.2.c_a_a_j_k_c$3$(not in LMFDB)
6.2.c_d_g_d_ac_c$3$(not in LMFDB)
6.2.f_m_v_bh_bu_ck$3$(not in LMFDB)
6.2.i_bh_ds_il_pq_yc$3$(not in LMFDB)
6.2.ae_h_ae_ah_u_abg$4$(not in LMFDB)
6.2.a_ab_a_b_a_ai$4$(not in LMFDB)
6.2.e_h_e_ah_au_abg$4$(not in LMFDB)
6.2.af_q_abi_cj_ado_fg$5$(not in LMFDB)
6.2.a_ae_b_l_ac_ay$5$(not in LMFDB)
6.2.ai_bh_ads_il_apq_yc$6$(not in LMFDB)
6.2.af_m_av_bh_abu_ck$6$(not in LMFDB)
6.2.ad_e_ad_h_as_bg$6$(not in LMFDB)
6.2.ac_a_a_j_ak_c$6$(not in LMFDB)
6.2.ac_d_ag_d_c_c$6$(not in LMFDB)
6.2.a_ac_a_n_a_aq$6$(not in LMFDB)
6.2.b_a_ad_ad_c_o$6$(not in LMFDB)
6.2.b_a_ad_d_c_i$6$(not in LMFDB)
6.2.d_e_d_h_s_bg$6$(not in LMFDB)
6.2.e_g_a_ad_u_ce$6$(not in LMFDB)
6.2.e_j_m_d_aw_abu$6$(not in LMFDB)
6.2.h_y_bz_cx_di_ea$6$(not in LMFDB)
6.2.ai_bj_aee_jx_asw_bdk$8$(not in LMFDB)
6.2.ag_p_as_ad_ci_aeu$8$(not in LMFDB)
6.2.ag_x_aco_ft_akq_qm$8$(not in LMFDB)
6.2.ae_l_ay_bp_ack_do$8$(not in LMFDB)
6.2.ac_d_ac_ad_k_au$8$(not in LMFDB)
6.2.ac_f_ag_f_c_ae$8$(not in LMFDB)
6.2.a_af_a_f_a_e$8$(not in LMFDB)
6.2.a_ad_a_ad_a_u$8$(not in LMFDB)
6.2.a_d_a_ad_a_au$8$(not in LMFDB)
6.2.a_f_a_f_a_ae$8$(not in LMFDB)
6.2.c_d_c_ad_ak_au$8$(not in LMFDB)
6.2.c_f_g_f_ac_ae$8$(not in LMFDB)
6.2.e_l_y_bp_ck_do$8$(not in LMFDB)
6.2.g_p_s_ad_aci_aeu$8$(not in LMFDB)
6.2.g_x_co_ft_kq_qm$8$(not in LMFDB)
6.2.i_bj_ee_jx_sw_bdk$8$(not in LMFDB)
6.2.ai_bc_abx_t_ec_ajo$10$(not in LMFDB)
6.2.ae_e_h_ar_ac_bg$10$(not in LMFDB)
6.2.ad_i_ao_bd_abs_cu$10$(not in LMFDB)
6.2.ab_e_ac_n_ai_bg$10$(not in LMFDB)
6.2.a_ae_ab_l_c_ay$10$(not in LMFDB)
6.2.b_e_c_n_i_bg$10$(not in LMFDB)
6.2.d_i_o_bd_bs_cu$10$(not in LMFDB)
6.2.e_e_ah_ar_c_bg$10$(not in LMFDB)
6.2.f_q_bi_cj_do_fg$10$(not in LMFDB)
6.2.i_bc_bx_t_aec_ajo$10$(not in LMFDB)
6.2.ah_ba_acn_ev_ahu_lk$12$(not in LMFDB)
6.2.af_o_abf_ch_adu_fq$12$(not in LMFDB)
6.2.ae_i_ai_l_abc_ce$12$(not in LMFDB)
6.2.ae_k_aq_bd_aca_dk$12$(not in LMFDB)
6.2.ad_g_aj_r_abe_bw$12$(not in LMFDB)
6.2.ac_b_ac_ab_k_ao$12$(not in LMFDB)
6.2.ac_c_ae_l_ao_o$12$(not in LMFDB)
6.2.ac_e_ai_r_aba_bi$12$(not in LMFDB)
6.2.ab_c_b_ab_c_c$12$(not in LMFDB)
6.2.ab_c_b_f_c_i$12$(not in LMFDB)
6.2.a_a_a_l_a_a$12$(not in LMFDB)
6.2.a_c_a_n_a_q$12$(not in LMFDB)
6.2.b_c_ab_ab_ac_c$12$(not in LMFDB)
6.2.b_c_ab_f_ac_i$12$(not in LMFDB)
6.2.c_b_c_ab_ak_ao$12$(not in LMFDB)
6.2.c_c_e_l_o_o$12$(not in LMFDB)
6.2.c_e_i_r_ba_bi$12$(not in LMFDB)
6.2.d_g_j_r_be_bw$12$(not in LMFDB)
6.2.e_i_i_l_bc_ce$12$(not in LMFDB)
6.2.e_k_q_bd_ca_dk$12$(not in LMFDB)
6.2.f_o_bf_ch_du_fq$12$(not in LMFDB)
6.2.h_ba_cn_ev_hu_lk$12$(not in LMFDB)
6.2.aj_bp_aev_lb_auk_bfk$15$(not in LMFDB)
6.2.ad_f_af_ab_k_as$15$(not in LMFDB)
6.2.ac_ac_l_al_ao_bu$15$(not in LMFDB)
6.2.b_b_f_h_k_q$15$(not in LMFDB)
6.2.b_e_i_n_w_bi$15$(not in LMFDB)
6.2.d_i_q_bd_bu_co$15$(not in LMFDB)
6.2.g_o_n_ah_abm_aco$15$(not in LMFDB)
6.2.h_z_cn_fj_jq_os$15$(not in LMFDB)
6.2.ag_r_abe_bj_ay_o$24$(not in LMFDB)
6.2.ag_v_acc_eh_ahk_le$24$(not in LMFDB)
6.2.af_o_abb_bp_aca_cq$24$(not in LMFDB)
6.2.af_q_abl_ct_aem_gq$24$(not in LMFDB)
6.2.ae_i_ai_ad_bc_ace$24$(not in LMFDB)
6.2.ad_a_j_aj_ag_u$24$(not in LMFDB)
6.2.ad_c_d_ah_g_ae$24$(not in LMFDB)
6.2.ad_c_d_ab_am_ba$24$(not in LMFDB)
6.2.ad_e_ad_f_am_w$24$(not in LMFDB)
6.2.ad_g_aj_p_ay_bm$24$(not in LMFDB)
6.2.ad_i_ap_x_abe_bs$24$(not in LMFDB)
6.2.ad_i_ap_bd_abw_cw$24$(not in LMFDB)
6.2.ad_k_av_bp_aco_dw$24$(not in LMFDB)
6.2.ac_c_ae_ad_o_ao$24$(not in LMFDB)
6.2.ac_c_a_f_ak_u$24$(not in LMFDB)
6.2.ac_e_ae_ad_o_abc$24$(not in LMFDB)
6.2.ac_e_ae_l_ao_bc$24$(not in LMFDB)
6.2.ac_g_ai_v_aba_ca$24$(not in LMFDB)
6.2.ab_c_ad_f_ai_u$24$(not in LMFDB)
6.2.ab_e_af_l_aq_bc$24$(not in LMFDB)
6.2.a_ag_a_v_a_aca$24$(not in LMFDB)
6.2.a_ae_a_ad_a_bc$24$(not in LMFDB)
6.2.a_ae_a_l_a_abc$24$(not in LMFDB)
6.2.a_ae_a_r_a_abi$24$(not in LMFDB)
6.2.a_ad_a_d_a_ac$24$(not in LMFDB)
6.2.a_ac_a_ad_a_o$24$(not in LMFDB)
6.2.a_ac_a_f_a_au$24$(not in LMFDB)
6.2.a_ac_a_l_a_ao$24$(not in LMFDB)
6.2.a_ab_a_ab_a_o$24$(not in LMFDB)
6.2.a_a_a_ad_a_a$24$(not in LMFDB)
6.2.a_a_a_j_a_ac$24$(not in LMFDB)
6.2.a_a_a_j_a_c$24$(not in LMFDB)
6.2.a_b_a_ab_a_ao$24$(not in LMFDB)
6.2.a_c_a_ad_a_ao$24$(not in LMFDB)
6.2.a_c_a_f_a_u$24$(not in LMFDB)
6.2.a_c_a_l_a_o$24$(not in LMFDB)
6.2.a_d_a_d_a_c$24$(not in LMFDB)
6.2.a_e_a_ad_a_abc$24$(not in LMFDB)
6.2.a_e_a_l_a_bc$24$(not in LMFDB)
6.2.a_e_a_r_a_bi$24$(not in LMFDB)
6.2.a_g_a_v_a_ca$24$(not in LMFDB)
6.2.b_c_d_f_i_u$24$(not in LMFDB)
6.2.b_e_f_l_q_bc$24$(not in LMFDB)
6.2.c_c_a_f_k_u$24$(not in LMFDB)
6.2.c_c_e_ad_ao_ao$24$(not in LMFDB)
6.2.c_e_e_ad_ao_abc$24$(not in LMFDB)
6.2.c_e_e_l_o_bc$24$(not in LMFDB)
6.2.c_g_i_v_ba_ca$24$(not in LMFDB)
6.2.d_a_aj_aj_g_u$24$(not in LMFDB)
6.2.d_c_ad_ah_ag_ae$24$(not in LMFDB)
6.2.d_c_ad_ab_m_ba$24$(not in LMFDB)
6.2.d_e_d_f_m_w$24$(not in LMFDB)
6.2.d_g_j_p_y_bm$24$(not in LMFDB)
6.2.d_i_p_x_be_bs$24$(not in LMFDB)
6.2.d_i_p_bd_bw_cw$24$(not in LMFDB)
6.2.d_k_v_bp_co_dw$24$(not in LMFDB)
6.2.e_i_i_ad_abc_ace$24$(not in LMFDB)
6.2.f_o_bb_bp_ca_cq$24$(not in LMFDB)
6.2.f_q_bl_ct_em_gq$24$(not in LMFDB)
6.2.g_r_be_bj_y_o$24$(not in LMFDB)
6.2.g_v_cc_eh_hk_le$24$(not in LMFDB)
6.2.ah_z_acn_fj_ajq_os$30$(not in LMFDB)
6.2.ag_o_an_ah_bm_aco$30$(not in LMFDB)
6.2.af_n_az_br_acs_ea$30$(not in LMFDB)
6.2.ad_i_aq_bd_abu_co$30$(not in LMFDB)
6.2.ab_b_af_h_ak_q$30$(not in LMFDB)
6.2.ab_e_ai_n_aw_bi$30$(not in LMFDB)
6.2.c_ac_al_al_o_bu$30$(not in LMFDB)
6.2.d_f_f_ab_ak_as$30$(not in LMFDB)
6.2.f_n_z_br_cs_ea$30$(not in LMFDB)
6.2.j_bp_ev_lb_uk_bfk$30$(not in LMFDB)
6.2.ag_q_av_b_ca_aee$40$(not in LMFDB)
6.2.ae_a_x_abh_abe_em$40$(not in LMFDB)
6.2.ae_i_aj_ab_ba_aca$40$(not in LMFDB)
6.2.ad_k_as_bl_aby_dg$40$(not in LMFDB)
6.2.ac_a_d_ad_a_e$40$(not in LMFDB)
6.2.ab_a_c_ad_a_ae$40$(not in LMFDB)
6.2.ab_g_ag_v_as_ca$40$(not in LMFDB)
6.2.ab_i_ag_bd_aq_cq$40$(not in LMFDB)
6.2.b_a_ac_ad_a_ae$40$(not in LMFDB)
6.2.b_g_g_v_s_ca$40$(not in LMFDB)
6.2.b_i_g_bd_q_cq$40$(not in LMFDB)
6.2.c_a_ad_ad_a_e$40$(not in LMFDB)
6.2.d_k_s_bl_by_dg$40$(not in LMFDB)
6.2.e_a_ax_abh_be_em$40$(not in LMFDB)
6.2.e_i_j_ab_aba_aca$40$(not in LMFDB)
6.2.g_q_v_b_aca_aee$40$(not in LMFDB)
6.2.ah_bb_acx_gj_alo_rs$120$(not in LMFDB)
6.2.af_j_af_aj_be_aca$120$(not in LMFDB)
6.2.af_l_ap_r_au_ba$120$(not in LMFDB)
6.2.af_p_abj_cr_aeq_ha$120$(not in LMFDB)
6.2.af_r_abt_dr_ago_ka$120$(not in LMFDB)
6.2.ae_c_p_az_aq_cw$120$(not in LMFDB)
6.2.ae_g_ab_aj_m_ak$120$(not in LMFDB)
6.2.ad_h_ap_z_abo_ci$120$(not in LMFDB)
6.2.ab_c_a_f_ae_o$120$(not in LMFDB)
6.2.ab_g_ae_v_am_by$120$(not in LMFDB)
6.2.b_c_a_f_e_o$120$(not in LMFDB)
6.2.b_g_e_v_m_by$120$(not in LMFDB)
6.2.d_h_p_z_bo_ci$120$(not in LMFDB)
6.2.e_c_ap_az_q_cw$120$(not in LMFDB)
6.2.e_g_b_aj_am_ak$120$(not in LMFDB)
6.2.f_j_f_aj_abe_aca$120$(not in LMFDB)
6.2.f_l_p_r_u_ba$120$(not in LMFDB)
6.2.f_p_bj_cr_eq_ha$120$(not in LMFDB)
6.2.f_r_bt_dr_go_ka$120$(not in LMFDB)
6.2.h_bb_cx_gj_lo_rs$120$(not in LMFDB)