Properties

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

Learn more about

Invariants

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

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 3 21375 1502748 24046875 2185691673 128484954000 4104434505363 179246007421875 14921014840996212 1306189834644234375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 10 21 26 54 103 120 146 417 1150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 1.2.a $\times$ 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 $\F_{2^{24}}$ is 1.16777216.amdc 4 $\times$ 1.16777216.mbf 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{24}}$.
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.af_p_abg_ce_adg_eq$2$(not in LMFDB)
6.2.ad_h_ai_i_e_ai$2$(not in LMFDB)
6.2.ab_d_ae_i_am_y$2$(not in LMFDB)
6.2.b_d_e_i_m_y$2$(not in LMFDB)
6.2.d_h_i_i_ae_ai$2$(not in LMFDB)
6.2.f_p_bg_ce_dg_eq$2$(not in LMFDB)
6.2.j_br_fk_ng_zs_boi$2$(not in LMFDB)
6.2.ag_t_abm_ce_acq_dk$3$(not in LMFDB)
6.2.ad_h_ai_c_q_abg$3$(not in LMFDB)
6.2.a_b_e_c_e_q$3$(not in LMFDB)
6.2.d_h_q_ba_bo_cm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_p_abg_ce_adg_eq$2$(not in LMFDB)
6.2.ad_h_ai_i_e_ai$2$(not in LMFDB)
6.2.ab_d_ae_i_am_y$2$(not in LMFDB)
6.2.b_d_e_i_m_y$2$(not in LMFDB)
6.2.d_h_i_i_ae_ai$2$(not in LMFDB)
6.2.f_p_bg_ce_dg_eq$2$(not in LMFDB)
6.2.j_br_fk_ng_zs_boi$2$(not in LMFDB)
6.2.ag_t_abm_ce_acq_dk$3$(not in LMFDB)
6.2.ad_h_ai_c_q_abg$3$(not in LMFDB)
6.2.a_b_e_c_e_q$3$(not in LMFDB)
6.2.d_h_q_ba_bo_cm$3$(not in LMFDB)
6.2.ah_bb_acy_go_ama_sm$6$(not in LMFDB)
6.2.ae_j_aq_ba_abk_bw$6$(not in LMFDB)
6.2.ad_h_aq_ba_abo_cm$6$(not in LMFDB)
6.2.ac_d_ac_i_am_y$6$(not in LMFDB)
6.2.ab_d_ae_c_a_a$6$(not in LMFDB)
6.2.a_b_ae_c_ae_q$6$(not in LMFDB)
6.2.b_d_e_c_a_a$6$(not in LMFDB)
6.2.c_d_c_i_m_y$6$(not in LMFDB)
6.2.d_h_i_c_aq_abg$6$(not in LMFDB)
6.2.e_j_q_ba_bk_bw$6$(not in LMFDB)
6.2.g_t_bm_ce_cq_dk$6$(not in LMFDB)
6.2.h_bb_cy_go_ma_sm$6$(not in LMFDB)
6.2.al_cj_aio_wq_abtw_cuy$8$(not in LMFDB)
6.2.ah_v_abe_a_dk_ahc$8$(not in LMFDB)
6.2.ah_z_acg_dw_afo_hs$8$(not in LMFDB)
6.2.ah_bd_adi_hs_aom_wm$8$(not in LMFDB)
6.2.af_l_am_ae_bs_adk$8$(not in LMFDB)
6.2.af_n_as_m_i_ay$8$(not in LMFDB)
6.2.af_t_aca_em_aie_mq$8$(not in LMFDB)
6.2.ad_ad_s_am_ay_ce$8$(not in LMFDB)
6.2.ad_b_g_ai_a_i$8$(not in LMFDB)
6.2.ad_f_ag_ae_y_abo$8$(not in LMFDB)
6.2.ad_f_ag_m_ay_bo$8$(not in LMFDB)
6.2.ad_j_as_bg_abw_cu$8$(not in LMFDB)
6.2.ad_n_abe_cq_aeq_hc$8$(not in LMFDB)
6.2.ab_ad_g_a_ai_i$8$(not in LMFDB)
6.2.ab_ab_a_ae_e_i$8$(not in LMFDB)
6.2.ab_b_c_e_a_i$8$(not in LMFDB)
6.2.ab_f_ac_i_i_i$8$(not in LMFDB)
6.2.ab_h_ai_u_abc_bo$8$(not in LMFDB)
6.2.b_ad_ag_a_i_i$8$(not in LMFDB)
6.2.b_ab_a_ae_ae_i$8$(not in LMFDB)
6.2.b_b_ac_e_a_i$8$(not in LMFDB)
6.2.b_f_c_i_ai_i$8$(not in LMFDB)
6.2.b_h_i_u_bc_bo$8$(not in LMFDB)
6.2.d_ad_as_am_y_ce$8$(not in LMFDB)
6.2.d_b_ag_ai_a_i$8$(not in LMFDB)
6.2.d_f_g_ae_ay_abo$8$(not in LMFDB)
6.2.d_f_g_m_y_bo$8$(not in LMFDB)
6.2.d_j_s_bg_bw_cu$8$(not in LMFDB)
6.2.d_n_be_cq_eq_hc$8$(not in LMFDB)
6.2.f_l_m_ae_abs_adk$8$(not in LMFDB)
6.2.f_n_s_m_ai_ay$8$(not in LMFDB)
6.2.f_t_ca_em_ie_mq$8$(not in LMFDB)
6.2.h_v_be_a_adk_ahc$8$(not in LMFDB)
6.2.h_z_cg_dw_fo_hs$8$(not in LMFDB)
6.2.h_bd_di_hs_om_wm$8$(not in LMFDB)
6.2.l_cj_io_wq_btw_cuy$8$(not in LMFDB)
6.2.ag_v_aby_ds_aga_iy$12$(not in LMFDB)
6.2.ae_l_ay_bu_acy_ei$12$(not in LMFDB)
6.2.ac_f_ag_q_au_bo$12$(not in LMFDB)
6.2.a_d_ae_g_am_q$12$(not in LMFDB)
6.2.a_d_e_g_m_q$12$(not in LMFDB)
6.2.c_f_g_q_u_bo$12$(not in LMFDB)
6.2.e_l_y_bu_cy_ei$12$(not in LMFDB)
6.2.g_v_by_ds_ga_iy$12$(not in LMFDB)
6.2.ad_f_ag_e_a_a$16$(not in LMFDB)
6.2.d_f_g_e_a_a$16$(not in LMFDB)
6.2.aj_bp_aew_li_avg_bgy$24$(not in LMFDB)
6.2.ai_bf_acu_ee_aei_eq$24$(not in LMFDB)
6.2.ai_bh_adk_gq_akm_pc$24$(not in LMFDB)
6.2.ah_x_abs_by_abc_i$24$(not in LMFDB)
6.2.ah_z_aco_fo_aka_pg$24$(not in LMFDB)
6.2.ah_bb_acu_fu_aka_pc$24$(not in LMFDB)
6.2.ag_r_abe_bq_aci_dk$24$(not in LMFDB)
6.2.ag_t_abq_da_afc_hs$24$(not in LMFDB)
6.2.af_j_ag_ag_bg_acm$24$(not in LMFDB)
6.2.af_l_aq_u_au_u$24$(not in LMFDB)
6.2.af_n_aba_bu_acu_ea$24$(not in LMFDB)
6.2.af_n_aw_ba_au_q$24$(not in LMFDB)
6.2.af_n_as_g_bg_acu$24$(not in LMFDB)
6.2.af_p_abk_cu_aeu_hg$24$(not in LMFDB)
6.2.af_r_abu_du_agu_km$24$(not in LMFDB)
6.2.af_r_abq_di_afs_iq$24$(not in LMFDB)
6.2.ae_d_m_ay_ai_ce$24$(not in LMFDB)
6.2.ae_f_e_aq_i_i$24$(not in LMFDB)
6.2.ae_f_e_ak_aq_ce$24$(not in LMFDB)
6.2.ae_h_am_y_abg_bk$24$(not in LMFDB)
6.2.ae_h_ae_c_aq_bo$24$(not in LMFDB)
6.2.ae_h_ae_e_ay_ce$24$(not in LMFDB)
6.2.ae_j_au_bo_acm_do$24$(not in LMFDB)
6.2.ae_j_am_s_abg_ce$24$(not in LMFDB)
6.2.ae_j_am_u_abo_cu$24$(not in LMFDB)
6.2.ae_l_au_bg_abo_ce$24$(not in LMFDB)
6.2.ae_l_au_bm_acm_ea$24$(not in LMFDB)
6.2.ae_n_abc_ce_adk_fg$24$(not in LMFDB)
6.2.ad_ab_m_ak_am_bg$24$(not in LMFDB)
6.2.ad_b_g_ae_am_bc$24$(not in LMFDB)
6.2.ad_d_a_ag_m_aq$24$(not in LMFDB)
6.2.ad_d_a_c_am_y$24$(not in LMFDB)
6.2.ad_f_ag_a_m_au$24$(not in LMFDB)
6.2.ad_f_ag_g_a_ai$24$(not in LMFDB)
6.2.ad_f_ag_i_am_u$24$(not in LMFDB)
6.2.ad_h_am_o_am_q$24$(not in LMFDB)
6.2.ad_h_am_w_abk_ce$24$(not in LMFDB)
6.2.ad_j_as_bk_aci_do$24$(not in LMFDB)
6.2.ad_l_ay_by_adg_ey$24$(not in LMFDB)
6.2.ac_ad_g_g_ae_aq$24$(not in LMFDB)
6.2.ac_ab_c_c_e_aq$24$(not in LMFDB)
6.2.ac_ab_c_i_ai_ae$24$(not in LMFDB)
6.2.ac_ab_g_ae_ae_i$24$(not in LMFDB)
6.2.ac_b_ac_i_ai_e$24$(not in LMFDB)
6.2.ac_b_ac_k_am_i$24$(not in LMFDB)
6.2.ac_b_c_ae_e_ai$24$(not in LMFDB)
6.2.ac_b_c_c_ai_q$24$(not in LMFDB)
6.2.ac_b_g_ag_ae_y$24$(not in LMFDB)
6.2.ac_d_ag_m_aq_u$24$(not in LMFDB)
6.2.ac_d_ag_o_au_y$24$(not in LMFDB)
6.2.ac_d_ac_g_ai_q$24$(not in LMFDB)
6.2.ac_d_c_ac_e_i$24$(not in LMFDB)
6.2.ac_f_ak_o_au_bg$24$(not in LMFDB)
6.2.ac_f_ak_u_abg_bs$24$(not in LMFDB)
6.2.ac_f_ag_o_aq_bg$24$(not in LMFDB)
6.2.ac_h_ao_ba_abs_cm$24$(not in LMFDB)
6.2.ac_h_ak_u_au_bo$24$(not in LMFDB)
6.2.ac_h_ak_ba_abg_cm$24$(not in LMFDB)
6.2.ac_j_ao_bk_abs_dk$24$(not in LMFDB)
6.2.ab_ad_g_ag_ai_bg$24$(not in LMFDB)
6.2.ab_ab_e_ae_ae_u$24$(not in LMFDB)
6.2.ab_ab_e_c_ae_i$24$(not in LMFDB)
6.2.ab_b_ag_a_e_m$24$(not in LMFDB)
6.2.ab_b_ag_g_ai_y$24$(not in LMFDB)
6.2.ab_b_ac_c_ae_q$24$(not in LMFDB)
6.2.ab_b_c_ac_a_i$24$(not in LMFDB)
6.2.ab_d_a_a_e_ae$24$(not in LMFDB)
6.2.ab_d_a_g_e_i$24$(not in LMFDB)
6.2.ab_f_ag_o_au_bg$24$(not in LMFDB)
6.2.ab_f_ac_c_i_aq$24$(not in LMFDB)
6.2.a_aj_a_bk_a_adk$24$(not in LMFDB)
6.2.a_ah_a_u_a_abo$24$(not in LMFDB)
6.2.a_ah_a_ba_a_acm$24$(not in LMFDB)
6.2.a_af_a_o_a_abg$24$(not in LMFDB)
6.2.a_af_a_q_a_abo$24$(not in LMFDB)
6.2.a_af_a_u_a_abs$24$(not in LMFDB)
6.2.a_ad_a_g_a_aq$24$(not in LMFDB)
6.2.a_ad_a_i_a_ay$24$(not in LMFDB)
6.2.a_ad_a_m_a_au$24$(not in LMFDB)
6.2.a_ad_a_o_a_ay$24$(not in LMFDB)
6.2.a_ab_a_ae_a_i$24$(not in LMFDB)
6.2.a_ab_a_a_a_e$24$(not in LMFDB)
6.2.a_ab_a_c_a_aq$24$(not in LMFDB)
6.2.a_ab_a_i_a_ae$24$(not in LMFDB)
6.2.a_ab_a_k_a_ai$24$(not in LMFDB)
6.2.a_ab_a_m_a_ai$24$(not in LMFDB)
6.2.a_b_a_ae_a_ai$24$(not in LMFDB)
6.2.a_b_a_a_a_ae$24$(not in LMFDB)
6.2.a_b_a_c_a_q$24$(not in LMFDB)
6.2.a_b_a_i_a_e$24$(not in LMFDB)
6.2.a_b_a_k_a_i$24$(not in LMFDB)
6.2.a_b_a_m_a_i$24$(not in LMFDB)
6.2.a_d_a_g_a_q$24$(not in LMFDB)
6.2.a_d_a_i_a_y$24$(not in LMFDB)
6.2.a_d_a_m_a_u$24$(not in LMFDB)
6.2.a_d_a_o_a_y$24$(not in LMFDB)
6.2.a_f_a_o_a_bg$24$(not in LMFDB)
6.2.a_f_a_q_a_bo$24$(not in LMFDB)
6.2.a_f_a_u_a_bs$24$(not in LMFDB)
6.2.a_h_a_u_a_bo$24$(not in LMFDB)
6.2.a_h_a_ba_a_cm$24$(not in LMFDB)
6.2.a_j_a_bk_a_dk$24$(not in LMFDB)
6.2.b_ad_ag_ag_i_bg$24$(not in LMFDB)
6.2.b_ab_ae_ae_e_u$24$(not in LMFDB)
6.2.b_ab_ae_c_e_i$24$(not in LMFDB)
6.2.b_b_ac_ac_a_i$24$(not in LMFDB)
6.2.b_b_c_c_e_q$24$(not in LMFDB)
6.2.b_b_g_a_ae_m$24$(not in LMFDB)
6.2.b_b_g_g_i_y$24$(not in LMFDB)
6.2.b_d_a_a_ae_ae$24$(not in LMFDB)
6.2.b_d_a_g_ae_i$24$(not in LMFDB)
6.2.b_f_c_c_ai_aq$24$(not in LMFDB)
6.2.b_f_g_o_u_bg$24$(not in LMFDB)
6.2.c_ad_ag_g_e_aq$24$(not in LMFDB)
6.2.c_ab_ag_ae_e_i$24$(not in LMFDB)
6.2.c_ab_ac_c_ae_aq$24$(not in LMFDB)
6.2.c_ab_ac_i_i_ae$24$(not in LMFDB)
6.2.c_b_ag_ag_e_y$24$(not in LMFDB)
6.2.c_b_ac_ae_ae_ai$24$(not in LMFDB)
6.2.c_b_ac_c_i_q$24$(not in LMFDB)
6.2.c_b_c_i_i_e$24$(not in LMFDB)
6.2.c_b_c_k_m_i$24$(not in LMFDB)
6.2.c_d_ac_ac_ae_i$24$(not in LMFDB)
6.2.c_d_c_g_i_q$24$(not in LMFDB)
6.2.c_d_g_m_q_u$24$(not in LMFDB)
6.2.c_d_g_o_u_y$24$(not in LMFDB)
6.2.c_f_g_o_q_bg$24$(not in LMFDB)
6.2.c_f_k_o_u_bg$24$(not in LMFDB)
6.2.c_f_k_u_bg_bs$24$(not in LMFDB)
6.2.c_h_k_u_u_bo$24$(not in LMFDB)
6.2.c_h_k_ba_bg_cm$24$(not in LMFDB)
6.2.c_h_o_ba_bs_cm$24$(not in LMFDB)
6.2.c_j_o_bk_bs_dk$24$(not in LMFDB)
6.2.d_ab_am_ak_m_bg$24$(not in LMFDB)
6.2.d_b_ag_ae_m_bc$24$(not in LMFDB)
6.2.d_d_a_ag_am_aq$24$(not in LMFDB)
6.2.d_d_a_c_m_y$24$(not in LMFDB)
6.2.d_f_g_a_am_au$24$(not in LMFDB)
6.2.d_f_g_g_a_ai$24$(not in LMFDB)
6.2.d_f_g_i_m_u$24$(not in LMFDB)
6.2.d_h_m_o_m_q$24$(not in LMFDB)
6.2.d_h_m_w_bk_ce$24$(not in LMFDB)
6.2.d_j_s_bk_ci_do$24$(not in LMFDB)
6.2.d_l_y_by_dg_ey$24$(not in LMFDB)
6.2.e_d_am_ay_i_ce$24$(not in LMFDB)
6.2.e_f_ae_aq_ai_i$24$(not in LMFDB)
6.2.e_f_ae_ak_q_ce$24$(not in LMFDB)
6.2.e_h_e_c_q_bo$24$(not in LMFDB)
6.2.e_h_e_e_y_ce$24$(not in LMFDB)
6.2.e_h_m_y_bg_bk$24$(not in LMFDB)
6.2.e_j_m_s_bg_ce$24$(not in LMFDB)
6.2.e_j_m_u_bo_cu$24$(not in LMFDB)
6.2.e_j_u_bo_cm_do$24$(not in LMFDB)
6.2.e_l_u_bg_bo_ce$24$(not in LMFDB)
6.2.e_l_u_bm_cm_ea$24$(not in LMFDB)
6.2.e_n_bc_ce_dk_fg$24$(not in LMFDB)
6.2.f_j_g_ag_abg_acm$24$(not in LMFDB)
6.2.f_l_q_u_u_u$24$(not in LMFDB)
6.2.f_n_s_g_abg_acu$24$(not in LMFDB)
6.2.f_n_w_ba_u_q$24$(not in LMFDB)
6.2.f_n_ba_bu_cu_ea$24$(not in LMFDB)
6.2.f_p_bk_cu_eu_hg$24$(not in LMFDB)
6.2.f_r_bq_di_fs_iq$24$(not in LMFDB)
6.2.f_r_bu_du_gu_km$24$(not in LMFDB)
6.2.g_r_be_bq_ci_dk$24$(not in LMFDB)
6.2.g_t_bq_da_fc_hs$24$(not in LMFDB)
6.2.h_x_bs_by_bc_i$24$(not in LMFDB)
6.2.h_z_co_fo_ka_pg$24$(not in LMFDB)
6.2.h_bb_cu_fu_ka_pc$24$(not in LMFDB)
6.2.i_bf_cu_ee_ei_eq$24$(not in LMFDB)
6.2.i_bh_dk_gq_km_pc$24$(not in LMFDB)
6.2.j_bp_ew_li_vg_bgy$24$(not in LMFDB)
6.2.af_n_aw_w_ai_ae$40$(not in LMFDB)
6.2.ad_d_a_ac_a_e$40$(not in LMFDB)
6.2.ad_h_am_s_ay_bk$40$(not in LMFDB)
6.2.ab_b_ac_ac_i_ae$40$(not in LMFDB)
6.2.b_b_c_ac_ai_ae$40$(not in LMFDB)
6.2.d_d_a_ac_a_e$40$(not in LMFDB)
6.2.d_h_m_s_y_bk$40$(not in LMFDB)
6.2.f_n_w_w_i_ae$40$(not in LMFDB)
6.2.a_ab_a_e_a_a$48$(not in LMFDB)
6.2.a_b_a_e_a_a$48$(not in LMFDB)
6.2.ac_b_c_ac_ai_u$120$(not in LMFDB)
6.2.ac_d_ac_c_ai_m$120$(not in LMFDB)
6.2.a_ad_a_k_a_au$120$(not in LMFDB)
6.2.a_ab_a_g_a_am$120$(not in LMFDB)
6.2.a_b_a_g_a_m$120$(not in LMFDB)
6.2.a_d_a_k_a_u$120$(not in LMFDB)
6.2.c_b_ac_ac_i_u$120$(not in LMFDB)
6.2.c_d_c_c_i_m$120$(not in LMFDB)