Properties

Label 6.2.aj_bq_afe_mm_axz_blm
Base Field $\F_{2}$
Dimension $6$
Ordinary No
$p$-rank $5$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0435981566527$, $\pm0.123548644961$, $\pm0.250000000000$, $\pm0.329312442367$, $\pm0.456881978294$, $\pm0.527830414776$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $5$
Slopes:  $[0, 0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1, 1]$

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 6745 415948 8802225 1009493021 78555939280 3889382899648 239540520733425 19039292470243084 1310431950759963475

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 8 12 8 29 74 113 216 543 1153

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac $\times$ 2.2.ad_f $\times$ 3.2.ae_j_ap 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 $\F_{2^{84}}$ is 1.19342813113834066795298816.auojdvfkpl 3 $\times$ 1.19342813113834066795298816.aptgzwqopl 2 $\times$ 1.19342813113834066795298816.bqdecdesiy. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{84}}$.
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_o_abe_ca_adb_ek$2$(not in LMFDB)
6.2.ad_g_ai_g_b_ak$2$(not in LMFDB)
6.2.ab_c_a_ac_h_ag$2$(not in LMFDB)
6.2.b_c_a_ac_ah_ag$2$(not in LMFDB)
6.2.d_g_i_g_ab_ak$2$(not in LMFDB)
6.2.f_o_be_ca_db_ek$2$(not in LMFDB)
6.2.j_bq_fe_mm_xz_blm$2$(not in LMFDB)
6.2.ag_s_abj_bz_acn_di$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_o_abe_ca_adb_ek$2$(not in LMFDB)
6.2.ad_g_ai_g_b_ak$2$(not in LMFDB)
6.2.ab_c_a_ac_h_ag$2$(not in LMFDB)
6.2.b_c_a_ac_ah_ag$2$(not in LMFDB)
6.2.d_g_i_g_ab_ak$2$(not in LMFDB)
6.2.f_o_be_ca_db_ek$2$(not in LMFDB)
6.2.j_bq_fe_mm_xz_blm$2$(not in LMFDB)
6.2.ag_s_abj_bz_acn_di$3$(not in LMFDB)
6.2.ac_c_ad_h_an_s$6$(not in LMFDB)
6.2.c_c_d_h_n_s$6$(not in LMFDB)
6.2.g_s_bj_bz_cn_di$6$(not in LMFDB)
6.2.ac_a_g_af_ah_w$7$(not in LMFDB)
6.2.ac_h_ap_be_abx_da$7$(not in LMFDB)
6.2.ah_bc_ade_hg_ann_uy$8$(not in LMFDB)
6.2.ab_e_ae_c_ad_ai$8$(not in LMFDB)
6.2.b_e_e_c_d_ai$8$(not in LMFDB)
6.2.h_bc_de_hg_nn_uy$8$(not in LMFDB)
6.2.ag_u_abv_dl_afr_ik$12$(not in LMFDB)
6.2.ac_e_ah_n_ax_be$12$(not in LMFDB)
6.2.c_e_h_n_x_be$12$(not in LMFDB)
6.2.g_u_bv_dl_fr_ik$12$(not in LMFDB)
6.2.ai_be_acs_en_agf_ik$14$(not in LMFDB)
6.2.ai_bl_aep_lg_avv_big$14$(not in LMFDB)
6.2.ag_x_acl_fi_ajp_os$14$(not in LMFDB)
6.2.ae_g_ag_n_abd_bu$14$(not in LMFDB)
6.2.ae_n_abf_cm_aeh_go$14$(not in LMFDB)
6.2.ae_n_abb_bw_act_dy$14$(not in LMFDB)
6.2.ac_a_c_d_af_c$14$(not in LMFDB)
6.2.ac_h_al_w_abh_by$14$(not in LMFDB)
6.2.ac_h_af_k_j_c$14$(not in LMFDB)
6.2.a_f_ad_m_ap_w$14$(not in LMFDB)
6.2.a_f_d_m_p_w$14$(not in LMFDB)
6.2.c_a_ag_af_h_w$14$(not in LMFDB)
6.2.c_a_ac_d_f_c$14$(not in LMFDB)
6.2.c_h_f_k_aj_c$14$(not in LMFDB)
6.2.c_h_l_w_bh_by$14$(not in LMFDB)
6.2.c_h_p_be_bx_da$14$(not in LMFDB)
6.2.e_g_g_n_bd_bu$14$(not in LMFDB)
6.2.e_n_bb_bw_ct_dy$14$(not in LMFDB)
6.2.e_n_bf_cm_eh_go$14$(not in LMFDB)
6.2.g_x_cl_fi_jp_os$14$(not in LMFDB)
6.2.i_be_cs_en_gf_ik$14$(not in LMFDB)
6.2.i_bl_ep_lg_vv_big$14$(not in LMFDB)
6.2.af_n_abb_bz_adh_ew$21$(not in LMFDB)
6.2.ac_b_ad_m_an_g$21$(not in LMFDB)
6.2.b_ad_a_q_f_aba$21$(not in LMFDB)
6.2.b_b_ad_ad_ab_g$21$(not in LMFDB)
6.2.b_e_a_j_f_be$21$(not in LMFDB)
6.2.ae_k_at_bd_abn_ca$24$(not in LMFDB)
6.2.ae_m_abb_bz_adh_eu$24$(not in LMFDB)
6.2.e_k_t_bd_bn_ca$24$(not in LMFDB)
6.2.e_m_bb_bz_dh_eu$24$(not in LMFDB)
6.2.ag_r_abb_s_v_ack$28$(not in LMFDB)
6.2.ae_h_ah_e_d_ak$28$(not in LMFDB)
6.2.ac_b_b_ac_ad_o$28$(not in LMFDB)
6.2.a_ab_ad_a_d_k$28$(not in LMFDB)
6.2.a_ab_d_a_ad_k$28$(not in LMFDB)
6.2.c_b_ab_ac_d_o$28$(not in LMFDB)
6.2.e_h_h_e_ad_ak$28$(not in LMFDB)
6.2.g_r_bb_s_av_ack$28$(not in LMFDB)
6.2.ah_z_acj_el_ahb_kg$42$(not in LMFDB)
6.2.af_j_ae_a_abd_cw$42$(not in LMFDB)
6.2.af_n_ar_b_bt_adq$42$(not in LMFDB)
6.2.af_q_abg_bx_acf_cw$42$(not in LMFDB)
6.2.ae_h_ah_k_abb_by$42$(not in LMFDB)
6.2.ad_f_aj_p_abb_bu$42$(not in LMFDB)
6.2.ad_f_ad_ad_p_aba$42$(not in LMFDB)
6.2.ad_i_am_v_abb_bu$42$(not in LMFDB)
6.2.ac_b_h_ai_ad_ba$42$(not in LMFDB)
6.2.ab_ad_a_q_af_aba$42$(not in LMFDB)
6.2.ab_b_ah_h_aj_ba$42$(not in LMFDB)
6.2.ab_b_ab_b_ad_c$42$(not in LMFDB)
6.2.ab_b_d_ad_b_g$42$(not in LMFDB)
6.2.ab_e_ae_n_aj_ba$42$(not in LMFDB)
6.2.ab_e_a_j_af_be$42$(not in LMFDB)
6.2.a_ab_ad_g_ad_ac$42$(not in LMFDB)
6.2.a_ab_d_g_d_ac$42$(not in LMFDB)
6.2.b_b_b_b_d_c$42$(not in LMFDB)
6.2.b_b_h_h_j_ba$42$(not in LMFDB)
6.2.b_e_e_n_j_ba$42$(not in LMFDB)
6.2.c_b_ah_ai_d_ba$42$(not in LMFDB)
6.2.c_b_d_m_n_g$42$(not in LMFDB)
6.2.d_f_d_ad_ap_aba$42$(not in LMFDB)
6.2.d_f_j_p_bb_bu$42$(not in LMFDB)
6.2.d_i_m_v_bb_bu$42$(not in LMFDB)
6.2.e_h_h_k_bb_by$42$(not in LMFDB)
6.2.f_j_e_a_bd_cw$42$(not in LMFDB)
6.2.f_n_r_b_abt_adq$42$(not in LMFDB)
6.2.f_n_bb_bz_dh_ew$42$(not in LMFDB)
6.2.f_q_bg_bx_cf_cw$42$(not in LMFDB)
6.2.h_z_cj_el_hb_kg$42$(not in LMFDB)
6.2.ag_s_abm_cn_adr_fc$56$(not in LMFDB)
6.2.ag_z_acv_go_amh_tc$56$(not in LMFDB)
6.2.ae_j_an_i_j_ay$56$(not in LMFDB)
6.2.ae_p_abl_dc_afl_ii$56$(not in LMFDB)
6.2.ac_d_af_c_d_a$56$(not in LMFDB)
6.2.ac_j_ar_bm_acl_ds$56$(not in LMFDB)
6.2.a_a_ac_ab_b_m$56$(not in LMFDB)
6.2.a_a_c_ab_ab_m$56$(not in LMFDB)
6.2.a_h_af_u_abd_bo$56$(not in LMFDB)
6.2.a_h_f_u_bd_bo$56$(not in LMFDB)
6.2.c_d_f_c_ad_a$56$(not in LMFDB)
6.2.c_j_r_bm_cl_ds$56$(not in LMFDB)
6.2.e_j_n_i_aj_ay$56$(not in LMFDB)
6.2.e_p_bl_dc_fl_ii$56$(not in LMFDB)
6.2.g_s_bm_cn_dr_fc$56$(not in LMFDB)
6.2.g_z_cv_go_mh_tc$56$(not in LMFDB)
6.2.af_l_ao_u_abv_di$84$(not in LMFDB)
6.2.af_s_abq_df_afb_hq$84$(not in LMFDB)
6.2.ae_j_ap_ba_abx_da$84$(not in LMFDB)
6.2.ad_c_g_aj_aj_bi$84$(not in LMFDB)
6.2.ad_e_a_ad_ad_o$84$(not in LMFDB)
6.2.ad_k_as_bn_acf_du$84$(not in LMFDB)
6.2.ac_d_ah_q_ax_ba$84$(not in LMFDB)
6.2.ac_d_d_ae_h_g$84$(not in LMFDB)
6.2.ab_ac_c_h_ad_ak$84$(not in LMFDB)
6.2.ab_ab_ac_m_ah_ag$84$(not in LMFDB)
6.2.ab_a_a_f_ab_ag$84$(not in LMFDB)
6.2.ab_g_ag_x_at_cc$84$(not in LMFDB)
6.2.ab_g_ac_t_ah_by$84$(not in LMFDB)
6.2.a_b_ad_g_aj_c$84$(not in LMFDB)
6.2.a_b_d_g_j_c$84$(not in LMFDB)
6.2.b_ac_ac_h_d_ak$84$(not in LMFDB)
6.2.b_ab_c_m_h_ag$84$(not in LMFDB)
6.2.b_a_a_f_b_ag$84$(not in LMFDB)
6.2.b_g_c_t_h_by$84$(not in LMFDB)
6.2.b_g_g_x_t_cc$84$(not in LMFDB)
6.2.c_d_ad_ae_ah_g$84$(not in LMFDB)
6.2.c_d_h_q_x_ba$84$(not in LMFDB)
6.2.d_c_ag_aj_j_bi$84$(not in LMFDB)
6.2.d_e_a_ad_d_o$84$(not in LMFDB)
6.2.d_k_s_bn_cf_du$84$(not in LMFDB)
6.2.e_j_p_ba_bx_da$84$(not in LMFDB)
6.2.f_l_o_u_bv_di$84$(not in LMFDB)
6.2.f_s_bq_df_fb_hq$84$(not in LMFDB)
6.2.af_p_abj_cn_aeb_ga$168$(not in LMFDB)
6.2.ad_d_ac_i_ar_y$168$(not in LMFDB)
6.2.ad_f_ai_q_abb_bo$168$(not in LMFDB)
6.2.ad_h_ar_bd_abv_cy$168$(not in LMFDB)
6.2.ad_h_ah_ab_x_abs$168$(not in LMFDB)
6.2.ad_k_aq_bd_abf_ca$168$(not in LMFDB)
6.2.ad_m_aw_bz_acr_eu$168$(not in LMFDB)
6.2.ac_d_af_i_ap_y$168$(not in LMFDB)
6.2.ac_f_aj_q_abd_bo$168$(not in LMFDB)
6.2.ab_a_c_ab_ad_m$168$(not in LMFDB)
6.2.ab_c_a_b_ab_e$168$(not in LMFDB)
6.2.ab_d_ab_ab_j_am$168$(not in LMFDB)
6.2.ab_g_ae_r_aj_bk$168$(not in LMFDB)
6.2.ab_i_ag_bf_at_cy$168$(not in LMFDB)
6.2.a_b_af_c_af_q$168$(not in LMFDB)
6.2.a_b_f_c_f_q$168$(not in LMFDB)
6.2.a_d_af_g_ap_q$168$(not in LMFDB)
6.2.a_d_f_g_p_q$168$(not in LMFDB)
6.2.b_a_ac_ab_d_m$168$(not in LMFDB)
6.2.b_c_a_b_b_e$168$(not in LMFDB)
6.2.b_d_b_ab_aj_am$168$(not in LMFDB)
6.2.b_g_e_r_j_bk$168$(not in LMFDB)
6.2.b_i_g_bf_t_cy$168$(not in LMFDB)
6.2.c_d_f_i_p_y$168$(not in LMFDB)
6.2.c_f_j_q_bd_bo$168$(not in LMFDB)
6.2.d_d_c_i_r_y$168$(not in LMFDB)
6.2.d_f_i_q_bb_bo$168$(not in LMFDB)
6.2.d_h_h_ab_ax_abs$168$(not in LMFDB)
6.2.d_h_r_bd_bv_cy$168$(not in LMFDB)
6.2.d_k_q_bd_bf_ca$168$(not in LMFDB)
6.2.d_m_w_bz_cr_eu$168$(not in LMFDB)
6.2.f_p_bj_cn_eb_ga$168$(not in LMFDB)