Properties

Label 6.2.aj_br_afj_na_aza_bnc
Base Field $\F_{2}$
Dimension $6$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.174442860055$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.546783656212$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 28000 1906996 56000000 2671653644 93442804000 3287686987204 214570944000000 16150985219678764 1054301319263500000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 10 24 38 64 82 92 190 456 930

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 1.2.ab $\times$ 2.2.ac_d 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 $\F_{2^{4}}$ is 1.16.ab $\times$ 1.16.i 3 $\times$ 2.16.ac_b. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.
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_bb_acv_gc_ala_qy$2$(not in LMFDB)
6.2.af_p_abf_cc_ade_eq$2$(not in LMFDB)
6.2.af_p_abb_bi_aba_y$2$(not in LMFDB)
6.2.ad_h_an_ba_abm_ce$2$(not in LMFDB)
6.2.ad_h_aj_o_ao_y$2$(not in LMFDB)
6.2.ab_d_ad_k_ak_y$2$(not in LMFDB)
6.2.ab_d_b_g_ac_y$2$(not in LMFDB)
6.2.b_d_ab_g_c_y$2$(not in LMFDB)
6.2.b_d_d_k_k_y$2$(not in LMFDB)
6.2.d_h_j_o_o_y$2$(not in LMFDB)
6.2.d_h_n_ba_bm_ce$2$(not in LMFDB)
6.2.f_p_bb_bi_ba_y$2$(not in LMFDB)
6.2.f_p_bf_cc_de_eq$2$(not in LMFDB)
6.2.h_bb_cv_gc_la_qy$2$(not in LMFDB)
6.2.j_br_fj_na_za_bnc$2$(not in LMFDB)
6.2.ad_h_ah_c_q_abc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ah_bb_acv_gc_ala_qy$2$(not in LMFDB)
6.2.af_p_abf_cc_ade_eq$2$(not in LMFDB)
6.2.af_p_abb_bi_aba_y$2$(not in LMFDB)
6.2.ad_h_an_ba_abm_ce$2$(not in LMFDB)
6.2.ad_h_aj_o_ao_y$2$(not in LMFDB)
6.2.ab_d_ad_k_ak_y$2$(not in LMFDB)
6.2.ab_d_b_g_ac_y$2$(not in LMFDB)
6.2.b_d_ab_g_c_y$2$(not in LMFDB)
6.2.b_d_d_k_k_y$2$(not in LMFDB)
6.2.d_h_j_o_o_y$2$(not in LMFDB)
6.2.d_h_n_ba_bm_ce$2$(not in LMFDB)
6.2.f_p_bb_bi_ba_y$2$(not in LMFDB)
6.2.f_p_bf_cc_de_eq$2$(not in LMFDB)
6.2.h_bb_cv_gc_la_qy$2$(not in LMFDB)
6.2.j_br_fj_na_za_bnc$2$(not in LMFDB)
6.2.ad_h_ah_c_q_abc$3$(not in LMFDB)
6.2.ah_bb_acx_gk_als_sa$6$(not in LMFDB)
6.2.af_p_abl_da_afg_hw$6$(not in LMFDB)
6.2.ad_h_ap_ba_abo_ci$6$(not in LMFDB)
6.2.ad_h_al_o_aq_u$6$(not in LMFDB)
6.2.ab_d_aj_k_aq_bk$6$(not in LMFDB)
6.2.ab_d_af_g_ai_m$6$(not in LMFDB)
6.2.ab_d_ab_c_i_ae$6$(not in LMFDB)
6.2.b_d_b_c_ai_ae$6$(not in LMFDB)
6.2.b_d_f_g_i_m$6$(not in LMFDB)
6.2.b_d_j_k_q_bk$6$(not in LMFDB)
6.2.d_h_h_c_aq_abc$6$(not in LMFDB)
6.2.d_h_l_o_q_u$6$(not in LMFDB)
6.2.d_h_p_ba_bo_ci$6$(not in LMFDB)
6.2.f_p_bl_da_fg_hw$6$(not in LMFDB)
6.2.h_bb_cx_gk_ls_sa$6$(not in LMFDB)
6.2.ah_bd_adh_ho_aoc_vw$8$(not in LMFDB)
6.2.af_l_al_ag_bq_adc$8$(not in LMFDB)
6.2.af_r_abr_do_agg_jo$8$(not in LMFDB)
6.2.af_t_abz_ek_ahy_mi$8$(not in LMFDB)
6.2.ad_d_ab_ac_o_abg$8$(not in LMFDB)
6.2.ad_f_af_ae_w_abo$8$(not in LMFDB)
6.2.ad_j_ar_bg_abu_cu$8$(not in LMFDB)
6.2.ad_j_an_u_ao_y$8$(not in LMFDB)
6.2.ad_l_az_cc_adm_fo$8$(not in LMFDB)
6.2.ad_n_abd_cq_aek_hc$8$(not in LMFDB)
6.2.ab_ab_b_ac_c_a$8$(not in LMFDB)
6.2.ab_ab_f_ag_ag_q$8$(not in LMFDB)
6.2.ab_b_ad_ae_k_ai$8$(not in LMFDB)
6.2.ab_f_ah_q_as_bo$8$(not in LMFDB)
6.2.ab_f_ad_m_ac_y$8$(not in LMFDB)
6.2.ab_h_ah_w_aw_bw$8$(not in LMFDB)
6.2.ab_h_ad_s_c_bg$8$(not in LMFDB)
6.2.ab_j_al_bk_abu_dk$8$(not in LMFDB)
6.2.b_ab_af_ag_g_q$8$(not in LMFDB)
6.2.b_ab_ab_ac_ac_a$8$(not in LMFDB)
6.2.b_b_d_ae_ak_ai$8$(not in LMFDB)
6.2.b_f_d_m_c_y$8$(not in LMFDB)
6.2.b_f_h_q_s_bo$8$(not in LMFDB)
6.2.b_h_d_s_ac_bg$8$(not in LMFDB)
6.2.b_h_h_w_w_bw$8$(not in LMFDB)
6.2.b_j_l_bk_bu_dk$8$(not in LMFDB)
6.2.d_d_b_ac_ao_abg$8$(not in LMFDB)
6.2.d_f_f_ae_aw_abo$8$(not in LMFDB)
6.2.d_j_n_u_o_y$8$(not in LMFDB)
6.2.d_j_r_bg_bu_cu$8$(not in LMFDB)
6.2.d_l_z_cc_dm_fo$8$(not in LMFDB)
6.2.d_n_bd_cq_ek_hc$8$(not in LMFDB)
6.2.f_l_l_ag_abq_adc$8$(not in LMFDB)
6.2.f_r_br_do_gg_jo$8$(not in LMFDB)
6.2.f_t_bz_ek_hy_mi$8$(not in LMFDB)
6.2.h_bd_dh_ho_oc_vw$8$(not in LMFDB)
6.2.b_d_b_c_ai_ae$12$(not in LMFDB)
6.2.af_n_av_y_au_u$24$(not in LMFDB)
6.2.af_r_abt_ds_agq_ke$24$(not in LMFDB)
6.2.af_r_abp_dg_afo_im$24$(not in LMFDB)
6.2.ad_f_ah_m_am_m$24$(not in LMFDB)
6.2.ad_h_al_o_am_q$24$(not in LMFDB)
6.2.ad_j_ax_bs_acy_eq$24$(not in LMFDB)
6.2.ad_j_at_bo_acm_dw$24$(not in LMFDB)
6.2.ad_l_ax_by_adc_ey$24$(not in LMFDB)
6.2.ab_b_ab_e_ae_m$24$(not in LMFDB)
6.2.ab_b_d_a_ae_u$24$(not in LMFDB)
6.2.ab_d_af_g_ae_q$24$(not in LMFDB)
6.2.ab_f_af_i_am_i$24$(not in LMFDB)
6.2.ab_f_af_q_aq_bk$24$(not in LMFDB)
6.2.ab_f_ab_e_m_ai$24$(not in LMFDB)
6.2.ab_f_ab_m_a_bc$24$(not in LMFDB)
6.2.ab_h_aj_ba_abg_cm$24$(not in LMFDB)
6.2.b_b_ad_a_e_u$24$(not in LMFDB)
6.2.b_b_b_e_e_m$24$(not in LMFDB)
6.2.b_d_f_g_e_q$24$(not in LMFDB)
6.2.b_f_b_e_am_ai$24$(not in LMFDB)
6.2.b_f_b_m_a_bc$24$(not in LMFDB)
6.2.b_f_f_i_m_i$24$(not in LMFDB)
6.2.b_f_f_q_q_bk$24$(not in LMFDB)
6.2.b_h_j_ba_bg_cm$24$(not in LMFDB)
6.2.d_f_h_m_m_m$24$(not in LMFDB)
6.2.d_h_l_o_m_q$24$(not in LMFDB)
6.2.d_j_t_bo_cm_dw$24$(not in LMFDB)
6.2.d_j_x_bs_cy_eq$24$(not in LMFDB)
6.2.d_l_x_by_dc_ey$24$(not in LMFDB)
6.2.f_n_v_y_u_u$24$(not in LMFDB)
6.2.f_r_bp_dg_fo_im$24$(not in LMFDB)
6.2.f_r_bt_ds_gq_ke$24$(not in LMFDB)