Properties

Label 6.2.ak_bz_agq_qm_abga_bye
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:  $( 1 - 2 x + 2 x^{2} )^{4}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.174442860055$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.546783656212$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 2 17500 1770782 87500000 4978990882 108460397500 2616257954606 167633550000000 14997343418273138 1116383111823437500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 7 23 47 83 91 63 127 419 987

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 4 $\times$ 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.i 4 $\times$ 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.ag_t_abo_cq_aea_fw$2$(not in LMFDB)
6.2.ag_t_abk_bs_abg_y$2$(not in LMFDB)
6.2.ac_d_ae_m_aq_y$2$(not in LMFDB)
6.2.ac_d_a_e_ai_y$2$(not in LMFDB)
6.2.c_d_a_e_i_y$2$(not in LMFDB)
6.2.c_d_e_m_q_y$2$(not in LMFDB)
6.2.g_t_bk_bs_bg_y$2$(not in LMFDB)
6.2.g_t_bo_cq_ea_fw$2$(not in LMFDB)
6.2.k_bz_gq_qm_bga_bye$2$(not in LMFDB)
6.2.ae_j_ak_c_u_abo$3$(not in LMFDB)
6.2.c_d_i_i_i_u$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ag_t_abo_cq_aea_fw$2$(not in LMFDB)
6.2.ag_t_abk_bs_abg_y$2$(not in LMFDB)
6.2.ac_d_ae_m_aq_y$2$(not in LMFDB)
6.2.ac_d_a_e_ai_y$2$(not in LMFDB)
6.2.c_d_a_e_i_y$2$(not in LMFDB)
6.2.c_d_e_m_q_y$2$(not in LMFDB)
6.2.g_t_bk_bs_bg_y$2$(not in LMFDB)
6.2.g_t_bo_cq_ea_fw$2$(not in LMFDB)
6.2.k_bz_gq_qm_bga_bye$2$(not in LMFDB)
6.2.ae_j_ak_c_u_abo$3$(not in LMFDB)
6.2.c_d_i_i_i_u$3$(not in LMFDB)
6.2.a_b_ac_ac_i_e$5$(not in LMFDB)
6.2.ai_bh_adq_ic_aoy_xc$6$(not in LMFDB)
6.2.ag_t_abw_ea_ahc_kq$6$(not in LMFDB)
6.2.ae_j_as_bi_aca_cu$6$(not in LMFDB)
6.2.ae_j_ao_s_au_y$6$(not in LMFDB)
6.2.ac_d_ai_i_ai_u$6$(not in LMFDB)
6.2.ac_d_ae_a_i_am$6$(not in LMFDB)
6.2.a_b_ag_c_ae_y$6$(not in LMFDB)
6.2.a_b_ac_c_ae_i$6$(not in LMFDB)
6.2.a_b_c_c_e_i$6$(not in LMFDB)
6.2.a_b_g_c_e_y$6$(not in LMFDB)
6.2.c_d_e_a_ai_am$6$(not in LMFDB)
6.2.e_j_k_c_au_abo$6$(not in LMFDB)
6.2.e_j_o_s_u_y$6$(not in LMFDB)
6.2.e_j_s_bi_ca_cu$6$(not in LMFDB)
6.2.g_t_bw_ea_hc_kq$6$(not in LMFDB)
6.2.i_bh_dq_ic_oy_xc$6$(not in LMFDB)
6.2.ai_bj_aec_jo_asa_bca$8$(not in LMFDB)
6.2.ag_p_aq_ai_ce_aea$8$(not in LMFDB)
6.2.ag_x_acm_fo_ake_ps$8$(not in LMFDB)
6.2.ae_h_ag_ae_bc_ace$8$(not in LMFDB)
6.2.ae_l_aw_bo_aci_dk$8$(not in LMFDB)
6.2.ae_l_as_y_au_y$8$(not in LMFDB)
6.2.ae_p_abm_dg_afs_iy$8$(not in LMFDB)
6.2.ac_af_m_e_aq_i$8$(not in LMFDB)
6.2.ac_ab_e_a_a_ai$8$(not in LMFDB)
6.2.ac_ab_i_ai_ai_y$8$(not in LMFDB)
6.2.ac_d_ae_ae_q_ay$8$(not in LMFDB)
6.2.ac_h_am_y_abg_ce$8$(not in LMFDB)
6.2.ac_h_ai_q_ai_y$8$(not in LMFDB)
6.2.ac_l_au_ca_adc_fg$8$(not in LMFDB)
6.2.a_ab_ac_ae_e_i$8$(not in LMFDB)
6.2.a_ab_c_ae_ae_i$8$(not in LMFDB)
6.2.a_d_ac_i_ae_y$8$(not in LMFDB)
6.2.a_d_c_i_e_y$8$(not in LMFDB)
6.2.a_h_ac_u_am_bo$8$(not in LMFDB)
6.2.a_h_c_u_m_bo$8$(not in LMFDB)
6.2.c_af_am_e_q_i$8$(not in LMFDB)
6.2.c_ab_ai_ai_i_y$8$(not in LMFDB)
6.2.c_ab_ae_a_a_ai$8$(not in LMFDB)
6.2.c_d_e_ae_aq_ay$8$(not in LMFDB)
6.2.c_h_i_q_i_y$8$(not in LMFDB)
6.2.c_h_m_y_bg_ce$8$(not in LMFDB)
6.2.c_l_u_ca_dc_fg$8$(not in LMFDB)
6.2.e_h_g_ae_abc_ace$8$(not in LMFDB)
6.2.e_l_s_y_u_y$8$(not in LMFDB)
6.2.e_l_w_bo_ci_dk$8$(not in LMFDB)
6.2.e_p_bm_dg_fs_iy$8$(not in LMFDB)
6.2.g_p_q_ai_ace_aea$8$(not in LMFDB)
6.2.g_x_cm_fo_ke_ps$8$(not in LMFDB)
6.2.i_bj_ec_jo_sa_bca$8$(not in LMFDB)
6.2.ae_j_ao_o_ai_e$10$(not in LMFDB)
6.2.a_b_c_ac_ai_e$10$(not in LMFDB)
6.2.e_j_o_o_i_e$10$(not in LMFDB)
6.2.ac_d_ae_e_a_a$16$(not in LMFDB)
6.2.c_d_e_e_a_a$16$(not in LMFDB)
6.2.ag_r_abc_be_ay_y$24$(not in LMFDB)
6.2.ag_v_ace_es_aim_my$24$(not in LMFDB)
6.2.ag_v_aca_ec_ahc_ku$24$(not in LMFDB)
6.2.ae_f_ac_ac_u_abw$24$(not in LMFDB)
6.2.ae_h_ak_q_aq_m$24$(not in LMFDB)
6.2.ae_j_ao_s_aq_q$24$(not in LMFDB)
6.2.ae_l_aba_ca_adk_fc$24$(not in LMFDB)
6.2.ae_n_abi_cs_aeu_hk$24$(not in LMFDB)
6.2.ae_n_abe_ck_aea_ge$24$(not in LMFDB)
6.2.ac_ad_i_c_ai_a$24$(not in LMFDB)
6.2.ac_ab_e_e_ai_e$24$(not in LMFDB)
6.2.ac_b_a_ac_i_aq$24$(not in LMFDB)
6.2.ac_b_a_g_ai_i$24$(not in LMFDB)
6.2.ac_b_e_ac_ai_y$24$(not in LMFDB)
6.2.ac_d_ae_i_ai_m$24$(not in LMFDB)
6.2.ac_f_am_s_abc_bw$24$(not in LMFDB)
6.2.ac_f_ai_k_am_q$24$(not in LMFDB)
6.2.ac_f_ai_k_ai_q$24$(not in LMFDB)
6.2.ac_f_ai_s_ay_bo$24$(not in LMFDB)
6.2.ac_f_ae_c_m_aq$24$(not in LMFDB)
6.2.ac_f_ae_k_ai_y$24$(not in LMFDB)
6.2.ac_h_am_bc_abo_cq$24$(not in LMFDB)
6.2.ac_j_aq_bm_ace_ds$24$(not in LMFDB)
6.2.a_ad_ac_ac_e_q$24$(not in LMFDB)
6.2.a_ad_c_ac_ae_q$24$(not in LMFDB)
6.2.a_ab_ac_a_a_m$24$(not in LMFDB)
6.2.a_ab_c_a_a_m$24$(not in LMFDB)
6.2.a_b_ac_c_a_q$24$(not in LMFDB)
6.2.a_b_c_c_a_q$24$(not in LMFDB)
6.2.a_d_ac_e_ai_e$24$(not in LMFDB)
6.2.a_d_c_e_i_e$24$(not in LMFDB)
6.2.a_f_ac_g_am_a$24$(not in LMFDB)
6.2.a_f_ac_o_ai_bg$24$(not in LMFDB)
6.2.a_f_c_g_m_a$24$(not in LMFDB)
6.2.a_f_c_o_i_bg$24$(not in LMFDB)
6.2.c_ad_ai_c_i_a$24$(not in LMFDB)
6.2.c_ab_ae_e_i_e$24$(not in LMFDB)
6.2.c_b_ae_ac_i_y$24$(not in LMFDB)
6.2.c_b_a_ac_ai_aq$24$(not in LMFDB)
6.2.c_b_a_g_i_i$24$(not in LMFDB)
6.2.c_d_e_i_i_m$24$(not in LMFDB)
6.2.c_f_e_c_am_aq$24$(not in LMFDB)
6.2.c_f_e_k_i_y$24$(not in LMFDB)
6.2.c_f_i_k_i_q$24$(not in LMFDB)
6.2.c_f_i_k_m_q$24$(not in LMFDB)
6.2.c_f_i_s_y_bo$24$(not in LMFDB)
6.2.c_f_m_s_bc_bw$24$(not in LMFDB)
6.2.c_h_m_bc_bo_cq$24$(not in LMFDB)
6.2.c_j_q_bm_ce_ds$24$(not in LMFDB)
6.2.e_f_c_ac_au_abw$24$(not in LMFDB)
6.2.e_h_k_q_q_m$24$(not in LMFDB)
6.2.e_j_o_s_q_q$24$(not in LMFDB)
6.2.e_l_ba_ca_dk_fc$24$(not in LMFDB)
6.2.e_n_be_ck_ea_ge$24$(not in LMFDB)
6.2.e_n_bi_cs_eu_hk$24$(not in LMFDB)
6.2.g_r_bc_be_y_y$24$(not in LMFDB)
6.2.g_v_ca_ec_hc_ku$24$(not in LMFDB)
6.2.g_v_ce_es_im_my$24$(not in LMFDB)
6.2.ac_b_a_c_a_ae$40$(not in LMFDB)
6.2.ac_f_ai_o_aq_bc$40$(not in LMFDB)
6.2.c_b_a_c_a_ae$40$(not in LMFDB)
6.2.c_f_i_o_q_bc$40$(not in LMFDB)