Properties

Label 6.2.ai_bg_adg_gj_aki_pc
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0755571399449$, $\pm0.203216343788$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.424442860055$, $\pm0.703216343788$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 2 7300 405938 53290000 1563467842 72602011300 5146903416146 216584202240000 13706001241610834 1152887506347182500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 5 13 37 45 65 149 189 373 1025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 4.2.ae_i_am_r 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 2 $\times$ 2.16.c_b 2 . The endomorphism algebra for each factor is:
  • 1.16.i 2 : $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over \(\Q\) ramified at $2$ and $\infty$.
  • 2.16.c_b 2 : $\mathrm{M}_{2}($4.0.1088.2$)$
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.ae_i_am_v_abo_cm$2$(not in LMFDB)
6.2.a_a_ae_f_ae_i$2$(not in LMFDB)
6.2.a_a_e_f_e_i$2$(not in LMFDB)
6.2.e_i_m_v_bo_cm$2$(not in LMFDB)
6.2.i_bg_dg_gj_ki_pc$2$(not in LMFDB)
6.2.ac_c_a_ad_c_c$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ae_i_am_v_abo_cm$2$(not in LMFDB)
6.2.a_a_ae_f_ae_i$2$(not in LMFDB)
6.2.a_a_e_f_e_i$2$(not in LMFDB)
6.2.e_i_m_v_bo_cm$2$(not in LMFDB)
6.2.i_bg_dg_gj_ki_pc$2$(not in LMFDB)
6.2.ac_c_a_ad_c_c$3$(not in LMFDB)
6.2.ag_s_abo_cz_afa_hm$6$(not in LMFDB)
6.2.c_c_a_ad_ac_c$6$(not in LMFDB)
6.2.g_s_bo_cz_fa_hm$6$(not in LMFDB)
6.2.ai_bi_adw_iv_aqm_zo$8$(not in LMFDB)
6.2.ag_u_abw_dp_afy_iu$8$(not in LMFDB)
6.2.ag_w_aci_fd_aji_oi$8$(not in LMFDB)
6.2.ae_e_e_al_i_ae$8$(not in LMFDB)
6.2.ae_g_ae_ad_y_aca$8$(not in LMFDB)
6.2.ae_g_a_al_m_ai$8$(not in LMFDB)
6.2.ae_k_au_bl_ace_dc$8$(not in LMFDB)
6.2.ae_k_aq_v_au_y$8$(not in LMFDB)
6.2.ae_m_abc_cb_adk_fc$8$(not in LMFDB)
6.2.ae_o_abk_cz_afg_ie$8$(not in LMFDB)
6.2.ac_c_a_ad_g_am$8$(not in LMFDB)
6.2.ac_e_ai_n_aw_bk$8$(not in LMFDB)
6.2.ac_g_am_v_abe_ca$8$(not in LMFDB)
6.2.ac_g_ai_n_ak_u$8$(not in LMFDB)
6.2.a_ag_a_n_a_au$8$(not in LMFDB)
6.2.a_ac_a_ad_a_m$8$(not in LMFDB)
6.2.a_ac_a_f_a_aq$8$(not in LMFDB)
6.2.a_c_ae_f_ae_y$8$(not in LMFDB)
6.2.a_c_a_ad_a_am$8$(not in LMFDB)
6.2.a_c_a_f_a_q$8$(not in LMFDB)
6.2.a_c_e_f_e_y$8$(not in LMFDB)
6.2.a_g_a_n_a_u$8$(not in LMFDB)
6.2.c_c_a_ad_ag_am$8$(not in LMFDB)
6.2.c_e_i_n_w_bk$8$(not in LMFDB)
6.2.c_g_i_n_k_u$8$(not in LMFDB)
6.2.c_g_m_v_be_ca$8$(not in LMFDB)
6.2.e_e_ae_al_ai_ae$8$(not in LMFDB)
6.2.e_g_a_al_am_ai$8$(not in LMFDB)
6.2.e_g_e_ad_ay_aca$8$(not in LMFDB)
6.2.e_k_q_v_u_y$8$(not in LMFDB)
6.2.e_k_u_bl_ce_dc$8$(not in LMFDB)
6.2.e_m_bc_cb_dk_fc$8$(not in LMFDB)
6.2.e_o_bk_cz_fg_ie$8$(not in LMFDB)
6.2.g_u_bw_dp_fy_iu$8$(not in LMFDB)
6.2.g_w_ci_fd_ji_oi$8$(not in LMFDB)
6.2.i_bi_dw_iv_qm_zo$8$(not in LMFDB)
6.2.ag_r_aba_r_q_abw$24$(not in LMFDB)
6.2.ag_u_aca_ej_ahu_lu$24$(not in LMFDB)
6.2.ae_g_ae_f_aq_be$24$(not in LMFDB)
6.2.ae_h_ai_h_c_ao$24$(not in LMFDB)
6.2.ae_i_am_r_aq_o$24$(not in LMFDB)
6.2.ae_j_am_j_g_au$24$(not in LMFDB)
6.2.ae_k_au_bl_acm_du$24$(not in LMFDB)
6.2.ae_m_abc_cf_ads_fq$24$(not in LMFDB)
6.2.ac_ad_k_ad_am_u$24$(not in LMFDB)
6.2.ac_ab_g_ab_ai_o$24$(not in LMFDB)
6.2.ac_a_a_b_g_ao$24$(not in LMFDB)
6.2.ac_b_c_b_ai_q$24$(not in LMFDB)
6.2.ac_b_c_b_ae_i$24$(not in LMFDB)
6.2.ac_d_ac_d_a_c$24$(not in LMFDB)
6.2.ac_e_ai_j_ak_s$24$(not in LMFDB)
6.2.ac_e_ae_b_k_ao$24$(not in LMFDB)
6.2.ac_f_ag_f_e_ae$24$(not in LMFDB)
6.2.a_ae_a_j_a_as$24$(not in LMFDB)
6.2.a_ab_ae_ab_c_s$24$(not in LMFDB)
6.2.a_ab_e_ab_ac_s$24$(not in LMFDB)
6.2.a_a_a_b_a_ao$24$(not in LMFDB)
6.2.a_a_a_b_a_o$24$(not in LMFDB)
6.2.a_b_a_b_ac_m$24$(not in LMFDB)
6.2.a_b_a_b_c_m$24$(not in LMFDB)
6.2.a_e_a_j_a_s$24$(not in LMFDB)
6.2.c_ad_ak_ad_m_u$24$(not in LMFDB)
6.2.c_ab_ag_ab_i_o$24$(not in LMFDB)
6.2.c_a_a_b_ag_ao$24$(not in LMFDB)
6.2.c_b_ac_b_e_i$24$(not in LMFDB)
6.2.c_b_ac_b_i_q$24$(not in LMFDB)
6.2.c_d_c_d_a_c$24$(not in LMFDB)
6.2.c_e_e_b_ak_ao$24$(not in LMFDB)
6.2.c_e_i_j_k_s$24$(not in LMFDB)
6.2.c_f_g_f_ae_ae$24$(not in LMFDB)
6.2.e_g_e_f_q_be$24$(not in LMFDB)
6.2.e_h_i_h_ac_ao$24$(not in LMFDB)
6.2.e_i_m_r_q_o$24$(not in LMFDB)
6.2.e_j_m_j_ag_au$24$(not in LMFDB)
6.2.e_k_u_bl_cm_du$24$(not in LMFDB)
6.2.e_m_bc_cf_ds_fq$24$(not in LMFDB)
6.2.g_r_ba_r_aq_abw$24$(not in LMFDB)
6.2.g_u_ca_ej_hu_lu$24$(not in LMFDB)