Properties

Label 6.2.ai_bd_acg_cf_i_adc
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0247483856139$, $\pm0.177336015878$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.344002682545$, $\pm0.858081718947$
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
$A(\F_{q^r})$ 1 1525 852436 48075625 1110571141 67598174800 2654320083493 248168731955625 14879912670919972 1084806584635763125

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 -1 19 35 35 65 65 227 415 959

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 4.2.ae_f_c_al 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 $\F_{2^{12}}$ is 1.4096.ey 2 $\times$ 2.4096.ahm_zkj 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{12}}$.
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_f_c_ah_am_bo$2$(not in LMFDB)
6.2.a_ad_ac_j_a_aq$2$(not in LMFDB)
6.2.a_ad_c_j_a_aq$2$(not in LMFDB)
6.2.e_f_ac_ah_m_bo$2$(not in LMFDB)
6.2.i_bd_cg_cf_ai_adc$2$(not in LMFDB)
6.2.ac_ab_i_aj_ak_bi$3$(not in LMFDB)
6.2.ac_c_c_ad_i_ai$3$(not in LMFDB)
6.2.ac_f_ae_j_ae_q$3$(not in LMFDB)
6.2.e_i_o_v_ba_bi$3$(not in LMFDB)
6.2.e_l_ba_bz_di_fa$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ae_f_c_ah_am_bo$2$(not in LMFDB)
6.2.a_ad_ac_j_a_aq$2$(not in LMFDB)
6.2.a_ad_c_j_a_aq$2$(not in LMFDB)
6.2.e_f_ac_ah_m_bo$2$(not in LMFDB)
6.2.i_bd_cg_cf_ai_adc$2$(not in LMFDB)
6.2.ac_ab_i_aj_ak_bi$3$(not in LMFDB)
6.2.ac_c_c_ad_i_ai$3$(not in LMFDB)
6.2.ac_f_ae_j_ae_q$3$(not in LMFDB)
6.2.e_i_o_v_ba_bi$3$(not in LMFDB)
6.2.e_l_ba_bz_di_fa$3$(not in LMFDB)
6.2.ag_v_aca_eb_agy_km$4$(not in LMFDB)
6.2.ac_f_ai_r_ay_bo$4$(not in LMFDB)
6.2.ac_f_ae_j_ae_q$4$(not in LMFDB)
6.2.c_f_e_j_e_q$4$(not in LMFDB)
6.2.c_f_i_r_y_bo$4$(not in LMFDB)
6.2.g_v_ca_eb_gy_km$4$(not in LMFDB)
6.2.ag_p_au_p_ag_c$6$(not in LMFDB)
6.2.ag_s_abi_bt_abw_ce$6$(not in LMFDB)
6.2.ag_v_aca_eb_agy_km$6$(not in LMFDB)
6.2.ae_i_ao_v_aba_bi$6$(not in LMFDB)
6.2.ae_l_aba_bz_adi_fa$6$(not in LMFDB)
6.2.ac_c_ac_f_am_q$6$(not in LMFDB)
6.2.ac_f_ai_r_ay_bo$6$(not in LMFDB)
6.2.a_a_ac_ad_g_c$6$(not in LMFDB)
6.2.a_a_c_ad_ag_c$6$(not in LMFDB)
6.2.a_d_ac_d_ag_c$6$(not in LMFDB)
6.2.a_d_c_d_g_c$6$(not in LMFDB)
6.2.c_ab_ai_aj_k_bi$6$(not in LMFDB)
6.2.c_c_ac_ad_ai_ai$6$(not in LMFDB)
6.2.c_c_c_f_m_q$6$(not in LMFDB)
6.2.c_f_e_j_e_q$6$(not in LMFDB)
6.2.c_f_i_r_y_bo$6$(not in LMFDB)
6.2.g_p_u_p_g_c$6$(not in LMFDB)
6.2.g_s_bi_bt_bw_ce$6$(not in LMFDB)
6.2.g_v_ca_eb_gy_km$6$(not in LMFDB)
6.2.ag_r_abc_z_ac_au$8$(not in LMFDB)
6.2.ae_b_s_abb_au_dg$8$(not in LMFDB)
6.2.ae_j_ao_n_ae_ae$8$(not in LMFDB)
6.2.ae_n_abe_cj_ady_ga$8$(not in LMFDB)
6.2.ac_b_a_ad_i_am$8$(not in LMFDB)
6.2.ac_b_a_b_ag_m$8$(not in LMFDB)
6.2.ac_j_aq_bl_ace_do$8$(not in LMFDB)
6.2.a_f_ac_n_ak_bc$8$(not in LMFDB)
6.2.a_f_c_n_k_bc$8$(not in LMFDB)
6.2.c_b_a_ad_ai_am$8$(not in LMFDB)
6.2.c_b_a_b_g_m$8$(not in LMFDB)
6.2.c_j_q_bl_ce_do$8$(not in LMFDB)
6.2.e_b_as_abb_u_dg$8$(not in LMFDB)
6.2.e_j_o_n_e_ae$8$(not in LMFDB)
6.2.e_n_be_cj_dy_ga$8$(not in LMFDB)
6.2.g_r_bc_z_c_au$8$(not in LMFDB)
6.2.ae_d_k_ar_aq_ck$24$(not in LMFDB)
6.2.ae_e_i_at_ae_bo$24$(not in LMFDB)
6.2.ae_h_ag_d_ai_s$24$(not in LMFDB)
6.2.ae_k_as_z_abe_bk$24$(not in LMFDB)
6.2.ae_m_ay_bt_acq_ea$24$(not in LMFDB)
6.2.ac_ac_e_f_ac_ao$24$(not in LMFDB)
6.2.ac_ac_g_ad_ae_m$24$(not in LMFDB)
6.2.ac_a_c_b_ai_o$24$(not in LMFDB)
6.2.ac_a_e_ad_ac_e$24$(not in LMFDB)
6.2.ac_d_ae_h_ai_o$24$(not in LMFDB)
6.2.ac_e_ag_j_aq_s$24$(not in LMFDB)
6.2.ac_g_am_v_abi_by$24$(not in LMFDB)
6.2.ac_g_ak_n_au_u$24$(not in LMFDB)
6.2.ac_h_am_bb_abo_co$24$(not in LMFDB)
6.2.ac_i_am_bd_abi_cq$24$(not in LMFDB)
6.2.a_ai_a_bd_a_acq$24$(not in LMFDB)
6.2.a_ag_a_v_a_aby$24$(not in LMFDB)
6.2.a_ae_a_n_a_abg$24$(not in LMFDB)
6.2.a_ac_a_f_a_ao$24$(not in LMFDB)
6.2.a_a_a_ad_a_ae$24$(not in LMFDB)
6.2.a_a_a_ad_a_e$24$(not in LMFDB)
6.2.a_c_ac_b_ak_e$24$(not in LMFDB)
6.2.a_c_a_f_a_o$24$(not in LMFDB)
6.2.a_c_c_b_k_e$24$(not in LMFDB)
6.2.a_e_a_n_a_bg$24$(not in LMFDB)
6.2.a_g_a_v_a_by$24$(not in LMFDB)
6.2.a_i_a_bd_a_cq$24$(not in LMFDB)
6.2.c_ac_ag_ad_e_m$24$(not in LMFDB)
6.2.c_ac_ae_f_c_ao$24$(not in LMFDB)
6.2.c_a_ae_ad_c_e$24$(not in LMFDB)
6.2.c_a_ac_b_i_o$24$(not in LMFDB)
6.2.c_d_e_h_i_o$24$(not in LMFDB)
6.2.c_e_g_j_q_s$24$(not in LMFDB)
6.2.c_g_k_n_u_u$24$(not in LMFDB)
6.2.c_g_m_v_bi_by$24$(not in LMFDB)
6.2.c_h_m_bb_bo_co$24$(not in LMFDB)
6.2.c_i_m_bd_bi_cq$24$(not in LMFDB)
6.2.e_d_ak_ar_q_ck$24$(not in LMFDB)
6.2.e_e_ai_at_e_bo$24$(not in LMFDB)
6.2.e_h_g_d_i_s$24$(not in LMFDB)
6.2.e_k_s_z_be_bk$24$(not in LMFDB)
6.2.e_m_y_bt_cq_ea$24$(not in LMFDB)