Properties

Label 6.2.ai_bg_adh_gq_ale_qq
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:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.139386741866$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.456881978294$, $\pm0.686170398078$
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
$A(\F_{q^r})$ 2 7600 333944 44460000 2264848282 96443027200 6291945767774 262178930520000 15623004528210248 1325604375213190000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 5 10 33 55 86 177 241 442 1165

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 2.2.ad_f $\times$ 2.2.ab_a 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.h 2 $\times$ 1.4096.ey 2 $\times$ 2.4096.agf_vki. 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.ag_s_abf_bc_c_abg$2$(not in LMFDB)
6.2.ae_i_an_y_abq_cm$2$(not in LMFDB)
6.2.ac_c_ab_e_ac_a$2$(not in LMFDB)
6.2.ac_c_b_a_ag_q$2$(not in LMFDB)
6.2.a_a_af_e_ac_q$2$(not in LMFDB)
6.2.a_a_f_e_c_q$2$(not in LMFDB)
6.2.c_c_ab_a_g_q$2$(not in LMFDB)
6.2.c_c_b_e_c_a$2$(not in LMFDB)
6.2.e_i_n_y_bq_cm$2$(not in LMFDB)
6.2.g_s_bf_bc_ac_abg$2$(not in LMFDB)
6.2.i_bg_dh_gq_le_qq$2$(not in LMFDB)
6.2.af_l_an_q_abm_cu$3$(not in LMFDB)
6.2.ac_c_ab_ac_e_a$3$(not in LMFDB)
6.2.ac_c_ab_e_ac_a$3$(not in LMFDB)
6.2.b_ab_ab_e_e_a$3$(not in LMFDB)
6.2.e_i_l_k_e_a$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.ag_s_abf_bc_c_abg$2$(not in LMFDB)
6.2.ae_i_an_y_abq_cm$2$(not in LMFDB)
6.2.ac_c_ab_e_ac_a$2$(not in LMFDB)
6.2.ac_c_b_a_ag_q$2$(not in LMFDB)
6.2.a_a_af_e_ac_q$2$(not in LMFDB)
6.2.a_a_f_e_c_q$2$(not in LMFDB)
6.2.c_c_ab_a_g_q$2$(not in LMFDB)
6.2.c_c_b_e_c_a$2$(not in LMFDB)
6.2.e_i_n_y_bq_cm$2$(not in LMFDB)
6.2.g_s_bf_bc_ac_abg$2$(not in LMFDB)
6.2.i_bg_dh_gq_le_qq$2$(not in LMFDB)
6.2.af_l_an_q_abm_cu$3$(not in LMFDB)
6.2.ac_c_ab_ac_e_a$3$(not in LMFDB)
6.2.ac_c_ab_e_ac_a$3$(not in LMFDB)
6.2.b_ab_ab_e_e_a$3$(not in LMFDB)
6.2.e_i_l_k_e_a$3$(not in LMFDB)
6.2.ag_s_abp_de_afk_ia$6$(not in LMFDB)
6.2.ae_i_al_k_ae_a$6$(not in LMFDB)
6.2.ad_d_af_q_au_q$6$(not in LMFDB)
6.2.ad_d_f_ai_ak_bo$6$(not in LMFDB)
6.2.ab_ab_ab_m_ag_ai$6$(not in LMFDB)
6.2.ab_ab_b_e_ae_a$6$(not in LMFDB)
6.2.a_a_af_ac_e_q$6$(not in LMFDB)
6.2.a_a_f_ac_ae_q$6$(not in LMFDB)
6.2.b_ab_b_m_g_ai$6$(not in LMFDB)
6.2.c_c_b_ac_ae_a$6$(not in LMFDB)
6.2.d_d_af_ai_k_bo$6$(not in LMFDB)
6.2.d_d_f_q_u_q$6$(not in LMFDB)
6.2.f_l_n_q_bm_cu$6$(not in LMFDB)
6.2.g_s_bp_de_fk_ia$6$(not in LMFDB)
6.2.ag_u_abx_du_agk_jo$8$(not in LMFDB)
6.2.ae_e_d_ai_k_aq$8$(not in LMFDB)
6.2.ae_k_ap_o_ac_ai$8$(not in LMFDB)
6.2.ae_m_abd_ce_adq_fo$8$(not in LMFDB)
6.2.ac_ac_j_ai_ak_bg$8$(not in LMFDB)
6.2.ac_e_aj_o_aw_bo$8$(not in LMFDB)
6.2.ac_g_ah_i_ac_a$8$(not in LMFDB)
6.2.a_c_ab_c_c_i$8$(not in LMFDB)
6.2.a_c_b_c_ac_i$8$(not in LMFDB)
6.2.c_ac_aj_ai_k_bg$8$(not in LMFDB)
6.2.c_e_j_o_w_bo$8$(not in LMFDB)
6.2.c_g_h_i_c_a$8$(not in LMFDB)
6.2.e_e_ad_ai_ak_aq$8$(not in LMFDB)
6.2.e_k_p_o_c_ai$8$(not in LMFDB)
6.2.e_m_bd_ce_dq_fo$8$(not in LMFDB)
6.2.g_u_bx_du_gk_jo$8$(not in LMFDB)
6.2.af_n_ax_bo_acw_eq$12$(not in LMFDB)
6.2.ad_f_al_y_abk_bw$12$(not in LMFDB)
6.2.ad_f_ab_a_ag_y$12$(not in LMFDB)
6.2.ab_b_ad_m_ak_i$12$(not in LMFDB)
6.2.ab_b_ab_e_ae_a$12$(not in LMFDB)
6.2.b_b_b_e_e_a$12$(not in LMFDB)
6.2.b_b_d_m_k_i$12$(not in LMFDB)
6.2.d_f_b_a_g_y$12$(not in LMFDB)
6.2.d_f_l_y_bk_bw$12$(not in LMFDB)
6.2.f_n_x_bo_cw_eq$12$(not in LMFDB)
6.2.ae_g_af_i_aq_y$24$(not in LMFDB)
6.2.ae_k_av_bo_acq_ea$24$(not in LMFDB)
6.2.ad_f_ah_o_aw_bg$24$(not in LMFDB)
6.2.ad_h_an_ba_abq_cm$24$(not in LMFDB)
6.2.ac_a_f_ae_ai_y$24$(not in LMFDB)
6.2.ac_e_ad_e_ae_i$24$(not in LMFDB)
6.2.ab_af_d_q_ac_abo$24$(not in LMFDB)
6.2.ab_ad_b_i_c_ay$24$(not in LMFDB)
6.2.ab_ad_b_o_ae_ay$24$(not in LMFDB)
6.2.ab_ab_ab_k_ae_ai$24$(not in LMFDB)
6.2.ab_b_ad_k_ai_i$24$(not in LMFDB)
6.2.ab_b_d_c_ac_q$24$(not in LMFDB)
6.2.ab_d_af_i_ak_y$24$(not in LMFDB)
6.2.ab_d_af_o_aq_y$24$(not in LMFDB)
6.2.ab_d_b_g_c_q$24$(not in LMFDB)
6.2.ab_f_ah_q_aw_bo$24$(not in LMFDB)
6.2.b_af_ad_q_c_abo$24$(not in LMFDB)
6.2.b_ad_ab_i_ac_ay$24$(not in LMFDB)
6.2.b_ad_ab_o_e_ay$24$(not in LMFDB)
6.2.b_ab_b_k_e_ai$24$(not in LMFDB)
6.2.b_b_ad_c_c_q$24$(not in LMFDB)
6.2.b_b_d_k_i_i$24$(not in LMFDB)
6.2.b_d_ab_g_ac_q$24$(not in LMFDB)
6.2.b_d_f_i_k_y$24$(not in LMFDB)
6.2.b_d_f_o_q_y$24$(not in LMFDB)
6.2.b_f_h_q_w_bo$24$(not in LMFDB)
6.2.c_a_af_ae_i_y$24$(not in LMFDB)
6.2.c_e_d_e_e_i$24$(not in LMFDB)
6.2.d_f_h_o_w_bg$24$(not in LMFDB)
6.2.d_h_n_ba_bq_cm$24$(not in LMFDB)
6.2.e_g_f_i_q_y$24$(not in LMFDB)
6.2.e_k_v_bo_cq_ea$24$(not in LMFDB)