Properties

Label 6.2.aj_bp_aet_ko_asw_bcq
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:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.105278500939$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.316838792568$, $\pm0.641249159631$
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 11500 663494 97750000 2952713482 49596176500 2976029892586 242283150000000 16448442165424022 1275479951927687500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 6 18 46 64 42 78 222 468 1126

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 3.2.ad_f_ah 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 3 $\times$ 3.16.f_br_fn. 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.af_n_ax_bm_aco_ea$2$(not in LMFDB)
6.2.ad_f_ab_ac_c_i$2$(not in LMFDB)
6.2.ab_b_ad_k_ak_i$2$(not in LMFDB)
6.2.b_b_d_k_k_i$2$(not in LMFDB)
6.2.d_f_b_ac_ac_i$2$(not in LMFDB)
6.2.f_n_x_bm_co_ea$2$(not in LMFDB)
6.2.j_bp_et_ko_sw_bcq$2$(not in LMFDB)
6.2.ad_f_ad_ac_i_am$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_n_ax_bm_aco_ea$2$(not in LMFDB)
6.2.ad_f_ab_ac_c_i$2$(not in LMFDB)
6.2.ab_b_ad_k_ak_i$2$(not in LMFDB)
6.2.b_b_d_k_k_i$2$(not in LMFDB)
6.2.d_f_b_ac_ac_i$2$(not in LMFDB)
6.2.f_n_x_bm_co_ea$2$(not in LMFDB)
6.2.j_bp_et_ko_sw_bcq$2$(not in LMFDB)
6.2.ad_f_ad_ac_i_am$3$(not in LMFDB)
6.2.ah_z_acl_fa_aiy_ns$6$(not in LMFDB)
6.2.ad_f_al_w_abg_bs$6$(not in LMFDB)
6.2.ab_b_ab_c_a_ae$6$(not in LMFDB)
6.2.b_b_b_c_a_ae$6$(not in LMFDB)
6.2.d_f_d_ac_ai_am$6$(not in LMFDB)
6.2.d_f_l_w_bg_bs$6$(not in LMFDB)
6.2.h_z_cl_fa_iy_ns$6$(not in LMFDB)
6.2.ah_bb_acv_ga_aks_qi$8$(not in LMFDB)
6.2.af_j_ad_ao_ba_abg$8$(not in LMFDB)
6.2.af_r_abr_dm_agc_jg$8$(not in LMFDB)
6.2.ad_d_ab_ae_o_ay$8$(not in LMFDB)
6.2.ad_h_an_y_abm_ce$8$(not in LMFDB)
6.2.ad_l_az_ca_adm_fg$8$(not in LMFDB)
6.2.ab_ad_b_g_c_aq$8$(not in LMFDB)
6.2.ab_d_b_e_g_i$8$(not in LMFDB)
6.2.ab_f_ah_o_aw_bg$8$(not in LMFDB)
6.2.b_ad_ab_g_ac_aq$8$(not in LMFDB)
6.2.b_d_ab_e_ag_i$8$(not in LMFDB)
6.2.b_f_h_o_w_bg$8$(not in LMFDB)
6.2.d_d_b_ae_ao_ay$8$(not in LMFDB)
6.2.d_h_n_y_bm_ce$8$(not in LMFDB)
6.2.d_l_z_ca_dm_fg$8$(not in LMFDB)
6.2.f_j_d_ao_aba_abg$8$(not in LMFDB)
6.2.f_r_br_dm_gc_jg$8$(not in LMFDB)
6.2.h_bb_cv_ga_ks_qi$8$(not in LMFDB)
6.2.af_l_an_m_au_bk$24$(not in LMFDB)
6.2.af_p_abl_cy_afc_hs$24$(not in LMFDB)
6.2.af_p_abh_cm_aei_gq$24$(not in LMFDB)
6.2.ad_f_ah_k_am_q$24$(not in LMFDB)
6.2.ad_j_at_bm_acm_ds$24$(not in LMFDB)
6.2.ab_ab_ab_i_ae_ae$24$(not in LMFDB)
6.2.ab_d_af_m_aq_u$24$(not in LMFDB)
6.2.ab_d_ab_a_e_ai$24$(not in LMFDB)
6.2.b_ab_b_i_e_ae$24$(not in LMFDB)
6.2.b_d_b_a_ae_ai$24$(not in LMFDB)
6.2.b_d_f_m_q_u$24$(not in LMFDB)
6.2.d_f_h_k_m_q$24$(not in LMFDB)
6.2.d_j_t_bm_cm_ds$24$(not in LMFDB)
6.2.f_l_n_m_u_bk$24$(not in LMFDB)
6.2.f_p_bh_cm_ei_gq$24$(not in LMFDB)
6.2.f_p_bl_cy_fc_hs$24$(not in LMFDB)