Properties

Label 6.2.aj_bo_aem_jp_aqq_yy
Base Field $\F_{2}$
Dimension $6$
Ordinary No
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $6$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$
Frobenius angles:  $\pm0.0635622003031$, $\pm0.165221137389$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.365221137389$, $\pm0.663562200303$
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 5275 314509 55519375 1759622051 51430084225 4397110890089 283427797359375 15777212909914651 1151200833717075625

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 4 12 36 49 46 127 260 444 1019

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 4.2.af_m_au_bd 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 $\F_{2^{20}}$ is 1.1048576.dau 2 $\times$ 2.1048576.dth_ibxft 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{20}}$.
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_m_au_bh_aci_ds$2$(not in LMFDB)
6.2.ab_a_ae_j_ai_i$2$(not in LMFDB)
6.2.b_a_e_j_i_i$2$(not in LMFDB)
6.2.f_m_u_bh_ci_ds$2$(not in LMFDB)
6.2.j_bo_em_jp_qq_yy$2$(not in LMFDB)
6.2.ad_e_ac_ad_g_ag$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
6.2.af_m_au_bh_aci_ds$2$(not in LMFDB)
6.2.ab_a_ae_j_ai_i$2$(not in LMFDB)
6.2.b_a_e_j_i_i$2$(not in LMFDB)
6.2.f_m_u_bh_ci_ds$2$(not in LMFDB)
6.2.j_bo_em_jp_qq_yy$2$(not in LMFDB)
6.2.ad_e_ac_ad_g_ag$3$(not in LMFDB)
6.2.ae_f_e_al_am_bw$5$(not in LMFDB)
6.2.ae_k_av_bn_ack_dk$5$(not in LMFDB)
6.2.ae_k_al_ab_bm_acu$5$(not in LMFDB)
6.2.b_a_e_j_i_i$5$(not in LMFDB)
6.2.ah_y_acg_en_ahy_mc$6$(not in LMFDB)
6.2.d_e_c_ad_ag_ag$6$(not in LMFDB)
6.2.h_y_cg_en_hy_mc$6$(not in LMFDB)
6.2.ah_ba_acq_fl_ajm_oi$8$(not in LMFDB)
6.2.af_i_a_ap_u_au$8$(not in LMFDB)
6.2.af_q_abo_dd_afk_ie$8$(not in LMFDB)
6.2.ad_g_am_v_abi_ca$8$(not in LMFDB)
6.2.d_g_m_v_bi_ca$8$(not in LMFDB)
6.2.f_i_a_ap_au_au$8$(not in LMFDB)
6.2.f_q_bo_dd_fk_ie$8$(not in LMFDB)
6.2.h_ba_cq_fl_jm_oi$8$(not in LMFDB)
6.2.a_ad_a_n_a_ay$10$(not in LMFDB)
6.2.a_c_af_d_ak_q$10$(not in LMFDB)
6.2.a_c_f_d_k_q$10$(not in LMFDB)
6.2.e_f_ae_al_m_bw$10$(not in LMFDB)
6.2.e_k_l_ab_abm_acu$10$(not in LMFDB)
6.2.e_k_v_bn_ck_dk$10$(not in LMFDB)
6.2.c_ab_ac_h_g_ag$15$(not in LMFDB)
6.2.c_e_d_ad_ao_aba$15$(not in LMFDB)
6.2.c_e_n_r_ba_cc$15$(not in LMFDB)
6.2.h_y_cg_en_hy_mc$15$(not in LMFDB)
6.2.ae_l_au_bl_aci_ds$20$(not in LMFDB)
6.2.a_d_a_n_a_y$20$(not in LMFDB)
6.2.e_l_u_bl_ci_ds$20$(not in LMFDB)
6.2.af_k_ak_j_au_bm$24$(not in LMFDB)
6.2.af_o_abe_cf_adw_fy$24$(not in LMFDB)
6.2.f_k_k_j_u_bm$24$(not in LMFDB)
6.2.f_o_be_cf_dw_fy$24$(not in LMFDB)
6.2.ac_ab_c_h_ag_ag$30$(not in LMFDB)
6.2.ac_e_an_r_aba_cc$30$(not in LMFDB)
6.2.ac_e_ad_ad_o_aba$30$(not in LMFDB)
6.2.ac_b_c_b_ag_m$40$(not in LMFDB)
6.2.ac_g_an_v_abk_ca$40$(not in LMFDB)
6.2.ac_g_ad_b_y_abc$40$(not in LMFDB)
6.2.ac_h_ak_z_abe_ci$40$(not in LMFDB)
6.2.a_ah_a_z_a_aci$40$(not in LMFDB)
6.2.a_ac_af_af_k_u$40$(not in LMFDB)
6.2.a_ac_f_af_ak_u$40$(not in LMFDB)
6.2.a_ab_a_b_a_am$40$(not in LMFDB)
6.2.a_b_a_b_a_m$40$(not in LMFDB)
6.2.a_g_af_l_abe_m$40$(not in LMFDB)
6.2.a_g_f_l_be_m$40$(not in LMFDB)
6.2.a_h_a_z_a_ci$40$(not in LMFDB)
6.2.c_b_ac_b_g_m$40$(not in LMFDB)
6.2.c_g_d_b_ay_abc$40$(not in LMFDB)
6.2.c_g_n_v_bk_ca$40$(not in LMFDB)
6.2.c_h_k_z_be_ci$40$(not in LMFDB)
6.2.ac_f_ak_t_abe_bq$60$(not in LMFDB)
6.2.c_f_k_t_be_bq$60$(not in LMFDB)
6.2.a_af_a_t_a_abq$120$(not in LMFDB)
6.2.a_ab_a_h_a_ag$120$(not in LMFDB)
6.2.a_a_af_ab_a_s$120$(not in LMFDB)
6.2.a_a_f_ab_a_s$120$(not in LMFDB)
6.2.a_b_a_h_a_g$120$(not in LMFDB)
6.2.a_e_af_h_au_o$120$(not in LMFDB)
6.2.a_e_f_h_u_o$120$(not in LMFDB)
6.2.a_f_a_t_a_bq$120$(not in LMFDB)