Properties

Label 5.2.ai_bh_adn_he_alk
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$
Frobenius angles:  $\pm0.0435981566527$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.329312442367$, $\pm0.527830414776$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

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 1775 71149 1286875 43068901 884026325 19931081024 770623216875 35038871758111 1205956146063125

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 7 16 23 40 52 58 167 511 1092

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 3.2.ae_j_ap 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 $\F_{2^{28}}$ is 1.268435456.blhf 3 $\times$ 1.268435456.bwmi 2 . The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{28}}$.
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
5.2.ae_j_ap_w_abg$2$(not in LMFDB)
5.2.a_b_ad_c_ai$2$(not in LMFDB)
5.2.a_b_d_c_i$2$(not in LMFDB)
5.2.e_j_p_w_bg$2$(not in LMFDB)
5.2.i_bh_dn_he_lk$2$(not in LMFDB)
5.2.ac_d_ab_ag_k$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_j_ap_w_abg$2$(not in LMFDB)
5.2.a_b_ad_c_ai$2$(not in LMFDB)
5.2.a_b_d_c_i$2$(not in LMFDB)
5.2.e_j_p_w_bg$2$(not in LMFDB)
5.2.i_bh_dn_he_lk$2$(not in LMFDB)
5.2.ac_d_ab_ag_k$3$(not in LMFDB)
5.2.ag_t_abt_di_afe$6$(not in LMFDB)
5.2.c_d_b_ag_ak$6$(not in LMFDB)
5.2.g_t_bt_di_fe$6$(not in LMFDB)
5.2.ab_ac_h_e_aq$7$(not in LMFDB)
5.2.ab_f_ah_s_aq$7$(not in LMFDB)
5.2.ag_v_acb_ea_agi$8$(not in LMFDB)
5.2.ae_f_b_ao_bc$8$(not in LMFDB)
5.2.ae_n_abf_cg_ado$8$(not in LMFDB)
5.2.ac_f_aj_m_au$8$(not in LMFDB)
5.2.c_f_j_m_u$8$(not in LMFDB)
5.2.e_f_ab_ao_abc$8$(not in LMFDB)
5.2.e_n_bf_cg_do$8$(not in LMFDB)
5.2.g_v_cb_ea_gi$8$(not in LMFDB)
5.2.ah_w_abn_bs_abw$14$(not in LMFDB)
5.2.ah_bd_add_go_akm$14$(not in LMFDB)
5.2.af_r_abn_cw_aei$14$(not in LMFDB)
5.2.ad_c_b_i_ay$14$(not in LMFDB)
5.2.ad_j_ar_bi_abw$14$(not in LMFDB)
5.2.ad_j_an_w_ay$14$(not in LMFDB)
5.2.ab_f_ad_o_ai$14$(not in LMFDB)
5.2.b_ac_ah_e_q$14$(not in LMFDB)
5.2.b_f_d_o_i$14$(not in LMFDB)
5.2.b_f_h_s_q$14$(not in LMFDB)
5.2.d_c_ab_i_y$14$(not in LMFDB)
5.2.d_j_n_w_y$14$(not in LMFDB)
5.2.d_j_r_bi_bw$14$(not in LMFDB)
5.2.f_r_bn_cw_ei$14$(not in LMFDB)
5.2.h_w_bn_bs_bw$14$(not in LMFDB)
5.2.h_bd_dd_go_km$14$(not in LMFDB)
5.2.ae_i_an_y_abo$21$(not in LMFDB)
5.2.c_c_ab_ag_ak$21$(not in LMFDB)
5.2.f_k_n_w_bm$21$(not in LMFDB)
5.2.f_r_bp_da_es$21$(not in LMFDB)
5.2.ae_h_ah_e_ac$24$(not in LMFDB)
5.2.ae_l_ax_bo_ack$24$(not in LMFDB)
5.2.e_h_h_e_c$24$(not in LMFDB)
5.2.e_l_x_bo_ck$24$(not in LMFDB)
5.2.af_l_aj_ak_bg$28$(not in LMFDB)
5.2.ad_d_b_ac_a$28$(not in LMFDB)
5.2.ab_ab_d_c_ai$28$(not in LMFDB)
5.2.b_ab_ad_c_i$28$(not in LMFDB)
5.2.d_d_ab_ac_a$28$(not in LMFDB)
5.2.f_l_j_ak_abg$28$(not in LMFDB)
5.2.ag_s_abj_ca_acu$42$(not in LMFDB)
5.2.af_k_an_w_abm$42$(not in LMFDB)
5.2.af_r_abp_da_aes$42$(not in LMFDB)
5.2.ae_i_ap_ba_abm$42$(not in LMFDB)
5.2.ae_i_ad_aq_bo$42$(not in LMFDB)
5.2.ad_j_at_bi_acc$42$(not in LMFDB)
5.2.ac_c_aj_o_ak$42$(not in LMFDB)
5.2.ac_c_ad_i_aq$42$(not in LMFDB)
5.2.ac_c_b_ag_k$42$(not in LMFDB)
5.2.ac_c_d_ae_i$42$(not in LMFDB)
5.2.ab_ac_d_c_ag$42$(not in LMFDB)
5.2.ab_f_aj_o_aba$42$(not in LMFDB)
5.2.ab_f_d_c_w$42$(not in LMFDB)
5.2.a_a_af_e_a$42$(not in LMFDB)
5.2.a_a_ab_ac_g$42$(not in LMFDB)
5.2.a_a_b_ac_ag$42$(not in LMFDB)
5.2.a_a_f_e_a$42$(not in LMFDB)
5.2.b_ac_ad_c_g$42$(not in LMFDB)
5.2.b_f_ad_c_aw$42$(not in LMFDB)
5.2.b_f_j_o_ba$42$(not in LMFDB)
5.2.c_c_ad_ae_ai$42$(not in LMFDB)
5.2.c_c_d_i_q$42$(not in LMFDB)
5.2.c_c_j_o_k$42$(not in LMFDB)
5.2.d_j_t_bi_cc$42$(not in LMFDB)
5.2.e_i_d_aq_abo$42$(not in LMFDB)
5.2.e_i_n_y_bo$42$(not in LMFDB)
5.2.e_i_p_ba_bm$42$(not in LMFDB)
5.2.g_s_bj_ca_cu$42$(not in LMFDB)
5.2.af_m_at_ba_abk$56$(not in LMFDB)
5.2.af_t_abv_ds_afs$56$(not in LMFDB)
5.2.ad_ac_n_a_abc$56$(not in LMFDB)
5.2.ad_f_ad_ae_m$56$(not in LMFDB)
5.2.ad_f_ab_ao_bc$56$(not in LMFDB)
5.2.ad_g_al_q_au$56$(not in LMFDB)
5.2.ad_l_av_bs_aci$56$(not in LMFDB)
5.2.ad_n_az_cg_acy$56$(not in LMFDB)
5.2.ab_af_h_g_au$56$(not in LMFDB)
5.2.ab_a_ad_g_ae$56$(not in LMFDB)
5.2.ab_b_ab_a_e$56$(not in LMFDB)
5.2.ab_b_b_ag_e$56$(not in LMFDB)
5.2.ab_d_ab_ac_e$56$(not in LMFDB)
5.2.ab_h_ah_y_au$56$(not in LMFDB)
5.2.ab_h_ad_u_ae$56$(not in LMFDB)
5.2.ab_j_ah_bi_au$56$(not in LMFDB)
5.2.b_af_ah_g_u$56$(not in LMFDB)
5.2.b_a_d_g_e$56$(not in LMFDB)
5.2.b_b_ab_ag_ae$56$(not in LMFDB)
5.2.b_b_b_a_ae$56$(not in LMFDB)
5.2.b_d_b_ac_ae$56$(not in LMFDB)
5.2.b_h_d_u_e$56$(not in LMFDB)
5.2.b_h_h_y_u$56$(not in LMFDB)
5.2.b_j_h_bi_u$56$(not in LMFDB)
5.2.d_ac_an_a_bc$56$(not in LMFDB)
5.2.d_f_b_ao_abc$56$(not in LMFDB)
5.2.d_f_d_ae_am$56$(not in LMFDB)
5.2.d_g_l_q_u$56$(not in LMFDB)
5.2.d_l_v_bs_ci$56$(not in LMFDB)
5.2.d_n_z_cg_cy$56$(not in LMFDB)
5.2.f_m_t_ba_bk$56$(not in LMFDB)
5.2.f_t_bv_ds_fs$56$(not in LMFDB)
5.2.ad_d_ab_ac_g$84$(not in LMFDB)
5.2.ab_ab_ad_c_k$84$(not in LMFDB)
5.2.b_ab_d_c_ak$84$(not in LMFDB)
5.2.d_d_b_ac_ag$84$(not in LMFDB)
5.2.ae_k_at_be_abs$168$(not in LMFDB)
5.2.ad_a_h_e_aba$168$(not in LMFDB)
5.2.ad_e_af_m_aw$168$(not in LMFDB)
5.2.ad_h_ah_e_c$168$(not in LMFDB)
5.2.ad_l_at_bo_aby$168$(not in LMFDB)
5.2.ac_ac_f_a_ae$168$(not in LMFDB)
5.2.ac_a_b_e_ak$168$(not in LMFDB)
5.2.ac_e_aj_o_au$168$(not in LMFDB)
5.2.ac_e_ah_m_aw$168$(not in LMFDB)
5.2.ac_e_b_ag_u$168$(not in LMFDB)
5.2.ac_g_al_q_abc$168$(not in LMFDB)
5.2.ab_ad_f_e_ao$168$(not in LMFDB)
5.2.ab_b_b_a_ac$168$(not in LMFDB)
5.2.ab_d_ab_e_ac$168$(not in LMFDB)
5.2.ab_h_af_y_ao$168$(not in LMFDB)
5.2.a_ae_af_e_u$168$(not in LMFDB)
5.2.a_ae_f_e_au$168$(not in LMFDB)
5.2.a_ac_af_e_k$168$(not in LMFDB)
5.2.a_ac_f_e_ak$168$(not in LMFDB)
5.2.a_c_af_e_ak$168$(not in LMFDB)
5.2.a_c_ad_c_am$168$(not in LMFDB)
5.2.a_c_d_c_m$168$(not in LMFDB)
5.2.a_c_f_e_k$168$(not in LMFDB)
5.2.a_e_af_e_au$168$(not in LMFDB)
5.2.a_e_f_e_u$168$(not in LMFDB)
5.2.b_ad_af_e_o$168$(not in LMFDB)
5.2.b_b_ab_a_c$168$(not in LMFDB)
5.2.b_d_b_e_c$168$(not in LMFDB)
5.2.b_h_f_y_o$168$(not in LMFDB)
5.2.c_ac_af_a_e$168$(not in LMFDB)
5.2.c_a_ab_e_k$168$(not in LMFDB)
5.2.c_e_ab_ag_au$168$(not in LMFDB)
5.2.c_e_h_m_w$168$(not in LMFDB)
5.2.c_e_j_o_u$168$(not in LMFDB)
5.2.c_g_l_q_bc$168$(not in LMFDB)
5.2.d_a_ah_e_ba$168$(not in LMFDB)
5.2.d_e_f_m_w$168$(not in LMFDB)
5.2.d_h_h_e_ac$168$(not in LMFDB)
5.2.d_l_t_bo_by$168$(not in LMFDB)
5.2.e_k_t_be_bs$168$(not in LMFDB)