Properties

Label 5.2.ag_s_abj_ca_acu
Base field $\F_{2}$
Dimension $5$
$p$-rank $3$
Ordinary No
Supersingular No
Simple No
Geometrically simple No
Primitive Yes
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0516399385854$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.718306605252$
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
$A(\F_{q^r})$ 2 1400 37856 2590000 27773482 741977600 32824323394 849649500000 30927679563872 1128089405135000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 5 12 33 27 38 123 193 444 1025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ab_ab 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.bv 3 $\times$ 1.4096.ey 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
5.2.ae_i_an_y_abo$2$(not in LMFDB)
5.2.ae_i_ad_aq_bo$2$(not in LMFDB)
5.2.ac_c_ad_i_aq$2$(not in LMFDB)
5.2.ac_c_d_ae_i$2$(not in LMFDB)
5.2.a_a_af_e_a$2$(not in LMFDB)
5.2.a_a_f_e_a$2$(not in LMFDB)
5.2.c_c_ad_ae_ai$2$(not in LMFDB)
5.2.c_c_d_i_q$2$(not in LMFDB)
5.2.e_i_d_aq_abo$2$(not in LMFDB)
5.2.e_i_n_y_bo$2$(not in LMFDB)
5.2.g_s_bj_ca_cu$2$(not in LMFDB)
5.2.ad_j_ar_bi_abw$3$(not in LMFDB)
5.2.a_a_b_ac_ag$3$(not in LMFDB)
5.2.d_j_t_bi_cc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ae_i_an_y_abo$2$(not in LMFDB)
5.2.ae_i_ad_aq_bo$2$(not in LMFDB)
5.2.ac_c_ad_i_aq$2$(not in LMFDB)
5.2.ac_c_d_ae_i$2$(not in LMFDB)
5.2.a_a_af_e_a$2$(not in LMFDB)
5.2.a_a_f_e_a$2$(not in LMFDB)
5.2.c_c_ad_ae_ai$2$(not in LMFDB)
5.2.c_c_d_i_q$2$(not in LMFDB)
5.2.e_i_d_aq_abo$2$(not in LMFDB)
5.2.e_i_n_y_bo$2$(not in LMFDB)
5.2.g_s_bj_ca_cu$2$(not in LMFDB)
5.2.ad_j_ar_bi_abw$3$(not in LMFDB)
5.2.a_a_b_ac_ag$3$(not in LMFDB)
5.2.d_j_t_bi_cc$3$(not in LMFDB)
5.2.ah_bd_add_go_akm$6$(not in LMFDB)
5.2.af_r_abp_da_aes$6$(not in LMFDB)
5.2.af_r_abn_cw_aei$6$(not in LMFDB)
5.2.ae_i_ap_ba_abm$6$(not in LMFDB)
5.2.ad_j_at_bi_acc$6$(not in LMFDB)
5.2.ad_j_an_w_ay$6$(not in LMFDB)
5.2.ac_c_aj_o_ak$6$(not in LMFDB)
5.2.ac_c_b_ag_k$6$(not in LMFDB)
5.2.ab_f_aj_o_aba$6$(not in LMFDB)
5.2.ab_f_ah_s_aq$6$(not in LMFDB)
5.2.ab_f_ad_o_ai$6$(not in LMFDB)
5.2.ab_f_d_c_w$6$(not in LMFDB)
5.2.a_a_ab_ac_g$6$(not in LMFDB)
5.2.b_f_ad_c_aw$6$(not in LMFDB)
5.2.b_f_d_o_i$6$(not in LMFDB)
5.2.b_f_h_s_q$6$(not in LMFDB)
5.2.b_f_j_o_ba$6$(not in LMFDB)
5.2.c_c_ab_ag_ak$6$(not in LMFDB)
5.2.c_c_j_o_k$6$(not in LMFDB)
5.2.d_j_n_w_y$6$(not in LMFDB)
5.2.d_j_r_bi_bw$6$(not in LMFDB)
5.2.e_i_p_ba_bm$6$(not in LMFDB)
5.2.f_r_bn_cw_ei$6$(not in LMFDB)
5.2.f_r_bp_da_es$6$(not in LMFDB)
5.2.h_bd_dd_go_km$6$(not in LMFDB)
5.2.ae_k_at_be_abs$8$(not in LMFDB)
5.2.ac_ac_f_a_ae$8$(not in LMFDB)
5.2.ac_e_aj_o_au$8$(not in LMFDB)
5.2.ac_e_b_ag_u$8$(not in LMFDB)
5.2.ac_g_al_q_abc$8$(not in LMFDB)
5.2.a_ae_af_e_u$8$(not in LMFDB)
5.2.a_ae_f_e_au$8$(not in LMFDB)
5.2.a_c_ad_c_am$8$(not in LMFDB)
5.2.a_c_d_c_m$8$(not in LMFDB)
5.2.a_e_af_e_au$8$(not in LMFDB)
5.2.a_e_f_e_u$8$(not in LMFDB)
5.2.c_ac_af_a_e$8$(not in LMFDB)
5.2.c_e_ab_ag_au$8$(not in LMFDB)
5.2.c_e_j_o_u$8$(not in LMFDB)
5.2.c_g_l_q_bc$8$(not in LMFDB)
5.2.e_k_t_be_bs$8$(not in LMFDB)
5.2.af_l_aj_ak_bg$12$(not in LMFDB)
5.2.ad_d_ab_ac_g$12$(not in LMFDB)
5.2.ad_d_b_ac_a$12$(not in LMFDB)
5.2.ab_ab_ad_c_k$12$(not in LMFDB)
5.2.ab_ab_d_c_ai$12$(not in LMFDB)
5.2.b_ab_ad_c_i$12$(not in LMFDB)
5.2.b_ab_d_c_ak$12$(not in LMFDB)
5.2.d_d_ab_ac_a$12$(not in LMFDB)
5.2.d_d_b_ac_ag$12$(not in LMFDB)
5.2.f_l_j_ak_abg$12$(not in LMFDB)
5.2.af_t_abv_ds_afs$24$(not in LMFDB)
5.2.ad_f_ad_ae_m$24$(not in LMFDB)
5.2.ad_f_ab_ao_bc$24$(not in LMFDB)
5.2.ad_h_ah_e_c$24$(not in LMFDB)
5.2.ad_l_av_bs_aci$24$(not in LMFDB)
5.2.ad_l_at_bo_aby$24$(not in LMFDB)
5.2.ad_n_az_cg_acy$24$(not in LMFDB)
5.2.ac_a_b_e_ak$24$(not in LMFDB)
5.2.ac_e_ah_m_aw$24$(not in LMFDB)
5.2.ab_af_h_g_au$24$(not in LMFDB)
5.2.ab_ad_f_e_ao$24$(not in LMFDB)
5.2.ab_b_ab_a_e$24$(not in LMFDB)
5.2.ab_b_b_ag_e$24$(not in LMFDB)
5.2.ab_b_b_a_ac$24$(not in LMFDB)
5.2.ab_d_ab_ac_e$24$(not in LMFDB)
5.2.ab_d_ab_e_ac$24$(not in LMFDB)
5.2.ab_h_ah_y_au$24$(not in LMFDB)
5.2.ab_h_af_y_ao$24$(not in LMFDB)
5.2.ab_h_ad_u_ae$24$(not in LMFDB)
5.2.ab_j_ah_bi_au$24$(not in LMFDB)
5.2.a_ac_af_e_k$24$(not in LMFDB)
5.2.a_ac_f_e_ak$24$(not in LMFDB)
5.2.a_c_af_e_ak$24$(not in LMFDB)
5.2.a_c_f_e_k$24$(not in LMFDB)
5.2.b_af_ah_g_u$24$(not in LMFDB)
5.2.b_ad_af_e_o$24$(not in LMFDB)
5.2.b_b_ab_ag_ae$24$(not in LMFDB)
5.2.b_b_ab_a_c$24$(not in LMFDB)
5.2.b_b_b_a_ae$24$(not in LMFDB)
5.2.b_d_b_ac_ae$24$(not in LMFDB)
5.2.b_d_b_e_c$24$(not in LMFDB)
5.2.b_h_d_u_e$24$(not in LMFDB)
5.2.b_h_f_y_o$24$(not in LMFDB)
5.2.b_h_h_y_u$24$(not in LMFDB)
5.2.b_j_h_bi_u$24$(not in LMFDB)
5.2.c_a_ab_e_k$24$(not in LMFDB)
5.2.c_e_h_m_w$24$(not in LMFDB)
5.2.d_f_b_ao_abc$24$(not in LMFDB)
5.2.d_f_d_ae_am$24$(not in LMFDB)
5.2.d_h_h_e_ac$24$(not in LMFDB)
5.2.d_l_t_bo_by$24$(not in LMFDB)
5.2.d_l_v_bs_ci$24$(not in LMFDB)
5.2.d_n_z_cg_cy$24$(not in LMFDB)
5.2.f_t_bv_ds_fs$24$(not in LMFDB)
5.2.ai_bh_adn_he_alk$42$(not in LMFDB)
5.2.ah_w_abn_bs_abw$42$(not in LMFDB)
5.2.ag_t_abt_di_afe$42$(not in LMFDB)
5.2.af_k_an_w_abm$42$(not in LMFDB)
5.2.ae_j_ap_w_abg$42$(not in LMFDB)
5.2.ad_c_b_i_ay$42$(not in LMFDB)
5.2.ac_d_ab_ag_k$42$(not in LMFDB)
5.2.ab_ac_d_c_ag$42$(not in LMFDB)
5.2.ab_ac_h_e_aq$42$(not in LMFDB)
5.2.a_b_ad_c_ai$42$(not in LMFDB)
5.2.a_b_d_c_i$42$(not in LMFDB)
5.2.b_ac_ah_e_q$42$(not in LMFDB)
5.2.b_ac_ad_c_g$42$(not in LMFDB)
5.2.c_d_b_ag_ak$42$(not in LMFDB)
5.2.d_c_ab_i_y$42$(not in LMFDB)
5.2.e_j_p_w_bg$42$(not in LMFDB)
5.2.f_k_n_w_bm$42$(not in LMFDB)
5.2.g_t_bt_di_fe$42$(not in LMFDB)
5.2.h_w_bn_bs_bw$42$(not in LMFDB)
5.2.i_bh_dn_he_lk$42$(not in LMFDB)
5.2.ag_v_acb_ea_agi$168$(not in LMFDB)
5.2.af_m_at_ba_abk$168$(not in LMFDB)
5.2.ae_f_b_ao_bc$168$(not in LMFDB)
5.2.ae_h_ah_e_ac$168$(not in LMFDB)
5.2.ae_l_ax_bo_ack$168$(not in LMFDB)
5.2.ae_n_abf_cg_ado$168$(not in LMFDB)
5.2.ad_ac_n_a_abc$168$(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_g_al_q_au$168$(not in LMFDB)
5.2.ac_f_aj_m_au$168$(not in LMFDB)
5.2.ab_a_ad_g_ae$168$(not in LMFDB)
5.2.b_a_d_g_e$168$(not in LMFDB)
5.2.c_f_j_m_u$168$(not in LMFDB)
5.2.d_ac_an_a_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_g_l_q_u$168$(not in LMFDB)
5.2.e_f_ab_ao_abc$168$(not in LMFDB)
5.2.e_h_h_e_c$168$(not in LMFDB)
5.2.e_l_x_bo_ck$168$(not in LMFDB)
5.2.e_n_bf_cg_do$168$(not in LMFDB)
5.2.f_m_t_ba_bk$168$(not in LMFDB)
5.2.g_v_cb_ea_gi$168$(not in LMFDB)