Properties

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

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$
Frobenius angles:  $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.384973271919$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 4 8000 430612 4000000 33357764 861224000 29094575108 944784000000 29860340011684 1009072361000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 11 31 39 35 47 107 223 427 911

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The isogeny class factors as 1.2.ac 3 $\times$ 1.2.ab 2 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.ab 2 $\times$ 1.16.i 3 . 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
5.2.ag_v_aby_dq_afo$2$(not in LMFDB)
5.2.ae_l_aw_bq_acm$2$(not in LMFDB)
5.2.ae_l_as_ba_abg$2$(not in LMFDB)
5.2.ac_f_ag_o_aq$2$(not in LMFDB)
5.2.a_d_ac_k_a$2$(not in LMFDB)
5.2.a_d_c_k_a$2$(not in LMFDB)
5.2.c_f_g_o_q$2$(not in LMFDB)
5.2.e_l_s_ba_bg$2$(not in LMFDB)
5.2.e_l_w_bq_cm$2$(not in LMFDB)
5.2.g_v_by_dq_fo$2$(not in LMFDB)
5.2.i_bj_dy_ik_no$2$(not in LMFDB)
5.2.af_l_ag_aw_ce$3$(not in LMFDB)
5.2.ac_f_a_ae_u$3$(not in LMFDB)
5.2.b_ab_g_i_ae$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.ag_v_aby_dq_afo$2$(not in LMFDB)
5.2.ae_l_aw_bq_acm$2$(not in LMFDB)
5.2.ae_l_as_ba_abg$2$(not in LMFDB)
5.2.ac_f_ag_o_aq$2$(not in LMFDB)
5.2.a_d_ac_k_a$2$(not in LMFDB)
5.2.a_d_c_k_a$2$(not in LMFDB)
5.2.c_f_g_o_q$2$(not in LMFDB)
5.2.e_l_s_ba_bg$2$(not in LMFDB)
5.2.e_l_w_bq_cm$2$(not in LMFDB)
5.2.g_v_by_dq_fo$2$(not in LMFDB)
5.2.i_bj_dy_ik_no$2$(not in LMFDB)
5.2.af_l_ag_aw_ce$3$(not in LMFDB)
5.2.ac_f_a_ae_u$3$(not in LMFDB)
5.2.b_ab_g_i_ae$3$(not in LMFDB)
5.2.ag_p_ao_ao_bw$4$(not in LMFDB)
5.2.ac_ab_g_c_aq$4$(not in LMFDB)
5.2.c_ab_ag_c_q$4$(not in LMFDB)
5.2.g_p_o_ao_abw$4$(not in LMFDB)
5.2.ah_x_abu_co_adk$6$(not in LMFDB)
5.2.ag_v_aca_dw_aga$6$(not in LMFDB)
5.2.af_l_as_bg_aca$6$(not in LMFDB)
5.2.ae_l_ay_bs_acq$6$(not in LMFDB)
5.2.ad_d_ac_k_ay$6$(not in LMFDB)
5.2.ad_d_c_ai_m$6$(not in LMFDB)
5.2.ac_f_am_u_abc$6$(not in LMFDB)
5.2.ac_f_ai_m_au$6$(not in LMFDB)
5.2.ab_ab_ag_i_e$6$(not in LMFDB)
5.2.ab_ab_c_a_ae$6$(not in LMFDB)
5.2.ab_ab_g_c_ai$6$(not in LMFDB)
5.2.a_d_ae_e_am$6$(not in LMFDB)
5.2.a_d_e_e_m$6$(not in LMFDB)
5.2.b_ab_ag_c_i$6$(not in LMFDB)
5.2.b_ab_ac_a_e$6$(not in LMFDB)
5.2.c_f_a_ae_au$6$(not in LMFDB)
5.2.c_f_i_m_u$6$(not in LMFDB)
5.2.c_f_m_u_bc$6$(not in LMFDB)
5.2.d_d_ac_ai_am$6$(not in LMFDB)
5.2.d_d_c_k_y$6$(not in LMFDB)
5.2.e_l_y_bs_cq$6$(not in LMFDB)
5.2.f_l_g_aw_ace$6$(not in LMFDB)
5.2.f_l_s_bg_ca$6$(not in LMFDB)
5.2.g_v_ca_dw_ga$6$(not in LMFDB)
5.2.h_x_bu_co_dk$6$(not in LMFDB)
5.2.ag_x_aci_es_ahk$8$(not in LMFDB)
5.2.ae_h_ae_ag_q$8$(not in LMFDB)
5.2.ae_h_ac_as_bo$8$(not in LMFDB)
5.2.ae_n_abc_cc_adc$8$(not in LMFDB)
5.2.ae_p_abi_cs_aea$8$(not in LMFDB)
5.2.ac_af_o_g_abo$8$(not in LMFDB)
5.2.ac_b_c_ag_i$8$(not in LMFDB)
5.2.ac_d_ac_ac_i$8$(not in LMFDB)
5.2.ac_d_a_ak_q$8$(not in LMFDB)
5.2.ac_h_am_ba_abg$8$(not in LMFDB)
5.2.ac_h_ai_s_aq$8$(not in LMFDB)
5.2.ac_j_ao_bi_abo$8$(not in LMFDB)
5.2.ac_l_aq_bu_abw$8$(not in LMFDB)
5.2.a_af_a_g_a$8$(not in LMFDB)
5.2.a_ab_ac_ac_i$8$(not in LMFDB)
5.2.a_ab_a_c_a$8$(not in LMFDB)
5.2.a_ab_c_ac_ai$8$(not in LMFDB)
5.2.a_b_a_ag_a$8$(not in LMFDB)
5.2.a_d_a_ac_a$8$(not in LMFDB)
5.2.a_f_a_o_a$8$(not in LMFDB)
5.2.a_h_ac_w_ai$8$(not in LMFDB)
5.2.a_h_c_w_i$8$(not in LMFDB)
5.2.a_j_a_bi_a$8$(not in LMFDB)
5.2.c_af_ao_g_bo$8$(not in LMFDB)
5.2.c_b_ac_ag_ai$8$(not in LMFDB)
5.2.c_d_a_ak_aq$8$(not in LMFDB)
5.2.c_d_c_ac_ai$8$(not in LMFDB)
5.2.c_h_i_s_q$8$(not in LMFDB)
5.2.c_h_m_ba_bg$8$(not in LMFDB)
5.2.c_j_o_bi_bo$8$(not in LMFDB)
5.2.c_l_q_bu_bw$8$(not in LMFDB)
5.2.e_h_c_as_abo$8$(not in LMFDB)
5.2.e_h_e_ag_aq$8$(not in LMFDB)
5.2.e_n_bc_cc_dc$8$(not in LMFDB)
5.2.e_p_bi_cs_ea$8$(not in LMFDB)
5.2.g_x_ci_es_hk$8$(not in LMFDB)
5.2.ae_f_a_ae_e$12$(not in LMFDB)
5.2.a_ad_ae_e_m$12$(not in LMFDB)
5.2.a_ad_e_e_am$12$(not in LMFDB)
5.2.e_f_a_ae_ae$12$(not in LMFDB)
5.2.af_n_ay_bm_ace$24$(not in LMFDB)
5.2.ae_j_ak_e_e$24$(not in LMFDB)
5.2.ae_n_abe_ce_adk$24$(not in LMFDB)
5.2.ae_n_aba_bw_acq$24$(not in LMFDB)
5.2.ad_ab_k_ac_aq$24$(not in LMFDB)
5.2.ad_b_e_e_au$24$(not in LMFDB)
5.2.ad_f_am_u_ay$24$(not in LMFDB)
5.2.ad_f_ai_q_abc$24$(not in LMFDB)
5.2.ad_f_a_ak_y$24$(not in LMFDB)
5.2.ad_h_ao_w_abg$24$(not in LMFDB)
5.2.ac_ad_k_e_abc$24$(not in LMFDB)
5.2.ac_b_ac_a_i$24$(not in LMFDB)
5.2.ac_b_c_a_ae$24$(not in LMFDB)
5.2.ac_d_ac_e_ae$24$(not in LMFDB)
5.2.ac_f_ae_e_a$24$(not in LMFDB)
5.2.ac_h_ao_y_abo$24$(not in LMFDB)
5.2.ac_h_ak_y_abc$24$(not in LMFDB)
5.2.ac_j_am_bg_abg$24$(not in LMFDB)
5.2.ab_af_k_g_abg$24$(not in LMFDB)
5.2.ab_ad_a_c_i$24$(not in LMFDB)
5.2.ab_ad_i_e_au$24$(not in LMFDB)
5.2.ab_ab_ac_e_a$24$(not in LMFDB)
5.2.ab_b_ae_g_ai$24$(not in LMFDB)
5.2.ab_b_a_ae_i$24$(not in LMFDB)
5.2.ab_b_e_a_e$24$(not in LMFDB)
5.2.ab_d_ag_i_aq$24$(not in LMFDB)
5.2.ab_d_c_ac_q$24$(not in LMFDB)
5.2.ab_f_ai_k_ay$24$(not in LMFDB)
5.2.a_ad_a_e_a$24$(not in LMFDB)
5.2.a_b_ac_e_e$24$(not in LMFDB)
5.2.a_b_a_a_a$24$(not in LMFDB)
5.2.a_b_c_e_ae$24$(not in LMFDB)
5.2.a_d_a_e_a$24$(not in LMFDB)
5.2.a_f_ag_i_ay$24$(not in LMFDB)
5.2.a_f_ac_q_ae$24$(not in LMFDB)
5.2.a_f_c_q_e$24$(not in LMFDB)
5.2.a_f_g_i_y$24$(not in LMFDB)
5.2.a_h_a_y_a$24$(not in LMFDB)
5.2.b_af_ak_g_bg$24$(not in LMFDB)
5.2.b_ad_ai_e_u$24$(not in LMFDB)
5.2.b_ad_a_c_ai$24$(not in LMFDB)
5.2.b_ab_c_e_a$24$(not in LMFDB)
5.2.b_b_ae_a_ae$24$(not in LMFDB)
5.2.b_b_a_ae_ai$24$(not in LMFDB)
5.2.b_b_e_g_i$24$(not in LMFDB)
5.2.b_d_ac_ac_aq$24$(not in LMFDB)
5.2.b_d_g_i_q$24$(not in LMFDB)
5.2.b_f_i_k_y$24$(not in LMFDB)
5.2.c_ad_ak_e_bc$24$(not in LMFDB)
5.2.c_b_ac_a_e$24$(not in LMFDB)
5.2.c_b_c_a_ai$24$(not in LMFDB)
5.2.c_d_c_e_e$24$(not in LMFDB)
5.2.c_f_e_e_a$24$(not in LMFDB)
5.2.c_h_k_y_bc$24$(not in LMFDB)
5.2.c_h_o_y_bo$24$(not in LMFDB)
5.2.c_j_m_bg_bg$24$(not in LMFDB)
5.2.d_ab_ak_ac_q$24$(not in LMFDB)
5.2.d_b_ae_e_u$24$(not in LMFDB)
5.2.d_f_a_ak_ay$24$(not in LMFDB)
5.2.d_f_i_q_bc$24$(not in LMFDB)
5.2.d_f_m_u_y$24$(not in LMFDB)
5.2.d_h_o_w_bg$24$(not in LMFDB)
5.2.e_j_k_e_ae$24$(not in LMFDB)
5.2.e_n_ba_bw_cq$24$(not in LMFDB)
5.2.e_n_be_ce_dk$24$(not in LMFDB)
5.2.f_n_y_bm_ce$24$(not in LMFDB)