Properties

Label 5.2.ah_ba_aco_ey_ahs
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
L-polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.0833333333333$, $\pm0.250000000000$, $\pm0.250000000000$, $\pm0.384973271919$, $\pm0.583333333333$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

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 2600 59150 1690000 48853222 999635000 26198897902 1086632820000 35596960530950 1065366638765000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 14 24 46 56 94 256 518 968

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.ac_c 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 $\times$ 1.4096.ey 4 . 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.af_o_abe_ce_adk$2$(not in LMFDB)
5.2.ad_g_ak_q_ay$2$(not in LMFDB)
5.2.ad_g_ac_ai_y$2$(not in LMFDB)
5.2.ab_c_ag_i_ai$2$(not in LMFDB)
5.2.ab_c_c_a_i$2$(not in LMFDB)
5.2.b_c_ac_a_ai$2$(not in LMFDB)
5.2.b_c_g_i_i$2$(not in LMFDB)
5.2.d_g_c_ai_ay$2$(not in LMFDB)
5.2.d_g_k_q_y$2$(not in LMFDB)
5.2.f_o_be_ce_dk$2$(not in LMFDB)
5.2.h_ba_co_ey_hs$2$(not in LMFDB)
5.2.ab_c_a_ae_e$3$(not in LMFDB)
5.2.ab_c_a_i_ai$3$(not in LMFDB)
5.2.f_o_be_ce_dk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
5.2.af_o_abe_ce_adk$2$(not in LMFDB)
5.2.ad_g_ak_q_ay$2$(not in LMFDB)
5.2.ad_g_ac_ai_y$2$(not in LMFDB)
5.2.ab_c_ag_i_ai$2$(not in LMFDB)
5.2.ab_c_c_a_i$2$(not in LMFDB)
5.2.b_c_ac_a_ai$2$(not in LMFDB)
5.2.b_c_g_i_i$2$(not in LMFDB)
5.2.d_g_c_ai_ay$2$(not in LMFDB)
5.2.d_g_k_q_y$2$(not in LMFDB)
5.2.f_o_be_ce_dk$2$(not in LMFDB)
5.2.h_ba_co_ey_hs$2$(not in LMFDB)
5.2.ab_c_a_ae_e$3$(not in LMFDB)
5.2.ab_c_a_i_ai$3$(not in LMFDB)
5.2.f_o_be_ce_dk$3$(not in LMFDB)
5.2.af_o_abe_ce_adk$4$(not in LMFDB)
5.2.ad_g_ak_q_ay$4$(not in LMFDB)
5.2.ad_g_ac_ai_y$4$(not in LMFDB)
5.2.ab_c_ag_i_ai$4$(not in LMFDB)
5.2.ab_c_c_a_i$4$(not in LMFDB)
5.2.b_c_ac_a_ai$4$(not in LMFDB)
5.2.b_c_g_i_i$4$(not in LMFDB)
5.2.d_g_c_ai_ay$4$(not in LMFDB)
5.2.d_g_k_q_y$4$(not in LMFDB)
5.2.f_o_be_ce_dk$4$(not in LMFDB)
5.2.h_ba_co_ey_hs$4$(not in LMFDB)
5.2.aj_bq_aey_ku_aro$6$(not in LMFDB)
5.2.ah_ba_acm_eq_ahc$6$(not in LMFDB)
5.2.af_o_abg_ci_ado$6$(not in LMFDB)
5.2.af_o_abe_ce_adk$6$(not in LMFDB)
5.2.af_o_ay_bg_abo$6$(not in LMFDB)
5.2.ad_g_aq_bc_abk$6$(not in LMFDB)
5.2.ad_g_ak_q_ay$6$(not in LMFDB)
5.2.ad_g_ai_q_ay$6$(not in LMFDB)
5.2.ad_g_ac_ai_y$6$(not in LMFDB)
5.2.ab_c_ag_i_ai$6$(not in LMFDB)
5.2.ab_c_a_ae_e$6$(not in LMFDB)
5.2.ab_c_a_i_ai$6$(not in LMFDB)
5.2.ab_c_c_a_i$6$(not in LMFDB)
5.2.b_c_ac_a_ai$6$(not in LMFDB)
5.2.b_c_a_ae_ae$6$(not in LMFDB)
5.2.b_c_a_i_i$6$(not in LMFDB)
5.2.b_c_g_i_i$6$(not in LMFDB)
5.2.d_g_c_ai_ay$6$(not in LMFDB)
5.2.d_g_i_q_y$6$(not in LMFDB)
5.2.d_g_k_q_y$6$(not in LMFDB)
5.2.d_g_q_bc_bk$6$(not in LMFDB)
5.2.f_o_y_bg_bo$6$(not in LMFDB)
5.2.f_o_be_ce_dk$6$(not in LMFDB)
5.2.f_o_bg_ci_do$6$(not in LMFDB)
5.2.h_ba_cm_eq_hc$6$(not in LMFDB)
5.2.h_ba_co_ey_hs$6$(not in LMFDB)
5.2.j_bq_ey_ku_ro$6$(not in LMFDB)
5.2.af_m_ao_e_i$8$(not in LMFDB)
5.2.af_q_abm_cu_aei$8$(not in LMFDB)
5.2.af_q_abi_ci_adk$8$(not in LMFDB)
5.2.ad_c_c_ai_q$8$(not in LMFDB)
5.2.ad_e_ac_e_ai$8$(not in LMFDB)
5.2.ad_g_ag_e_a$8$(not in LMFDB)
5.2.ad_i_as_bg_abw$8$(not in LMFDB)
5.2.ad_i_ao_bc_abo$8$(not in LMFDB)
5.2.ad_k_aw_bo_acm$8$(not in LMFDB)
5.2.ad_k_as_bk_abw$8$(not in LMFDB)
5.2.ab_ae_g_e_aq$8$(not in LMFDB)
5.2.ab_ac_ac_a_q$8$(not in LMFDB)
5.2.ab_a_c_ae_a$8$(not in LMFDB)
5.2.ab_a_c_e_ai$8$(not in LMFDB)
5.2.ab_c_ac_e_a$8$(not in LMFDB)
5.2.ab_e_ag_i_aq$8$(not in LMFDB)
5.2.ab_e_ac_e_a$8$(not in LMFDB)
5.2.ab_e_ac_m_ai$8$(not in LMFDB)
5.2.ab_e_c_a_q$8$(not in LMFDB)
5.2.ab_g_ak_q_abg$8$(not in LMFDB)
5.2.ab_g_ag_u_aq$8$(not in LMFDB)
5.2.ab_i_ag_bc_aq$8$(not in LMFDB)
5.2.b_ae_ag_e_q$8$(not in LMFDB)
5.2.b_ac_c_a_aq$8$(not in LMFDB)
5.2.b_a_ac_ae_a$8$(not in LMFDB)
5.2.b_a_ac_e_i$8$(not in LMFDB)
5.2.b_c_c_e_a$8$(not in LMFDB)
5.2.b_e_ac_a_aq$8$(not in LMFDB)
5.2.b_e_c_e_a$8$(not in LMFDB)
5.2.b_e_c_m_i$8$(not in LMFDB)
5.2.b_e_g_i_q$8$(not in LMFDB)
5.2.b_g_g_u_q$8$(not in LMFDB)
5.2.b_g_k_q_bg$8$(not in LMFDB)
5.2.b_i_g_bc_q$8$(not in LMFDB)
5.2.d_c_ac_ai_aq$8$(not in LMFDB)
5.2.d_e_c_e_i$8$(not in LMFDB)
5.2.d_g_g_e_a$8$(not in LMFDB)
5.2.d_i_o_bc_bo$8$(not in LMFDB)
5.2.d_i_s_bg_bw$8$(not in LMFDB)
5.2.d_k_s_bk_bw$8$(not in LMFDB)
5.2.d_k_w_bo_cm$8$(not in LMFDB)
5.2.f_m_o_e_ai$8$(not in LMFDB)
5.2.f_q_bi_ci_dk$8$(not in LMFDB)
5.2.f_q_bm_cu_ei$8$(not in LMFDB)
5.2.aj_bq_aey_ku_aro$12$(not in LMFDB)
5.2.ah_ba_acm_eq_ahc$12$(not in LMFDB)
5.2.af_o_abg_ci_ado$12$(not in LMFDB)
5.2.af_o_abe_ce_adk$12$(not in LMFDB)
5.2.af_o_ay_bg_abo$12$(not in LMFDB)
5.2.ad_g_aq_bc_abk$12$(not in LMFDB)
5.2.ad_g_ak_q_ay$12$(not in LMFDB)
5.2.ad_g_ai_q_ay$12$(not in LMFDB)
5.2.ad_g_ac_ai_y$12$(not in LMFDB)
5.2.ab_c_ag_i_ai$12$(not in LMFDB)
5.2.ab_c_a_ae_e$12$(not in LMFDB)
5.2.ab_c_a_i_ai$12$(not in LMFDB)
5.2.ab_c_c_a_i$12$(not in LMFDB)
5.2.b_c_ac_a_ai$12$(not in LMFDB)
5.2.b_c_a_ae_ae$12$(not in LMFDB)
5.2.b_c_a_i_i$12$(not in LMFDB)
5.2.b_c_g_i_i$12$(not in LMFDB)
5.2.d_g_c_ai_ay$12$(not in LMFDB)
5.2.d_g_i_q_y$12$(not in LMFDB)
5.2.d_g_k_q_y$12$(not in LMFDB)
5.2.d_g_q_bc_bk$12$(not in LMFDB)
5.2.f_o_y_bg_bo$12$(not in LMFDB)
5.2.f_o_be_ce_dk$12$(not in LMFDB)
5.2.f_o_bg_ci_do$12$(not in LMFDB)
5.2.h_ba_cm_eq_hc$12$(not in LMFDB)
5.2.h_ba_co_ey_hs$12$(not in LMFDB)
5.2.j_bq_ey_ku_ro$12$(not in LMFDB)
5.2.ah_bc_acy_ga_ajo$24$(not in LMFDB)
5.2.af_k_ae_ay_ce$24$(not in LMFDB)
5.2.af_m_ao_e_i$24$(not in LMFDB)
5.2.af_q_abm_cu_aei$24$(not in LMFDB)
5.2.af_q_abk_cq_aea$24$(not in LMFDB)
5.2.af_q_abi_ci_adk$24$(not in LMFDB)
5.2.af_s_abs_dk_afg$24$(not in LMFDB)
5.2.ad_c_c_ai_q$24$(not in LMFDB)
5.2.ad_c_e_ai_i$24$(not in LMFDB)
5.2.ad_e_ae_e_ae$24$(not in LMFDB)
5.2.ad_e_ac_e_ai$24$(not in LMFDB)
5.2.ad_e_a_am_y$24$(not in LMFDB)
5.2.ad_g_ag_e_a$24$(not in LMFDB)
5.2.ad_i_as_bg_abw$24$(not in LMFDB)
5.2.ad_i_aq_bc_abs$24$(not in LMFDB)
5.2.ad_i_ao_bc_abo$24$(not in LMFDB)
5.2.ad_i_am_u_ay$24$(not in LMFDB)
5.2.ad_k_aw_bo_acm$24$(not in LMFDB)
5.2.ad_k_au_bo_ace$24$(not in LMFDB)
5.2.ad_k_as_bk_abw$24$(not in LMFDB)
5.2.ad_m_ay_ca_acu$24$(not in LMFDB)
5.2.ab_ag_i_i_ay$24$(not in LMFDB)
5.2.ab_ae_g_e_aq$24$(not in LMFDB)
5.2.ab_ac_ac_a_q$24$(not in LMFDB)
5.2.ab_ac_e_a_ai$24$(not in LMFDB)
5.2.ab_ac_e_e_am$24$(not in LMFDB)
5.2.ab_a_ae_e_e$24$(not in LMFDB)
5.2.ab_a_a_ae_i$24$(not in LMFDB)
5.2.ab_a_c_ae_a$24$(not in LMFDB)
5.2.ab_a_c_e_ai$24$(not in LMFDB)
5.2.ab_c_ac_e_a$24$(not in LMFDB)
5.2.ab_c_a_ai_i$24$(not in LMFDB)
5.2.ab_c_a_e_ae$24$(not in LMFDB)
5.2.ab_e_ai_m_au$24$(not in LMFDB)
5.2.ab_e_ag_i_aq$24$(not in LMFDB)
5.2.ab_e_ae_m_ai$24$(not in LMFDB)
5.2.ab_e_ac_e_a$24$(not in LMFDB)
5.2.ab_e_ac_m_ai$24$(not in LMFDB)
5.2.ab_e_c_a_q$24$(not in LMFDB)
5.2.ab_g_ak_q_abg$24$(not in LMFDB)
5.2.ab_g_ag_u_aq$24$(not in LMFDB)
5.2.ab_g_ae_q_ai$24$(not in LMFDB)
5.2.ab_g_ae_u_am$24$(not in LMFDB)
5.2.ab_i_ai_bc_ay$24$(not in LMFDB)
5.2.ab_i_ag_bc_aq$24$(not in LMFDB)
5.2.ab_k_ai_bo_ay$24$(not in LMFDB)
5.2.b_ag_ai_i_y$24$(not in LMFDB)
5.2.b_ae_ag_e_q$24$(not in LMFDB)
5.2.b_ac_ae_a_i$24$(not in LMFDB)
5.2.b_ac_ae_e_m$24$(not in LMFDB)
5.2.b_ac_c_a_aq$24$(not in LMFDB)
5.2.b_a_ac_ae_a$24$(not in LMFDB)
5.2.b_a_ac_e_i$24$(not in LMFDB)
5.2.b_a_a_ae_ai$24$(not in LMFDB)
5.2.b_a_e_e_ae$24$(not in LMFDB)
5.2.b_c_a_ai_ai$24$(not in LMFDB)
5.2.b_c_a_e_e$24$(not in LMFDB)
5.2.b_c_c_e_a$24$(not in LMFDB)
5.2.b_e_ac_a_aq$24$(not in LMFDB)
5.2.b_e_c_e_a$24$(not in LMFDB)
5.2.b_e_c_m_i$24$(not in LMFDB)
5.2.b_e_e_m_i$24$(not in LMFDB)
5.2.b_e_g_i_q$24$(not in LMFDB)
5.2.b_e_i_m_u$24$(not in LMFDB)
5.2.b_g_e_q_i$24$(not in LMFDB)
5.2.b_g_e_u_m$24$(not in LMFDB)
5.2.b_g_g_u_q$24$(not in LMFDB)
5.2.b_g_k_q_bg$24$(not in LMFDB)
5.2.b_i_g_bc_q$24$(not in LMFDB)
5.2.b_i_i_bc_y$24$(not in LMFDB)
5.2.b_k_i_bo_y$24$(not in LMFDB)
5.2.d_c_ae_ai_ai$24$(not in LMFDB)
5.2.d_c_ac_ai_aq$24$(not in LMFDB)
5.2.d_e_a_am_ay$24$(not in LMFDB)
5.2.d_e_c_e_i$24$(not in LMFDB)
5.2.d_e_e_e_e$24$(not in LMFDB)
5.2.d_g_g_e_a$24$(not in LMFDB)
5.2.d_i_m_u_y$24$(not in LMFDB)
5.2.d_i_o_bc_bo$24$(not in LMFDB)
5.2.d_i_q_bc_bs$24$(not in LMFDB)
5.2.d_i_s_bg_bw$24$(not in LMFDB)
5.2.d_k_s_bk_bw$24$(not in LMFDB)
5.2.d_k_u_bo_ce$24$(not in LMFDB)
5.2.d_k_w_bo_cm$24$(not in LMFDB)
5.2.d_m_y_ca_cu$24$(not in LMFDB)
5.2.f_k_e_ay_ace$24$(not in LMFDB)
5.2.f_m_o_e_ai$24$(not in LMFDB)
5.2.f_q_bi_ci_dk$24$(not in LMFDB)
5.2.f_q_bk_cq_ea$24$(not in LMFDB)
5.2.f_q_bm_cu_ei$24$(not in LMFDB)
5.2.f_s_bs_dk_fg$24$(not in LMFDB)
5.2.h_bc_cy_ga_jo$24$(not in LMFDB)
5.2.ad_g_ag_a_e$30$(not in LMFDB)
5.2.ab_c_ac_a_ae$30$(not in LMFDB)
5.2.b_c_c_a_e$30$(not in LMFDB)
5.2.d_g_g_a_ae$30$(not in LMFDB)
5.2.ab_c_a_a_a$48$(not in LMFDB)
5.2.b_c_a_a_a$48$(not in LMFDB)
5.2.ad_g_ag_a_e$60$(not in LMFDB)
5.2.ab_c_ac_a_ae$60$(not in LMFDB)
5.2.b_c_c_a_e$60$(not in LMFDB)
5.2.d_g_g_a_ae$60$(not in LMFDB)
5.2.ab_a_c_a_ae$120$(not in LMFDB)
5.2.ab_e_ac_i_ae$120$(not in LMFDB)
5.2.b_a_ac_a_e$120$(not in LMFDB)
5.2.b_e_c_i_e$120$(not in LMFDB)